Effects of Helicity on Lagrangian and Eulerian Time Correlations in Turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Zhou, Ye
1998-01-01
Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences Eulerian time correlations more strongly than Lagrangian time correlations: to second order in time, the helicity effect on Lagrangian time correlations vanishes, but the helicity effect on Eulerian time correlations is nonzero. Fourier analysis shows that the helicity effect on Eulerian time correlations is confined to the largest inertial range scales. Some implications for sound radiation by swirling flows are discussed.
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.
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
Gravity, Time, and Lagrangians
NASA Astrophysics Data System (ADS)
Huggins, Elisha
2010-11-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one subtract potential energy from kinetic energy?) In this paper we discuss a thought experiment that relates gravity and time. Then we use a Feynman thought experiment to explain the minus sign in the Lagrangian. Our surprise was that these two topics are related.
Correlating Lagrangian structures with forcing in two-dimensional flow
NASA Astrophysics Data System (ADS)
Ouellette, Nicholas; Hogg, Charlie; Liao, Yang
2015-11-01
Lagrangian coherent structures (LCSs) are the dominant transport barriers in unsteady, aperiodic flows, and their role in organizing mixing and transport has been well documented. However, nearly all that is known about LCSs has been gleaned from passive observations: they are computed in a post-processing step after a flow has been observed, and used to understand why the mixing and transport proceeded as it did. Here, we instead take a first step toward controlling the presence or locations of LCSs by studying the relationship between LCSs and external forcing in an experimental quasi-two-dimensional weakly turbulent flow. We find that the likelihood of finding a repelling LCS at a given location is positively correlated with the mean strain rate injected at that point and negatively correlated with the mean speed, and that it is not correlated with the vorticity. We also find that mean time between successive LCSs appearing at a fixed location is related to the structure of the forcing field. Finally, we demonstrate a surprising difference in our results between LCSs computed forward and backwards in time, with forward-time (repelling) LCSs showing much more correlation with the forcing than backwards-time (attracting) LCSs.
Correlating Lagrangian structures with forcing in two-dimensional flow
NASA Astrophysics Data System (ADS)
Ouellette, Nicholas T.; Hogg, Charlie A. R.; Liao, Yang
2016-01-01
Lagrangian coherent structures (LCSs) are the dominant transport barriers in unsteady, aperiodic flows, and their role in organizing mixing and transport has been well documented. However, nearly all that is known about LCSs has been gleaned from passive observations: they are computed in a post-processing step after a flow has been observed and used to understand why the mixing and transport proceeded as it did. In many applications, the ability instead to control the presence or location of LCSs via imposed forcing would be valuable. With this goal in mind, we study the relationship between LCSs and external forcing in an experimental quasi-two-dimensional weakly turbulent flow. We find that the likelihood of finding a repelling LCS at a given location is positively correlated with the mean strain rate injected at that point and negatively correlated with the mean speed, and that it is not correlated with the vorticity. We also find that mean time between successive LCSs appearing at a fixed location is related to the structure of the forcing field. Finally, we demonstrate a surprising difference in our results between LCSs computed forward and backward in time, with forward-time (repelling) LCSs showing much more correlation with the forcing than backwards-time (attracting) LCSs.
Gravity, Time, and Lagrangians
ERIC Educational Resources Information Center
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
Correlational signatures of time-reversal symmetry breaking in two-dimensional flow
NASA Astrophysics Data System (ADS)
Hogg, Charlie; Ouellette, Nicholas
2015-11-01
Classical turbulence theories posit that broken spatial symmetries should be (statistically) restored at small scales. But since turbulent flows are inherently dissipative, time reversal symmetry is expected to remain broken throughout the cascade. However, the precise dynamical signature of this broken symmetry is not well understood. Recent work has shed new light on this fundamental question by considering the Lagrangian structure functions of power. Here, we take a somewhat different approach by studying the Lagrangian correlation functions of velocity and acceleration. We measured these correlations using particle tracking velocimetry in a quasi-two-dimensional electromagnetically driven flow that displayed net inverse energy transfer. We show that the correlation functions of the velocity and acceleration magnitudes are not symmetric in time, and that the degree of asymmetry can be related to the flux of energy between scales, suggesting that the asymmetry has a dynamical origin.
NASA Astrophysics Data System (ADS)
Huhn, F.; Schanz, D.; Manovski, P.; Gesemann, S.; Schröder, A.
2018-05-01
Time-resolved volumetric pressure fields are reconstructed from Lagrangian particle tracking with high seeding concentration using the Shake-The-Box algorithm in a perpendicular impinging jet flow with exit velocity U=4 m/s (Re˜ 36,000) and nozzle-plate spacing H/D=5. Helium-filled soap bubbles are used as tracer particles which are illuminated with pulsed LED arrays. A large measurement volume has been covered (cloud of tracked particles in a volume of 54 L, ˜ 180,000 particles). The reconstructed pressure field has been validated against microphone recordings at the wall with high correlation coefficients up to 0.88. In a reduced measurement volume (13 L), dense Lagrangian particle tracking is shown to be feasable up to the maximal possible jet velocity of U=16 m/s.
Lagrangian space consistency relation for large scale structure
DOE Office of Scientific and Technical Information (OSTI.GOV)
Horn, Bart; Hui, Lam; Xiao, Xiao
Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present.more » Furthermore, the simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.« less
Lagrangian space consistency relation for large scale structure
Horn, Bart; Hui, Lam; Xiao, Xiao
2015-09-29
Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present.more » Furthermore, the simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.« less
Effective pore-scale dispersion upscaling with a correlated continuous time random walk approach
NASA Astrophysics Data System (ADS)
Le Borgne, T.; Bolster, D.; Dentz, M.; de Anna, P.; Tartakovsky, A.
2011-12-01
We investigate the upscaling of dispersion from a pore-scale analysis of Lagrangian velocities. A key challenge in the upscaling procedure is to relate the temporal evolution of spreading to the pore-scale velocity field properties. We test the hypothesis that one can represent Lagrangian velocities at the pore scale as a Markov process in space. The resulting effective transport model is a continuous time random walk (CTRW) characterized by a correlated random time increment, here denoted as correlated CTRW. We consider a simplified sinusoidal wavy channel model as well as a more complex heterogeneous pore space. For both systems, the predictions of the correlated CTRW model, with parameters defined from the velocity field properties (both distribution and correlation), are found to be in good agreement with results from direct pore-scale simulations over preasymptotic and asymptotic times. In this framework, the nontrivial dependence of dispersion on the pore boundary fluctuations is shown to be related to the competition between distribution and correlation effects. In particular, explicit inclusion of spatial velocity correlation in the effective CTRW model is found to be important to represent incomplete mixing in the pore throats.
Lagrangian space consistency relation for large scale structure
DOE Office of Scientific and Technical Information (OSTI.GOV)
Horn, Bart; Hui, Lam; Xiao, Xiao, E-mail: bh2478@columbia.edu, E-mail: lh399@columbia.edu, E-mail: xx2146@columbia.edu
Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias and Riotto and Peloso and Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present.more » The simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.« less
Lagrangian 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.
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
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
NASA Astrophysics Data System (ADS)
Mancho, Ana M.; Wiggins, Stephen; Curbelo, Jezabel; Mendoza, Carolina
2013-11-01
Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a ``heuristic argument'' that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (``time averages''). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We thank CESGA for computing facilities. This research was supported by MINECO grants: MTM2011-26696, I-Math C3-0104, ICMAT Severo Ochoa project SEV-2011-0087, and CSIC grant OCEANTECH. SW acknowledges the support of the ONR (Grant No. N00014-01-1-0769).
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.
NASA Astrophysics Data System (ADS)
Rockwood, Matthew P.
The flow around a circular cylinder, a canonical bluff body, has been extensively studied in the literature to determine the mechanisms that cause the formation of vortices in the cylinder wake. Understanding of these mechanisms has led to myriad attempts to control the vortices either to mitigate the oscillating forces they cause, or to augment them in order to enhance mixing in the near-wake. While these flow control techniques have been effective at low Reynolds numbers, they generally lose effectiveness or require excessive power at Reynolds numbers commonly experienced in practical applications. For this reason, new methods for identifying the locations of vortices and their shedding time could increase the effectiveness of the control techniques. In the current work, two-dimensional, two-component velocity data was collected in the wake of a circular cylinder using a planar digital particle image velocimetry (DPIV) measurement system at Reynolds numbers of 9,000 and 19,000. This experimental data, as well as two-dimensional simulation data at a Reynolds number of 150, and three-dimensional simulation data at a Reynolds number of 400, is used to calculate the finite-time Lyapunov exponent (FTLE) field. The locations of Lagrangian saddles, identified as non-parallel intersections of positive and negative time FTLE ridges, are shown to indicate the timing of von Karman vortex shedding in the wake of a circular cylinder. The Lagrangian saddle found upstream of a forming and subsequently shedding vortex is shown to clearly accelerate away from the cylinder surface as the vortex begins to shed. This provides a novel, objective method to determine the timing of vortex shedding. The saddles are impossible to track in real-time, however, since future flow field data is needed for the computation of the FTLE fields. In order to detect the Lagrangian saddle acceleration without direct access to the FTLE, the saddle dynamics are connected to measurable surface quantities
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.
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.
Identifying finite-time coherent sets from limited quantities of Lagrangian data.
Williams, Matthew O; Rypina, Irina I; Rowley, Clarence W
2015-08-01
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or "mesh-free" methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.
Identifying finite-time coherent sets from limited quantities of Lagrangian data
DOE Office of Scientific and Technical Information (OSTI.GOV)
Williams, Matthew O.; Rypina, Irina I.; Rowley, Clarence W.
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods basedmore » on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.« less
Lagrangian statistics in compressible isotropic homogeneous turbulence
NASA Astrophysics Data System (ADS)
Yang, Yantao; Wang, Jianchun; Shi, Yipeng; Chen, Shiyi
2011-11-01
In this work we conducted the Direct Numerical Simulation (DNS) of a forced compressible isotropic homogeneous turbulence and investigated the flow statistics from the Lagrangian point of view, namely the statistics is computed following the passive tracers trajectories. The numerical method combined the Eulerian field solver which was developed by Wang et al. (2010, J. Comp. Phys., 229, 5257-5279), and a Lagrangian module for tracking the tracers and recording the data. The Lagrangian probability density functions (p.d.f.'s) have then been calculated for both kinetic and thermodynamic quantities. In order to isolate the shearing part from the compressing part of the flow, we employed the Helmholtz decomposition to decompose the flow field (mainly the velocity field) into the solenoidal and compressive parts. The solenoidal part was compared with the incompressible case, while the compressibility effect showed up in the compressive part. The Lagrangian structure functions and cross-correlation between various quantities will also be discussed. This work was supported in part by the China's Turbulence Program under Grant No.2009CB724101.
Lagrangian postprocessing of computational hemodynamics.
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
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
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.
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.
An Augmented Lagrangian Filter Method for Real-Time Embedded Optimization
Chiang, Nai -Yuan; Huang, Rui; Zavala, Victor M.
2017-04-17
We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented Lagrangian function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. The proposed method enables primal–dual regularization of the linear algebra system that in turn permits the use of solution strategies with lower computing overheads. We prove that the proposed algorithm is globally convergent and we demonstrate the developments using a nonconvex real-time optimization application for a building heating, ventilation, and airmore » conditioning system. Our numerical tests are performed on a standard processor and on an embedded platform. Lastly, we demonstrate that the approach reduces solution times by a factor of over 1000.« less
An Augmented Lagrangian Filter Method for Real-Time Embedded Optimization
DOE Office of Scientific and Technical Information (OSTI.GOV)
Chiang, Nai -Yuan; Huang, Rui; Zavala, Victor M.
We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented Lagrangian function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. The proposed method enables primal–dual regularization of the linear algebra system that in turn permits the use of solution strategies with lower computing overheads. We prove that the proposed algorithm is globally convergent and we demonstrate the developments using a nonconvex real-time optimization application for a building heating, ventilation, and airmore » conditioning system. Our numerical tests are performed on a standard processor and on an embedded platform. Lastly, we demonstrate that the approach reduces solution times by a factor of over 1000.« less
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1992-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.
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.
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
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.
An online-coupled NWP/ACT model with conserved Lagrangian levels
NASA Astrophysics Data System (ADS)
Sørensen, B.; Kaas, E.; Lauritzen, P. H.
2012-04-01
Numerical weather and climate modelling is under constant development. Semi-implicit semi-Lagrangian (SISL) models have proven to be numerically efficient in both short-range weather forecasts and climate models, due to the ability to use long time steps. Chemical/aerosol feedback mechanism are becoming more and more relevant in NWP as well as climate models, since the biogenic and anthropogenic emissions can have a direct effect on the dynamics and radiative properties of the atmosphere. To include chemical feedback mechanisms in the NWP models, on-line coupling is crucial. In 3D semi-Lagrangian schemes with quasi-Lagrangian vertical coordinates the Lagrangian levels are remapped to Eulerian model levels each time step. This remapping introduces an undesirable tendency to smooth sharp gradients and creates unphysical numerical diffusion in the vertical distribution. A semi-Lagrangian advection method is introduced, it combines an inherently mass conserving 2D semi-Lagrangian scheme, with a SISL scheme employing both hybrid vertical coordinates and a fully Lagrangian vertical coordinate. This minimizes the vertical diffusion and thus potentially improves the simulation of the vertical profiles of moisture, clouds, and chemical constituents. Since the Lagrangian levels suffer from traditional Lagrangian limitations caused by the convergence and divergence of the flow, remappings to the Eulerian model levels are generally still required - but this need only be applied after a number of time steps - unless dynamic remapping methods are used. For this several different remapping methods has been implemented. The combined scheme is mass conserving, consistent, and multi-tracer efficient.
Parallel computing using a Lagrangian formulation
NASA Technical Reports Server (NTRS)
Liou, May-Fun; Loh, Ching Yuen
1991-01-01
A new Lagrangian formulation of the Euler equation is adopted for the calculation of 2-D supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, a better than six times speed-up was achieved on a 8192-processor CM-2 over a single processor of a CRAY-2.
Parallel computing using a Lagrangian formulation
NASA Technical Reports Server (NTRS)
Liou, May-Fun; Loh, Ching-Yuen
1992-01-01
This paper adopts a new Lagrangian formulation of the Euler equation for the calculation of two dimensional supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, we have achieved better than six times speed-up on a 8192-processor CM-2 over a single processor of a CRAY-2.
Lagrangian descriptors in dissipative systems.
Junginger, Andrej; Hernandez, Rigoberto
2016-11-09
The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory-that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of Lagrangian descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the Lagrangian descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the Lagrangian descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.
Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics.
Martínez, Enrique; Cawkwell, Marc J; Voter, Arthur F; Niklasson, Anders M N
2015-04-21
Extended Lagrangian Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended Lagrangian Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached at each time step. The thermostated extended Lagrangian framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.
Lagrangian Statistics and Intermittency in Gulf of Mexico.
Lin, Liru; Zhuang, Wei; Huang, Yongxiang
2017-12-12
Due to the nonlinear interaction between different flow patterns, for instance, ocean current, meso-scale eddies, waves, etc, the movement of ocean is extremely complex, where a multiscale statistics is then relevant. In this work, a high time-resolution velocity with a time step 15 minutes obtained by the Lagrangian drifter deployed in the Gulf of Mexico (GoM) from July 2012 to October 2012 is considered. The measured Lagrangian velocity correlation function shows a strong daily cycle due to the diurnal tidal cycle. The estimated Fourier power spectrum E(f) implies a dual-power-law behavior which is separated by the daily cycle. The corresponding scaling exponents are close to -1.75 and -2.75 respectively for the time scale larger (resp. 0.1 ≤ f ≤ 0.4 day -1 ) and smaller (resp. 2 ≤ f ≤ 8 day -1 ) than 1 day. A Hilbert-based approach is then applied to this data set to identify the possible multifractal property of the cascade process. The results show an intermittent dynamics for the time scale larger than 1 day, while a less intermittent dynamics for the time scale smaller than 1 day. It is speculated that the energy is partially injected via the diurnal tidal movement and then transferred to larger and small scales through a complex cascade process, which needs more studies in the near future.
Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.
Huang, Yongxiang; Biferale, Luca; Calzavarini, Enrico; Sun, Chao; Toschi, Federico
2013-04-01
The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)].
Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.
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.
Analytical solution of the problem of a shock wave in the collapsing gas in Lagrangian coordinates
NASA Astrophysics Data System (ADS)
Kuropatenko, V. F.; Shestakovskaya, E. S.
2016-10-01
It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in Lagrangian coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t0 the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and Lagrangian coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For Lagrangian coordinates the problem is first solved. It is fundamentally different from previously known formulations of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.
Lagrangian continuum dynamics in ALEGRA.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Wong, Michael K. W.; Love, Edward
Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.
Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics
DOE Office of Scientific and Technical Information (OSTI.GOV)
Martínez, Enrique; Cawkwell, Marc J.; Voter, Arthur F.
Here, Extended Lagrangian Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended Lagrangian Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached atmore » each time step. Lastly, the thermostated extended Lagrangian framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.« less
Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics
Martínez, Enrique; Cawkwell, Marc J.; Voter, Arthur F.; ...
2015-04-21
Here, Extended Lagrangian Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended Lagrangian Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached atmore » each time step. Lastly, the thermostated extended Lagrangian framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.« less
Holguín-Gallego, Fernando José; Chávez-Calvillo, Rodrigo; García-Revilla, Marco; Francisco, Evelio; Pendás, Ángel Martín; Rocha-Rinza, Tomás
2016-07-15
The electronic energy partition established by the Interacting Quantum Atoms (IQA) approach is an important method of wavefunction analyses which has yielded valuable insights about different phenomena in physical chemistry. Most of the IQA applications have relied upon approximations, which do not include either dynamical correlation (DC) such as Hartree-Fock (HF) or external DC like CASSCF theory. Recently, DC was included in the IQA method by means of HF/Coupled-Cluster (CC) transition densities (Chávez-Calvillo et al., Comput. Theory Chem. 2015, 1053, 90). Despite the potential utility of this approach, it has a few drawbacks, for example, it is not consistent with the calculation of CC properties different from the total electronic energy. To improve this situation, we have implemented the IQA energy partition based on CC Lagrangian one- and two-electron orbital density matrices. The development presented in this article is tested and illustrated with the H2 , LiH, H2 O, H2 S, N2 , and CO molecules for which the IQA results obtained under the consideration of (i) the CC Lagrangian, (ii) HF/CC transition densities, and (iii) HF are critically analyzed and compared. Additionally, the effect of the DC in the different components of the electronic energy in the formation of the T-shaped (H2 )2 van der Waals cluster and the bimolecular nucleophilic substitution between F(-) and CH3 F is examined. We anticipate that the approach put forward in this article will provide new understandings on subjects in physical chemistry wherein DC plays a crucial role like molecular interactions along with chemical bonding and reactivity. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
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.
Learn the Lagrangian: A Vector-Valued RKHS Approach to Identifying Lagrangian Systems.
Cheng, Ching-An; Huang, Han-Pang
2016-12-01
We study the modeling of Lagrangian systems with multiple degrees of freedom. Based on system dynamics, canonical parametric models require ad hoc derivations and sometimes simplification for a computable solution; on the other hand, due to the lack of prior knowledge in the system's structure, modern nonparametric models in machine learning face the curse of dimensionality, especially in learning large systems. In this paper, we bridge this gap by unifying the theories of Lagrangian systems and vector-valued reproducing kernel Hilbert space. We reformulate Lagrangian systems with kernels that embed the governing Euler-Lagrange equation-the Lagrangian kernels-and show that these kernels span a subspace capturing the Lagrangian's projection as inverse dynamics. By such property, our model uses only inputs and outputs as in machine learning and inherits the structured form as in system dynamics, thereby removing the need for the mundane derivations for new systems as well as the generalization problem in learning from scratches. In effect, it learns the system's Lagrangian, a simpler task than directly learning the dynamics. To demonstrate, we applied the proposed kernel to identify the robot inverse dynamics in simulations and experiments. Our results present a competitive novel approach to identifying Lagrangian systems, despite using only inputs and outputs.
Lagrangian description of warm plasmas
NASA Technical Reports Server (NTRS)
Kim, H.
1970-01-01
Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.
Lagrangian coherent structures along atmospheric rivers.
Garaboa-Paz, Daniel; Eiras-Barca, Jorge; Huhn, Florian; Pérez-Muñuzuri, Vicente
2015-06-01
We show that filamentous Atmospheric Rivers (ARs) over the Northern Atlantic Ocean are closely linked to attracting Lagrangian Coherent Structures (LCSs) in the large scale wind field. The detected LCSs represent lines of attraction in the evolving flow with a significant impact on all passive tracers. Using Finite-Time Lyapunov Exponents, we extract LCSs from a two-dimensional flow derived from water vapor flux of atmospheric reanalysis data and compare them to the three-dimensional LCS obtained from the wind flow. We correlate the typical filamentous water vapor patterns of ARs with LCSs and find that LCSs bound the filaments on the back side. Passive advective transport of water vapor in the AR from tropical latitudes is potentially possible.
Computing eddy-driven effective diffusivity using Lagrangian particles
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.
Mean-Lagrangian formalism and covariance of fluid turbulence.
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.
Two-dimensional Lagrangian simulation of suspended sediment
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.
An Eulerian/Lagrangian coupling procedure for three-dimensional vortical flows
NASA Technical Reports Server (NTRS)
Felici, Helene M.; Drela, Mark
1993-01-01
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of 3D vortical flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method, added to the Eulerian time-marching procedure, provides a correction of the Eulerian solution. In turn, the Eulerian solution is used to integrate the Lagrangian state-vector along the particles trajectories. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers describe accurately the convection properties and enhance the vorticity and entropy capturing capabilities of the Eulerian solver. The Eulerian/Lagrangian coupling strategies are discussed and the combined scheme is tested on a constant stagnation pressure flow in a 90 deg bend and on a swirling pipe flow. As the numerical diffusion is reduced when using the Lagrangian correction, a vorticity gradient augmentation is identified as a basic problem of this inviscid calculation.
Can lagrangian models reproduce the migration time of European eel obtained from otolith analysis?
NASA Astrophysics Data System (ADS)
Rodríguez-Díaz, L.; Gómez-Gesteira, M.
2017-12-01
European eel can be found at the Bay of Biscay after a long migration across the Atlantic. The duration of migration, which takes place at larval stage, is of primary importance to understand eel ecology and, hence, its survival. This duration is still a controversial matter since it can range from 7 months to > 4 years depending on the method to estimate duration. The minimum migration duration estimated from our lagrangian model is similar to the duration obtained from the microstructure of eel otoliths, which is typically on the order of 7-9 months. The lagrangian model showed to be sensitive to different conditions like spatial and time resolution, release depth, release area and initial distribution. In general, migration showed to be faster when decreasing the depth and increasing the resolution of the model. In average, the fastest migration was obtained when only advective horizontal movement was considered. However, faster migration was even obtained in some cases when locally oriented random migration was taken into account.
Acoustic streaming: an arbitrary Lagrangian-Eulerian perspective.
Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco
2017-08-25
We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.
On tide-induced Lagrangian residual current and residual transport: 1. Lagrangian residual current
Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi
1986-01-01
Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long-term transport processes. It has been pointed out by previous studies that it is more relevant to use a Lagrangian mean velocity than an Eulerian mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k, which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two-dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the Lagrangian and Eulerian residual currents. When k is small, the first-order Lagrangian residual is shown to be the sum of the Eulerian residual current and the Stokes drift. The Lagrangian residual drift velocity or the second-order Lagrangian residual current has been shown to be dependent on the phase of tidal current. The Lagrangian drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first-order residual currents, and it takes the form of an ellipse on a hodograph plane. Several examples are given to further demonstrate the unique properties of the Lagrangian residual current.
Lagrangian motion, coherent structures, and lines of persistent material strain.
Samelson, R M
2013-01-01
Lagrangian motion in geophysical fluids may be strongly influenced by coherent structures that support distinct regimes in a given flow. The problems of identifying and demarcating Lagrangian regime boundaries associated with dynamical coherent structures in a given velocity field can be studied using approaches originally developed in the context of the abstract geometric theory of ordinary differential equations. An essential insight is that when coherent structures exist in a flow, Lagrangian regime boundaries may often be indicated as material curves on which the Lagrangian-mean principal-axis strain is large. This insight is the foundation of many numerical techniques for identifying such features in complex observed or numerically simulated ocean flows. The basic theoretical ideas are illustrated with a simple, kinematic traveling-wave model. The corresponding numerical algorithms for identifying candidate Lagrangian regime boundaries and lines of principal Lagrangian strain (also called Lagrangian coherent structures) are divided into parcel and bundle schemes; the latter include the finite-time and finite-size Lyapunov exponent/Lagrangian strain (FTLE/FTLS and FSLE/FSLS) metrics. Some aspects and results of oceanographic studies based on these approaches are reviewed, and the results are discussed in the context of oceanographic observations of dynamical coherent structures.
About non standard Lagrangians in cosmology
DOE Office of Scientific and Technical Information (OSTI.GOV)
Dimitrijevic, Dragoljub D.; Milosevic, Milan
A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.
Lagrangian ocean analysis: Fundamentals and practices
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
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.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1993-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.
Extended Lagrangian Excited State Molecular Dynamics.
Bjorgaard, J A; Sheppard, D; Tretiak, S; Niklasson, A M N
2018-02-13
An extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).
Deconstructing field-induced ketene isomerization through Lagrangian descriptors.
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.
Next generation extended Lagrangian first principles molecular dynamics
NASA Astrophysics Data System (ADS)
Niklasson, Anders M. N.
2017-08-01
Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.
Next generation extended Lagrangian first principles molecular dynamics.
Niklasson, Anders M N
2017-08-07
Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.
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.
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.
Cotter, C J; Gottwald, G A; Holm, D D
2017-09-01
In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.
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.
Effective Lagrangian in de Sitter spacetime
NASA Astrophysics Data System (ADS)
Kitamoto, Hiroyuki; Kitazawa, Yoshihisa
2017-01-01
Scale invariant fluctuations of metric are a universal feature of quantum gravity in de Sitter spacetime. We construct an effective Lagrangian which summarizes their implications on local physics by integrating superhorizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective Lagrangian as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.
Extreme Lagrangian acceleration in confined turbulent flow.
Kadoch, Benjamin; Bos, Wouter J T; Schneider, Kai
2008-05-09
A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.
Seakeeping with the semi-Lagrangian particle finite element method
NASA Astrophysics Data System (ADS)
Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio
2017-07-01
The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.
Cotter, C. J.
2017-01-01
In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PMID:28989316
DOE Office of Scientific and Technical Information (OSTI.GOV)
Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.
2014-09-01
We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while themore » second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥/X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.« less
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.
NASA Astrophysics Data System (ADS)
Danesh-Yazdi, Mohammad; Botter, Gianluca; Foufoula-Georgiou, Efi
2017-05-01
Lack of hydro-bio-chemical data at subcatchment scales necessitates adopting an aggregated system approach for estimating water and solute transport properties, such as residence and travel time distributions, at the catchment scale. In this work, we show that within-catchment spatial heterogeneity, as expressed in spatially variable discharge-storage relationships, can be appropriately encapsulated within a lumped time-varying stochastic Lagrangian formulation of transport. This time (variability) for space (heterogeneity) substitution yields mean travel times (MTTs) that are not significantly biased to the aggregation of spatial heterogeneity. Despite the significant variability of MTT at small spatial scales, there exists a characteristic scale above which the MTT is not impacted by the aggregation of spatial heterogeneity. Extensive simulations of randomly generated river networks reveal that the ratio between the characteristic scale and the mean incremental area is on average independent of river network topology and the spatial arrangement of incremental areas.
Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics
NASA Astrophysics Data System (ADS)
Webb, G. M.; Anco, S. C.
2016-02-01
The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.
"Lagrangian" for a Non-Lagrangian Field Theory with N=2 Supersymmetry.
Gadde, Abhijit; Razamat, Shlomo S; Willett, Brian
2015-10-23
We suggest that at least some of the strongly coupled N=2 quantum field theories in 4D can have a nonconformal N=1 Lagrangian description flowing to them at low energies. In particular, we construct such a description for the N=2 rank one superconformal field theory with E(6) flavor symmetry, for which a Lagrangian description was previously unavailable. We utilize this description to compute several supersymmetric partition functions.
Lorentz Invariance of Gravitational Lagrangians in the Space of Reference Frames
NASA Astrophysics Data System (ADS)
Cognola, G.
1980-06-01
The recently proposed theories of gravitation in the space of reference frames S are based on a Lagrangian invariant with respect to the homogeneous Lorentz group. However, in theories of this kind, the Lorentz invariance is not a necessary consequence of some physical principles, as in the theories formulated in space-time, but rather a purely esthetic request. In the present paper, we give a systematic method for the construction of gravitational theories in the space S, without assuming a priori the Lorentz invariance of the Lagrangian. The Einstein-Cartan equations of gravitation are obtained requiring only that the Lagrangian is invariant under proper rotations and has particular transformation properties under space reflections and space-time dilatations
Extended Lagrangian Excited State Molecular Dynamics
Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei; ...
2018-01-09
In this work, an extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both formore » the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).« less
Extended Lagrangian Excited State Molecular Dynamics
DOE Office of Scientific and Technical Information (OSTI.GOV)
Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei
In this work, an extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both formore » the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).« less
Generalized extended Lagrangian Born-Oppenheimer molecular dynamics
Niklasson, Anders M. N.; Cawkwell, Marc J.
2014-10-29
Extended Lagrangian Born-Oppenheimer molecular dynamics based on Kohn-Sham density functional theory is generalized in the limit of vanishing self-consistent field optimization prior to the force evaluations. The equations of motion are derived directly from the extended Lagrangian under the condition of an adiabatic separation between the nuclear and the electronic degrees of freedom. We show how this separation is automatically fulfilled and system independent. The generalized equations of motion require only one diagonalization per time step and are applicable to a broader range of materials with improved accuracy and stability compared to previous formulations.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1995-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.
Lagrangian averaging with geodesic mean
NASA Astrophysics Data System (ADS)
Oliver, Marcel
2017-11-01
This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler-α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.
Lagrangian averaging with geodesic mean.
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.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Anderson, A.B.; Wackerle, J.
1983-07-01
This report describes a package of five computer codes for analyzing stress-gauge data from shock-wave experiments on reactive materials. The aim of the analysis is to obtain rate laws from experiment. A Lagrangian analysis of the stress records, performed by program LANAL, provides flow histories of particle velocity, density, and energy. Three postprocessing programs, LOOKIT, LOOK1, and LOOK2, are included in the package of codes for producing graphical output of the results of LANAL. Program RATE uses the flow histories in conjunction with an equation of state to calculate reaction-rate histories. RATE can be programmed to examine correlations between themore » rate histories and thermodynamic variables. Observed correlations can be incorporated into an appropriately parameterized rate law. Program RATE determines the values of these parameters that best reproduce the observed rate histories. The procedure is illustrated with a sample problem.« less
Lagrangian statistics and flow topology in forced two-dimensional turbulence.
Kadoch, B; Del-Castillo-Negrete, D; Bos, W J T; Schneider, K
2011-03-01
A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.
Intermittent Lagrangian velocities and accelerations in three-dimensional porous medium flow.
Holzner, M; Morales, V L; Willmann, M; Dentz, M
2015-07-01
Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors.
Spectral-clustering approach to Lagrangian vortex detection.
Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George
2016-06-01
One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.
A new method to calibrate Lagrangian model with ASAR images for oil slick trajectory.
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.
A Combined Eulerian-Lagrangian Data Representation for Large-Scale Applications.
Sauer, Franz; Xie, Jinrong; Ma, Kwan-Liu
2017-10-01
The Eulerian and Lagrangian reference frames each provide a unique perspective when studying and visualizing results from scientific systems. As a result, many large-scale simulations produce data in both formats, and analysis tasks that simultaneously utilize information from both representations are becoming increasingly popular. However, due to their fundamentally different nature, drawing correlations between these data formats is a computationally difficult task, especially in a large-scale setting. In this work, we present a new data representation which combines both reference frames into a joint Eulerian-Lagrangian format. By reorganizing Lagrangian information according to the Eulerian simulation grid into a "unit cell" based approach, we can provide an efficient out-of-core means of sampling, querying, and operating with both representations simultaneously. We also extend this design to generate multi-resolution subsets of the full data to suit the viewer's needs and provide a fast flow-aware trajectory construction scheme. We demonstrate the effectiveness of our method using three large-scale real world scientific datasets and provide insight into the types of performance gains that can be achieved.
Influence of compressibility on the Lagrangian statistics of vorticity-strain-rate interactions.
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.
Generalized Lagrangian coherent structures
NASA Astrophysics Data System (ADS)
Balasuriya, Sanjeeva; Ouellette, Nicholas T.; Rypina, Irina I.
2018-06-01
The notion of a Lagrangian Coherent Structure (LCS) is by now well established as a way to capture transient coherent transport dynamics in unsteady and aperiodic fluid flows that are known over finite time. We show that the concept of an LCS can be generalized to capture coherence in other quantities of interest that are transported by, but not fully locked to, the fluid. Such quantities include those with dynamic, biological, chemical, or thermodynamic relevance, such as temperature, pollutant concentration, vorticity, kinetic energy, plankton density, and so on. We provide a conceptual framework for identifying the Generalized Lagrangian Coherent Structures (GLCSs) associated with such evolving quantities. We show how LCSs can be seen as a special case within this framework, and provide an overarching discussion of various methods for identifying LCSs. The utility of this more general viewpoint is highlighted through a variety of examples. We also show that although LCSs approximate GLCSs in certain limiting situations under restrictive assumptions on how the velocity field affects the additional quantities of interest, LCSs are not in general sufficient to describe their coherent transport.
NASA Astrophysics Data System (ADS)
Ramji, Sarah Ann
Improved understanding of turbulence-flame interactions in premixed combustion can be achieved using fully 3D time-resolved multi-kHz multi-scalar experimental measurements. These interactions may be represented by the evolution of various Lagrangian quantities described by theoretical Lagrangian Fluid Elements (LFEs). The data used in this work came from two experimental campaigns that used simultaneous T-PIV and OH/CH2O PLIF, at Sandia National Labs and the Air Force Research Lab at Wright-Patterson. In this thesis, an algorithm to accurately track LFEs through this 4D experimental space has been developed and verified by cross-correlation with the T-PIV seed particle fields. A novel method to measure the local instantaneous displacement speed in 3D has been developed, using this algorithm to track control masses of fluid that interact with the flame front. Statistics of the displacement speed have been presented, and the effects of local turbulence and flame topological properties on the displacement speed have been studied.
Forecasting Future Sea Ice Conditions: A Lagrangian Approach
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
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.
Next Generation Extended Lagrangian Quantum-based Molecular Dynamics
NASA Astrophysics Data System (ADS)
Negre, Christian
2017-06-01
A new framework for extended Lagrangian first-principles molecular dynamics simulations is presented, which overcomes shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while maintaining important advantages of the unified extended Lagrangian formulation of density functional theory pioneered by Car and Parrinello three decades ago. The new framework allows, for the first time, energy conserving, linear-scaling Born-Oppenheimer molecular dynamics simulations, which is necessary to study larger and more realistic systems over longer simulation times than previously possible. Expensive, self-consinstent-field optimizations are avoided and normal integration time steps of regular, direct Born-Oppenheimer molecular dynamics can be used. Linear scaling electronic structure theory is presented using a graph-based approach that is ideal for parallel calculations on hybrid computer platforms. For the first time, quantum based Born-Oppenheimer molecular dynamics simulation is becoming a practically feasible approach in simulations of +100,000 atoms-representing a competitive alternative to classical polarizable force field methods. In collaboration with: Anders Niklasson, Los Alamos National Laboratory.
The Gaussian streaming model and convolution Lagrangian effective field theory
Vlah, Zvonimir; Castorina, Emanuele; White, Martin
2016-12-05
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM tomore » a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.« less
The Gaussian streaming model and convolution Lagrangian effective field theory
DOE Office of Scientific and Technical Information (OSTI.GOV)
Vlah, Zvonimir; Castorina, Emanuele; White, Martin, E-mail: zvlah@stanford.edu, E-mail: ecastorina@berkeley.edu, E-mail: mwhite@berkeley.edu
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM tomore » a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.« less
Coherent Lagrangian swirls among submesoscale motions.
Beron-Vera, F J; Hadjighasem, A; Xia, Q; Olascoaga, M J; Haller, G
2018-03-05
The emergence of coherent Lagrangian swirls (CLSs) among submesoscale motions in the ocean is illustrated. This is done by applying recent nonlinear dynamics tools for Lagrangian coherence detection on a surface flow realization produced by a data-assimilative submesoscale-permitting ocean general circulation model simulation of the Gulf of Mexico. Both mesoscale and submesoscale CLSs are extracted. These extractions prove the relevance of coherent Lagrangian eddies detected in satellite-altimetry-based geostrophic flow data for the arguably more realistic ageostrophic multiscale flow.
Alternative kinetic energy metrics for Lagrangian systems
NASA Astrophysics Data System (ADS)
Sarlet, W.; Prince, G.
2010-11-01
We examine Lagrangian systems on \\ {R}^n with standard kinetic energy terms for the possibility of additional, alternative Lagrangians with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such Lagrangians. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous Lagrangians for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom.
NASA Technical Reports Server (NTRS)
Felici, Helene M.; Drela, Mark
1993-01-01
A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.
Implications of Lagrangian transport for coupled chemistry-climate simulations
NASA Astrophysics Data System (ADS)
Stenke, A.; Dameris, M.; Grewe, V.; Garny, H.
2008-10-01
For the first time a purely Lagrangian transport algorithm is applied in a fully coupled chemistry-climate model (CCM). We use the Lagrangian scheme ATTILA for the transport of water vapour, cloud water and chemical trace species in the ECHAM4.L39(DLR)/CHEM (E39C) CCM. The advantage of the Lagrangian approach is that it is numerically non-diffusive and therefore maintains steeper and more realistic gradients than the operational semi-Lagrangian transport scheme. In case of radiatively active species changes in the simulated distributions feed back to model dynamics which in turn affect the modelled transport. The implications of the Lagrangian transport scheme for stratospheric model dynamics and tracer distributions in the upgraded model version E39C-ATTILA (E39C-A) are evaluated by comparison with observations and results of the E39C model with the operational semi-Lagrangian advection scheme. We find that several deficiencies in stratospheric dynamics in E39C seem to originate from a pronounced modelled wet bias and an associated cold bias in the extra-tropical lowermost stratosphere. The reduction of the simulated moisture and temperature bias in E39C-A leads to a significant advancement of stratospheric dynamics in terms of the mean state as well as annual and interannual variability. As a consequence of the favourable numerical characteristics of the Lagrangian transport scheme and the improved model dynamics, E39C-A generally shows more realistic stratospheric tracer distributions: Compared to E39C high stratospheric chlorine (Cly) concentrations extend further downward and agree now well with analyses derived from observations. Therefore E39C-A realistically covers the altitude of maximum ozone depletion in the stratosphere. The location of the ozonopause, i.e. the transition from low tropospheric to high stratospheric ozone values, is also clearly improved in E39C-A. Furthermore, the simulated temporal evolution of stratospheric Cly in the past is
Multi-Lagrangians for integrable systems
NASA Astrophysics Data System (ADS)
Nutku, Y.; Pavlov, M. V.
2002-03-01
We propose a general scheme to construct multiple Lagrangians for completely integrable nonlinear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit N-fold first order local Hamiltonian structure can be cast into variational form with 2N-1 Lagrangians which will be local functionals of Clebsch potentials. This number increases to 3N-2 when the Miura transformation is invertible. Furthermore we construct a new Lagrangian for polytropic gas dynamics in 1+1 dimensions which is a free, local functional of the physical field variables, namely density and velocity, thus dispensing with the necessity of introducing Clebsch potentials entirely. This is a consequence of bi-Hamiltonian structure with a compatible pair of first and third order Hamiltonian operators derived from Sheftel's recursion operator.
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.
Statistical scaling of pore-scale Lagrangian velocities in natural porous media.
Siena, M; Guadagnini, A; Riva, M; Bijeljic, B; Pereira Nunes, J P; Blunt, M J
2014-08-01
We investigate the scaling behavior of sample statistics of pore-scale Lagrangian velocities in two different rock samples, Bentheimer sandstone and Estaillades limestone. The samples are imaged using x-ray computer tomography with micron-scale resolution. The scaling analysis relies on the study of the way qth-order sample structure functions (statistical moments of order q of absolute increments) of Lagrangian velocities depend on separation distances, or lags, traveled along the mean flow direction. In the sandstone block, sample structure functions of all orders exhibit a power-law scaling within a clearly identifiable intermediate range of lags. Sample structure functions associated with the limestone block display two diverse power-law regimes, which we infer to be related to two overlapping spatially correlated structures. In both rocks and for all orders q, we observe linear relationships between logarithmic structure functions of successive orders at all lags (a phenomenon that is typically known as extended power scaling, or extended self-similarity). The scaling behavior of Lagrangian velocities is compared with the one exhibited by porosity and specific surface area, which constitute two key pore-scale geometric observables. The statistical scaling of the local velocity field reflects the behavior of these geometric observables, with the occurrence of power-law-scaling regimes within the same range of lags for sample structure functions of Lagrangian velocity, porosity, and specific surface area.
Toroidal regularization of the guiding center Lagrangian
Burby, J. W.; Ellison, C. L.
2017-11-22
In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less
Toroidal regularization of the guiding center Lagrangian
DOE Office of Scientific and Technical Information (OSTI.GOV)
Burby, J. W.; Ellison, C. L.
In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less
Target Lagrangian kinematic simulation for particle-laden flows.
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.
Time-lag and Correlation between ACE and RBSPICE Injection Event Observations during Storm Times
NASA Astrophysics Data System (ADS)
Madanian, H.; Patterson, J. D.; Manweiler, J. W.; Soto-chavez, A. R.; Gerrard, A. J.; Lanzerotti, L. J.
2017-12-01
The Radiation Belt Storm Probes Ion Composition Experiment (RBSPICE) on the Van Allen Probes mission measures energetic charged particles [ 20 keV to 1 MeV] in the inner magnetosphere and ring current. During geomagnetic storms, injections of energetic ions into the ring current change the ion population and produce geomagnetic field depressions on Earth's surface. We analyzed the magnetic field strength and particle composition in the interplanetary medium measured by instruments on the Advanced Composition Explorer (ACE) spacecraft near the inner Lagrangian point. The Electron, Proton, and Alpha Monitor-Low Energy Magnetic Spectrometer (EPAM-LEMS) sensor on ACE measures energetic particles [ 50 keV to 5 MeV] in the interplanetary space. The SYM-H index is utilized to classify the storm events by magnitude and to select more than 60 storm events between 2013 and 2017. We cross-compared ACE observations at storm times, with the RBSPICE ion measurements at dusk to midnight magnetic local time and over the 3-6 L-shell range. We report on the relative composition of the solar particles and the relative composition of the inner magnetospheric hot plasma during storm times. The data correlation is accomplished by shifting the observation time from ACE to RBSPICE using the solar wind velocity at the time of the observation. We will discuss time lags between storm onset at the magnetopause and injection events measured for each storm.
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.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding.
Krause, Katharina; Klopper, Wim
2016-01-28
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding
DOE Office of Scientific and Technical Information (OSTI.GOV)
Krause, Katharina; Klopper, Wim, E-mail: klopper@kit.edu
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.
A Chiang-type lagrangian in CP^2
NASA Astrophysics Data System (ADS)
Cannas da Silva, Ana
2018-03-01
We analyse a monotone lagrangian in CP^2 that is hamiltonian isotopic to the standard lagrangian RP^2, yet exhibits a distinguishing behaviour under reduction by one of the toric circle actions, namely it intersects transversally the reduction level set and it projects one-to-one onto a great circle in CP^1. This lagrangian thus provides an example of embedded composition fitting work of Wehrheim-Woodward and Weinstein.
Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere
DOE Office of Scientific and Technical Information (OSTI.GOV)
Tang Wenbo; Mahalov, Alex
2013-03-15
We develop a three-dimensional numerical model for the E-F region ionosphere and study the Lagrangian dynamics for plasma flows in this region. Our interest rests on the charge-neutral interactions and the statistics associated with stochastic Lagrangian motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology-the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using Lagrangian measures such as the finite-time Lyapunov exponents, we locate the Lagrangian skeletons for mixing in plasma,more » hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic Lagrangian motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of non-Gaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.« less
Cucco, Andrea; Umgiesser, Georg
2015-09-15
In this work, we investigated if the Eulerian and the Lagrangian approaches for the computation of the Transport Time Scales (TTS) of semi-enclosed water bodies can be used univocally to define the spatial variability of basin flushing features. The Eulerian and Lagrangian TTS were computed for both simplified test cases and a realistic domain: the Venice Lagoon. The results confirmed the two approaches cannot be adopted univocally and that the spatial variability of the water renewal capacity can be investigated only through the computation of both the TTS. A specific analysis, based on the computation of a so-called Trapping Index, was then suggested to integrate the information provided by the two different approaches. The obtained results proved the Trapping Index to be useful to avoid any misleading interpretation due to the evaluation of the basin renewal features just from an Eulerian only or from a Lagrangian only perspective. Copyright © 2015 Elsevier Ltd. All rights reserved.
Lagrangian statistics in weakly forced two-dimensional turbulence.
Rivera, Michael K; Ecke, Robert E
2016-01-01
Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.
Lagrangian statistics in weakly forced two-dimensional turbulence
DOE Office of Scientific and Technical Information (OSTI.GOV)
Rivera, Michael K.; Ecke, Robert E.
Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r i. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in termsmore » of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.« less
Lagrangian statistics in weakly forced two-dimensional turbulence
Rivera, Michael K.; Ecke, Robert E.
2016-01-14
Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r i. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in termsmore » of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.« less
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.
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
Three dimensional Lagrangian structures in the Antarctic Polar Vortex.
NASA Astrophysics Data System (ADS)
Mancho, Ana M.; Garcia-Garrido, Victor J.; Curbelo, Jezabel; Niang, Coumba; Mechoso, Carlos R.; Wiggins, Stephen
2017-04-01
Dynamical systems theory has supported the description of transport processes in fluid dynamics. For understanding trajectory patterns in chaotic advection the geometrical approach by Poincaré seeks for spatial structures that separate regions corresponding to qualitatively different types of trajectories. These structures have been referred to as Lagrangian Coherent Structures (LCS), which typically in geophysical flows are well described under the approach of incompressible 2D flows. Different tools have been used to visualize LCS. In this presentation we use Lagrangian Descriptors [1,2,3,4] (function M) for visualizing 3D Lagrangian structures in the atmosphere, in particular in the Antarctic Polar Vortex. The function M is computed in a fully 3D incompressible flow obtained from data provided by the European Centre for Medium-Range Weather Forecast and it is represented in 2D surfaces. We discuss the findings during the final warming that took place in the spring of 1979 [5]. This research is supported by MINECO grant MTM2014-56392-R. Support is acknowledged also from CSIC grant COOPB20265, U.S. NSF grant AGS-1245069 and ONR grant No. N00014- 01-1-0769. C. Niang acknowledges Fundacion Mujeres por Africa and ICMAT Severo Ochoa project SEV-2011-0087 for financial support. [1] C. Mendoza, A. M. Mancho. The hidden geometry of ocean flows. Physical Review Letters 105 (2010), 3, 038501-1-038501-4. [2] A. M. Mancho, S. Wiggins, J. Curbelo, C. Mendoza. Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems. Communications in Nonlinear Science and Numerical Simulation. 18 (2013) 3530-3557. [3] C. Lopesino, F. Balibrea-Iniesta, S. Wiggins and A. M. Mancho. Lagrangian descriptors for two dimensional, area preserving autonomous and nonautonomous maps. Communications in Nonlinear Science and Numerical Simulations, 27 (2015) (1-3), 40-51. [4] C. Lopesino, F. Balibrea-Iniesta, V. J. García-Garrido, S. Wiggins, and A
NASA Astrophysics Data System (ADS)
Jakovetic, Dusan; Xavier, João; Moura, José M. F.
2011-08-01
We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x=x^\\star. The objective function of the corresponding optimization problem is the sum of private (known only by a node,) convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, decentralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l_1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.
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.
Path integral for equities: Dynamic correlation and empirical analysis
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.; Cao, Yang; Lau, Ada; Tang, Pan
2012-02-01
This paper develops a model to describe the unequal time correlation between rate of returns of different stocks. A non-trivial fourth order derivative Lagrangian is defined to provide an unequal time propagator, which can be fitted to the market data. A calibration algorithm is designed to find the empirical parameters for this model and different de-noising methods are used to capture the signals concealed in the rate of return. The detailed results of this Gaussian model show that the different stocks can have strong correlation and the empirical unequal time correlator can be described by the model's propagator. This preliminary study provides a novel model for the correlator of different instruments at different times.
Network-based study of Lagrangian transport and mixing
NASA Astrophysics Data System (ADS)
Padberg-Gehle, Kathrin; Schneide, Christiane
2017-10-01
Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterization of these Lagrangian objects is a topic of intense current research. While established mathematical approaches such as variational methods or transfer-operator-based schemes require full knowledge of the flow field or at least high-resolution trajectory data, this information may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from Lagrangian trajectory data, that is, numerical or measured time series of particle positions in a fluid flow. In this context, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, where Lagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph concepts are then employed to analyze the resulting network. In particular, local network measures such as the node degree, the average degree of neighboring nodes, and the clustering coefficient serve as indicators of highly mixing regions, whereas spectral graph partitioning schemes allow us to extract coherent sets. The proposed methodology is very fast to run and we demonstrate its applicability in two geophysical flows - the Bickley jet as well as the Antarctic stratospheric polar vortex.
Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics.
Glavatskiy, K S
2015-05-28
We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an "integral of evolution" which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.
Quasi Real Time Cruise Deployment Guidance to Coherent Regions Using Lagrangian Methods
NASA Astrophysics Data System (ADS)
Dehghani Ashkezari, M.; Barone, B.; Follows, M. J.; Hill, C. N.; Wilson, S. T.; Karl, D. M.
2016-02-01
We describe Lagrangian strategies that were used to help plan a field experiment in the North Pacific Subtropical Gyre in July 2015 close to Station ALOHA. The field study, part of the Simons Collaboration on Ocean Processes and Ecology (SCOPE), aimed to characterize diel changes in the composition and activity of the surface ocean microbial community. The study required forecasting a coherent water mass would remain relatively isolated from neighboring waters over 10 days. To this end, we used near-real-time remote-sensed altimetric data with 0.25 degree resolution (provided by Colorado Center for Astrodynamics Research) to compute particle trajectories and Finite-Time Lyapunov Exponent (FTLE) techniques to pinpoint the candidate coherent regions and exclude undesirable, highly dispersive regimes. We will demonstrate the utility of the approach, which was successful at the identification of the coherent region as evidenced by the trajectories of Surface Velocity Program drifters. It accurately identified a poorly suited field of strong transport close to Station ALOHA and identified a well suited region, associated with an anti-cylonic eddy that provided an ideal context for the field campaign. This talk will describe the methodology and the results from the Summer 2015 expedition as well as the potential to apply the approach more broadly.
Lagrangian transport properties of pulmonary interfacial flows
Smith, Bradford J.; Lukens, Sarah; Yamaguchi, Eiichiro; Gaver, Donald P.
2012-01-01
Disease states characterized by airway fluid occlusion and pulmonary surfactant insufficiency, such as respiratory distress syndrome, have a high mortality rate. Understanding the mechanics of airway reopening, particularly involving surfactant transport, may provide an avenue to increase patient survival via optimized mechanical ventilation waveforms. We model the occluded airway as a liquid-filled rigid tube with the fluid phase displaced by a finger of air that propagates with both mean and sinusoidal velocity components. Finite-time Lyapunov exponent (FTLE) fields are employed to analyse the convective transport characteristics, taking note of Lagrangian coherent structures (LCSs) and their effects on transport. The Lagrangian perspective of these techniques reveals flow characteristics that are not readily apparent by observing Eulerian measures. These analysis techniques are applied to surfactant-free velocity fields determined computationally, with the boundary element method, and measured experimentally with micro particle image velocimetry (μ-PIV). We find that the LCS divides the fluid into two regimes, one advected upstream (into the thin residual film) and the other downstream ahead of the advancing bubble. At higher oscillatory frequencies particles originating immediately inside the LCS experience long residence times at the air–liquid interface, which may be conducive to surfactant transport. At high frequencies a well-mixed attractor region is identified; this volume of fluid cyclically travels along the interface and into the bulk fluid. The Lagrangian analysis is applied to velocity data measured with 0.01 mg ml−1 of the clinical pulmonary surfactant Infasurf in the bulk fluid, demonstrating flow field modifications with respect to the surfactant-free system that were not visible in the Eulerian frame. PMID:23049141
A LES-based Eulerian-Lagrangian approach to predict the dynamics of bubble plumes
NASA Astrophysics Data System (ADS)
Fraga, Bruño; Stoesser, Thorsten; Lai, Chris C. K.; Socolofsky, Scott A.
2016-01-01
An approach for Eulerian-Lagrangian large-eddy simulation of bubble plume dynamics is presented and its performance evaluated. The main numerical novelties consist in defining the gas-liquid coupling based on the bubble size to mesh resolution ratio (Dp/Δx) and the interpolation between Eulerian and Lagrangian frameworks through the use of delta functions. The model's performance is thoroughly validated for a bubble plume in a cubic tank in initially quiescent water using experimental data obtained from high-resolution ADV and PIV measurements. The predicted time-averaged velocities and second-order statistics show good agreement with the measurements, including the reproduction of the anisotropic nature of the plume's turbulence. Further, the predicted Eulerian and Lagrangian velocity fields, second-order turbulence statistics and interfacial gas-liquid forces are quantified and discussed as well as the visualization of the time-averaged primary and secondary flow structure in the tank.
Getting Things Sorted With Lagrangian Coherent Structures
NASA Astrophysics Data System (ADS)
Atis, Severine; Peacock, Thomas; Environmental Dynamics Laboratory Team
2014-11-01
The dispersion of a tracer in a fluid flow is influenced by the Lagrangian motion of fluid elements. Even in laminar regimes, the irregular chaotic behavior of a fluid flow can lead to effective stirring that rapidly redistributes a tracer throughout the domain. For flows with arbitrary time-dependence, the modern approach of Lagrangian Coherent Structures (LCSs) provide a method for identifying the key material lines that organize flow transport. When the advected tracer particles possess a finite size and nontrivial shape, however, their dynamics can differ markedly from passive tracers, thus affecting the dispersion phenomena. We present details of numerical simulations and laboratory experiments that investigate the behavior of finite size particles in 2-dimensional chaotic flows. We show that the shape and the size of the particles alter the underlying LCSs, facilitating segregation between tracers of different shape in the same flow field.
Lagrangian coherent structures separate dynamically distinct regions in fluid flows.
Kelley, Douglas H; Allshouse, Michael R; Ouellette, Nicholas T
2013-07-01
Using filter-space techniques, we study the scale-to-scale transport of energy in a quasi-two-dimensional, weakly turbulent fluid flow averaged along the trajectories of fluid elements. We find that although the spatial mean of this Lagrangian-averaged flux is nearly unchanged from its Eulerian counterpart, the spatial structure of the scale-to-scale energy flux changes significantly. In particular, its features appear to correlate with the positions of Lagrangian coherent structures (LCS's). We show that the LCS's tend to lie at zeros of the scale-to-scale flux, and therefore that the LCS's separate regions that have qualitatively different dynamics. Since LCS's are also known to be impenetrable barriers to advection and mixing, we therefore find that the fluid on either side of an LCS is both kinematically and dynamically distinct. Our results extend the utility of LCS's by making clear the role they play in the flow dynamics in addition to the kinematics.
Lagrangian Hotspots of In-Use NOX Emissions from Transit Buses.
Kotz, Andrew J; Kittelson, David B; Northrop, William F
2016-06-07
In-use, spatiotemporal NOX emissions were measured from a conventional powertrain transit bus and a series electric hybrid bus over gradients of route kinetic intensity and ambient temperature. This paper introduces a new method for identifying NOX emissions hotspots along a bus route using high fidelity Lagrangian vehicle data to explore spatial interactions that may influence emissions production. Our study shows that the studied transit buses emit higher than regulated emissions because on-route operation does not accurately represent the range of engine operation tested according to regulatory standards. Using the Lagrangian hotspot detection, we demonstrate that NOX hotspots occurred at bus stops, during cold starts, on inclines, and for accelerations. On the selected routes, bus stops resulted in 3.3 times the route averaged emissions factor in grams/km without significant dependence on bus type or climate. The buses also emitted 2.3 times the route averaged NOX emissions factor at the beginning of each route due to cold selective catalytic reduction aftertreatment temperature. The Lagrangian hotspot detection technique demonstrated here could be employed in future connected vehicles empowered by advances in computational power, data storage capability, and improved sensor technology to optimize emissions as a function of spatial location.
Comparing High-latitude Ionospheric and Thermospheric Lagrangian Coherent Structures
NASA Astrophysics Data System (ADS)
Wang, N.; Ramirez, U.; Flores, F.; Okic, D.; Datta-Barua, S.
2015-12-01
Lagrangian Coherent Structures (LCSs) are invisible boundaries in time varying flow fields that may be subject to mixing and turbulence. The LCS is defined by the local maxima of the finite time Lyapunov exponent (FTLE), a scalar field quantifying the degree of stretching of fluid elements over the flow domain. Although the thermosphere is dominated by neutral wind processes and the ionosphere is governed by plasma electrodynamics, we can compare the LCS in the two modeled flow fields to yield insight into transport and interaction processes in the high-latitude IT system. For obtaining thermospheric LCS, we use the Horizontal Wind Model 2014 (HWM14) [1] at a single altitude to generate the two-dimensional velocity field. The FTLE computation is applied to study the flow field of the neutral wind, and to visualize the forward-time Lagrangian Coherent Structures in the flow domain. The time-varying structures indicate a possible thermospheric LCS ridge in the auroral oval area. The results of a two-day run during a geomagnetically quiet period show that the structures are diurnally quasi-periodic, thus that solar radiation influences the neutral wind flow field. To find the LCS in the high-latitude ionospheric drifts, the Weimer 2001 [2] polar electric potential model and the International Geomagnetic Reference Field 11 [3] are used to compute the ExB drift flow field in ionosphere. As with the neutral winds, the Lagrangian Coherent Structures are obtained by applying the FTLE computation. The relationship between the thermospheric and ionospheric LCS is analyzed by comparing overlapping FTLE maps. Both a publicly available FTLE solver [4] and a custom-built FTLE computation are used and compared for validation [5]. Comparing the modeled IT LCSs on a quiet day with the modeled IT LCSs on a storm day indicates important factors on the structure and time evolution of the LCS.
Variational Lagrangian data assimilation in open channel networks
NASA Astrophysics Data System (ADS)
Wu, Qingfang; Tinka, Andrew; Weekly, Kevin; Beard, Jonathan; Bayen, Alexandre M.
2015-04-01
This article presents a data assimilation method in a tidal system, where data from both Lagrangian drifters and Eulerian flow sensors were fused to estimate water velocity. The system is modeled by first-order, hyperbolic partial differential equations subject to periodic forcing. The estimation problem can then be formulated as the minimization of the difference between the observed variables and model outputs, and eventually provide the velocity and water stage of the hydrodynamic system. The governing equations are linearized and discretized using an implicit discretization scheme, resulting in linear equality constraints in the optimization program. Thus, the flow estimation can be formed as an optimization problem and efficiently solved. The effectiveness of the proposed method was substantiated by a large-scale field experiment in the Sacramento-San Joaquin River Delta in California. A fleet of 100 sensors developed at the University of California, Berkeley, were deployed in Walnut Grove, CA, to collect a set of Lagrangian data, a time series of positions as the sensors moved through the water. Measurements were also taken from Eulerian sensors in the region, provided by the United States Geological Survey. It is shown that the proposed method can effectively integrate Lagrangian and Eulerian measurement data, resulting in a suited estimation of the flow variables within the hydraulic system.
Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics
DOE Office of Scientific and Technical Information (OSTI.GOV)
Glavatskiy, K. S.
We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called “mirror-image” system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such thatmore » there exists an “integral of evolution” which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.« less
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.
A Lagrangian stochastic model for aerial spray transport above an oak forest
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.
A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain
NASA Astrophysics Data System (ADS)
Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.
2018-05-01
The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.
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.
Lagrangian formulation and symmetrical description of liquid dynamics.
Trachenko, K
2017-12-01
Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.
Lagrangian formulation and symmetrical description of liquid dynamics
NASA Astrophysics Data System (ADS)
Trachenko, K.
2017-12-01
Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k -space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k -space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.
Direct Lagrangian tracking simulations of particles in vertically-developing atmospheric clouds
NASA Astrophysics Data System (ADS)
Onishi, Ryo; Kunishima, Yuichi
2017-11-01
We have been developing the Lagrangian Cloud Simulator (LCS), which follows the so-called Euler-Lagrangian framework, where flow motion and scalar transportations (i.e., temperature and humidity) are computed with the Euler method and particle motion with the Lagrangian method. The LCS simulation considers the hydrodynamic interaction between approaching particles for robust collision detection. This leads to reliable simulations of collision growth of cloud droplets. Recently the activation process, in which aerosol particles become tiny liquid droplets, has been implemented in the LCS. The present LCS can therefore consider the whole warm-rain precipitation processes -activation, condensation, collision and drop precipitation. In this talk, after briefly introducing the LCS, we will show kinematic simulations using the LCS for quasi-one dimensional domain, i.e., vertically elongated 3D domain. They are compared with one-dimensional kinematic simulations using a spectral-bin cloud microphysics scheme, which is based on the Euler method. The comparisons show fairly good agreement with small discrepancies, the source of which will be presented. The Lagrangian statistics, obtained for the first time for the vertical domain, will be the center of discussion. This research was supported by MEXT as ``Exploratory Challenge on Post-K computer'' (Frontiers of Basic Science: Challenging the Limits).
Uncovering the Geometry of Barrierless Reactions Using Lagrangian Descriptors.
Junginger, Andrej; Hernandez, Rigoberto
2016-03-03
Transition-state theories describing barrierless chemical reactions, or more general activated problems, are often hampered by the lack of a saddle around which the dividing surface can be constructed. For example, the time-dependent transition-state trajectory uncovering the nonrecrossing dividing surface in thermal reactions in the framework of the Langevin equation has relied on perturbative approaches in the vicinity of the saddle. We recently obtained an alternative approach using Lagrangian descriptors to construct time-dependent and recrossing-free dividing surfaces. This is a nonperturbative approach making no reference to a putative saddle. Here we show how the Lagrangian descriptor can be used to obtain the transition-state geometry of a dissipated and thermalized reaction across barrierless potentials. We illustrate the method in the case of a 1D Brownian motion for both barrierless and step potentials; however, the method is not restricted and can be directly applied to different kinds of potentials and higher dimensional systems.
Chaotic Lagrangian models for turbulent relative dispersion.
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.
NASA Astrophysics Data System (ADS)
Al Roumi, Fosca; Buchert, Thomas; Wiegand, Alexander
2017-12-01
The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given to any order of the perturbations, together with extensions and applications for accessing the nonperturbative regime. We here discuss more in detail the general first-order scheme within the Cartan formalism including and concentrating on the gravitational wave propagation in matter. We provide master equations for all parts of Lagrangian-linearized perturbations propagating in the perturbed spacetime, and we outline the solution procedure that allows one to find general solutions. Particular emphasis is given to global properties of the Lagrangian perturbation fields by employing results of Hodge-de Rham theory. We here discuss how the Hodge decomposition relates to the standard scalar-vector-tensor decomposition. Finally, we demonstrate that we obtain the known linear perturbation solutions of the standard relativistic perturbation scheme by performing two steps: first, by restricting our solutions to perturbations that propagate on a flat unperturbed background spacetime and, second, by transforming to Eulerian background coordinates with truncation of nonlinear terms.
Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash
NASA Technical Reports Server (NTRS)
Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in FLASH
NASA Astrophysics Data System (ADS)
Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.
2012-08-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid-structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
A Lagrangian particle method with remeshing for tracer transport on the sphere
Bosler, Peter Andrew; Kent, James; Krasny, Robert; ...
2017-03-30
A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.« less
A Lagrangian particle method with remeshing for tracer transport on the sphere
DOE Office of Scientific and Technical Information (OSTI.GOV)
Bosler, Peter Andrew; Kent, James; Krasny, Robert
A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.« less
COLAcode: COmoving Lagrangian Acceleration code
NASA Astrophysics Data System (ADS)
Tassev, Svetlin V.
2016-02-01
COLAcode is a serial particle mesh-based N-body code illustrating the COLA (COmoving Lagrangian Acceleration) method; it solves for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory (LPT). It differs from standard N-body code by trading accuracy at small-scales to gain computational speed without sacrificing accuracy at large scales. This is useful for generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing; such catalogs are needed to perform detailed error analysis for ongoing and future surveys of LSS.
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.
Buican, Matthew; Laczko, Zoltan
2018-02-23
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories
NASA Astrophysics Data System (ADS)
Buican, Matthew; Laczko, Zoltan
2018-02-01
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
NASA Astrophysics Data System (ADS)
Besse, Nicolas; Frisch, Uriel
2017-04-01
The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or absence of boundaries. For a good understanding, it is crucial to carry out, besides mathematical studies, high-accuracy and well-resolved numerical exploration. Such studies can be very demanding in computational resources, but recently it has been shown that very substantial gains can be achieved first, by using Cauchy's Lagrangian formulation of the Euler equations and second, by taking advantage of analyticity results of the Lagrangian trajectories for flows whose initial vorticity is Hölder-continuous. The latter has been known for about 20 years (Serfati in J Math Pures Appl 74:95-104, 1995), but the combination of the two, which makes use of recursion relations among time-Taylor coefficients to obtain constructively the time-Taylor series of the Lagrangian map, has been achieved only recently (Frisch and Zheligovsky in Commun Math Phys 326:499-505, 2014; Podvigina et al. in J Comput Phys 306:320-342, 2016 and references therein). Here we extend this methodology to incompressible Euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity. Non-constructive regularity results for these cases have already been obtained by Glass et al. (Ann Sci Éc Norm Sup 45:1-51, 2012). Using the invariance of the boundary under the Lagrangian flow, we establish novel recursion relations that include contributions from the boundary. This leads to a constructive proof of time-analyticity of the Lagrangian trajectories with analytic boundaries, which can then be used subsequently for the design of a very high-order Cauchy-Lagrangian method.
An adaptive reconstruction for Lagrangian, direct-forcing, immersed-boundary methods
NASA Astrophysics Data System (ADS)
Posa, Antonio; Vanella, Marcos; Balaras, Elias
2017-12-01
Lagrangian, direct-forcing, immersed boundary (IB) methods have been receiving increased attention due to their robustness in complex fluid-structure interaction problems. They are very sensitive, however, on the selection of the Lagrangian grid, which is typically used to define a solid or flexible body immersed in a fluid flow. In the present work we propose a cost-efficient solution to this problem without compromising accuracy. Central to our approach is the use of isoparametric mapping to bridge the relative resolution requirements of Lagrangian IB, and Eulerian grids. With this approach, the density of surface Lagrangian markers, which is essential to properly enforce boundary conditions, is adapted dynamically based on the characteristics of the underlying Eulerian grid. The markers are not stored and the Lagrangian data-structure is not modified. The proposed scheme is implemented in the framework of a moving least squares reconstruction formulation, but it can be adapted to any Lagrangian, direct-forcing formulation. The accuracy and robustness of the approach is demonstrated in a variety of test cases of increasing complexity.
NASA Astrophysics Data System (ADS)
Di Bernardino, Annalisa; Monti, Paolo; Leuzzi, Giovanni; Querzoli, Giorgio
2017-11-01
Lagrangian and Eulerian statistics are obtained from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. The objective is to quantify the Eulerian (TE) and Lagrangian (TL) time scales of the turbulence above the canopy layer as well as to investigate their dependence on the aspect ratio of the canopy, AR, as the latter is the ratio of the width ( W) to the height ( H) of the canyon. Experiments are also conducted for the case of flat terrain, which can be thought of as equivalent to a classical one-directional shear flow. The values found for the Eulerian time scales on flat terrain are in agreement with previous numerical results found in the literature. It is found that both the streamwise and vertical components of the Lagrangian time scale, T_u^L and T_w^L , follow Raupach's linear law within the constant-flux layer. The same holds true for T_w^L in both the canopies analyzed (AR= 1 and AR= 2) and also for T_u^L when AR = 1. In contrast, for AR = 2, T_u^L follows Raupach's law only above z=2H. Below that level, T_u^L is nearly constant with height, showing at z=H a value approximately one order of magnitude greater than that found for AR = 1. It is shown that the assumption usually adopted for flat terrain, that β =TL/TE is proportional to the inverse of the turbulence intensity, also holds true even for the canopy flow in the constant-flux layer. In particular, γ /i_u fits well β _u =T_u^L /T_u^E in both the configurations by choosing γ to be 0.35 (here, i_u =σ _u / \\bar{u} , where \\bar{u} and σ _u are the mean and the root-mean-square of the streamwise velocity component, respectively). On the other hand, β _w =T_w^L /T_w^E follows approximately γ /i_w =0.65/( {σ _w /\\bar{u} } ) for z > 2H, irrespective of the AR value. The second main objective is to estimate other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum (KT) and the Kolmogorov constant (C_0). It is
2012-12-03
paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time- dependent flows...the low- to mid- level embryonic vortex from adverse conditions, while the 1The glossary on NOAA’s Hurricane Research Division’s web - site uses...wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation
A Theoretical Framework for Lagrangian Descriptors
NASA Astrophysics Data System (ADS)
Lopesino, C.; Balibrea-Iniesta, F.; García-Garrido, V. J.; Wiggins, S.; Mancho, A. M.
This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigorous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for LDs. The definition is stated for n-dimensional systems with general time dependence, however we rigorously prove that this method reveals the stable and unstable manifolds of hyperbolic points in four particular 2D cases: a hyperbolic saddle point for linear autonomous systems, a hyperbolic saddle point for nonlinear autonomous systems, a hyperbolic saddle point for linear nonautonomous systems and a hyperbolic saddle point for nonlinear nonautonomous systems. We also discuss further rigorous results which show the ability of LDs to highlight additional invariants sets, such as n-tori. These results are just a simple extension of the ergodic partition theory which we illustrate by applying this methodology to well-known examples, such as the planar field of the harmonic oscillator and the 3D ABC flow. Finally, we provide a thorough discussion on the requirement of the objectivity (frame-invariance) property for tools designed to reveal phase space structures and their implications for Lagrangian descriptors.
Nonconservative Lagrangian Mechanics: Purely Causal Equations of Motion
NASA Astrophysics Data System (ADS)
Dreisigmeyer, David W.; Young, Peter M.
2015-06-01
This work builds on the Volterra series formalism presented in Dreisigmeyer and Young (J Phys A 36: 8297, 2003) to model nonconservative systems. Here we treat Lagrangians and actions as `time dependent' Volterra series. We present a new family of kernels to be used in these Volterra series that allow us to derive a single retarded equation of motion using a variational principle.
Scalar curvature of Lagrangian Riemannian submersions and their harmonicity
NASA Astrophysics Data System (ADS)
Eken Meri˙ç, Şemsi; Kiliç, Erol; Sağiroğlu, Yasemi˙n
In this paper, we consider a Lagrangian Riemannian submersion from a Hermitian manifold to a Riemannian manifold and establish some basic inequalities to obtain relationships between the intrinsic and extrinsic invariants for such a submersion. Indeed, using these inequalities, we provide necessary and sufficient conditions for which a Lagrangian Riemannian submersion π has totally geodesic or totally umbilical fibers. Moreover, we study the harmonicity of Lagrangian Riemannian submersions and obtain a characterization for such submersions to be harmonic.
Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics
Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul
2015-03-11
Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less
Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics
DOE Office of Scientific and Technical Information (OSTI.GOV)
Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul
Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less
Lagrangian methods of cosmic web classification
NASA Astrophysics Data System (ADS)
Fisher, J. D.; Faltenbacher, A.; Johnson, M. S. T.
2016-05-01
The cosmic web defines the large-scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid-based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or haloes) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian nature admits a straightforward inclusion of the Hubble flow negating the necessity of a visually defined threshold value which is commonly employed by grid-based classification methods.
Higher-Order Advection-Based Remap of Magnetic Fields in an Arbitrary Lagrangian-Eulerian Code
NASA Astrophysics Data System (ADS)
Cornille, Brian; White, Dan
2017-10-01
We will present methods formulated for the Eulerian advection stage of an arbitrary Lagrangian-Eulerian code for the new addition of magnetohydrodynamic (MHD) effects. The various physical fields are advanced in time using a Lagrangian formulation of the system. When this Lagrangian motion produces substantial distortion of the mesh, it can be difficult or impossible to progress the simulation forward. This is overcome by relaxation of the mesh while the physical fields are frozen. The code has already successfully been extended to include evolution of magnetic field diffusion during the Lagrangian motion stage. This magnetic field is discretized using an H(div) compatible finite element basis. The advantage of this basis is that the divergence-free constraint of magnetic fields is maintained exactly during the Lagrangian motion evolution. Our goal is to preserve this property during Eulerian advection as well. We will demonstrate this property and the importance of MHD effects in several numerical experiments. In pulsed-power experiments magnetic fields may be imposed or spontaneously generated. When these magnetic fields are present, the evolution of the experiment may differ from a comparable configuration without magnetic fields. Prepared by LLNL under Contract DE-AC52-07NA27344. Supported by DOE CSGF under Grant Number DE-FG02-97ER25308.
Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data
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
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.;
2006-01-01
The International Consortium for Atmospheric Research on Transport and Transformation (ICARTT)-Lagrangian 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 using two Lagrangian models that were used to direct the aircraft into target air masses. A novel technique is then used to identify 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.
Euler-Lagrangian computation for estuarine hydrodynamics
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.
Böckmann, Marcus; Doltsinis, Nikos L; Marx, Dominik
2015-06-09
An extended Lagrangian formalism that allows for a smooth transition between two different descriptions of interactions during a molecular dynamics simulation is presented. This time-adaptive method is particularly useful in the context of multiscale simulation as it provides a sound recipe to switch on demand between different hierarchical levels of theory, for instance between ab initio ("QM") and force field ("MM") descriptions of a given (sub)system in the course of a molecular dynamics simulation. The equations of motion can be integrated straightforwardly using the usual propagators, such as the Verlet algorithm. First test cases include a bath of harmonic oscillators, of which a subset is switched to a different force constant and/or equilibrium position, as well as an all-MM to QM/MM transition in a hydrogen-bonded water dimer. The method is then applied to a smectic 8AB8 liquid crystal and is shown to be able to switch dynamically a preselected 8AB8 molecule from an all-MM to a QM/MM description which involves partition boundaries through covalent bonds. These examples show that the extended Lagrangian approach is not only easy to implement into existing code but that it is also efficient and robust. The technique moreover provides easy access to a conserved energy quantity, also in cases when Nosé-Hoover chain thermostatting is used throughout dynamical switching. A simple quadratic driving potential proves to be sufficient to guarantee a smooth transition whose time scale can be easily tuned by varying the fictitious mass parameter associated with the auxiliary variable used to extend the Lagrangian. The method is general and can be applied to time-adaptive switching on demand between two different levels of theory within the framework of hybrid scale-bridging simulations.
A semi-Lagrangian approach to the shallow water equation
NASA Technical Reports Server (NTRS)
Bates, J. R.; Mccormick, Stephen F.; Ruge, John; Sholl, David S.; Yavneh, Irad
1993-01-01
We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-Lagrangian time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.
Renormalization in Coulomb-gauge QCD within the Lagrangian formalism
DOE Office of Scientific and Technical Information (OSTI.GOV)
Niegawa, A.
2006-08-15
We study renormalization of Coulomb-gauge QCD within the Lagrangian, second-order, formalism. We derive a Ward identity and the Zinn-Justin equation, and, with the help of the latter, we give a proof of algebraic renormalizability of the theory. Through diagrammatic analysis, we show that, in the strict Coulomb gauge, g{sup 2}D{sup 00} is invariant under renormalization. (D{sup 00} is the time-time component of the gluon propagator.)
Extended hamiltonian formalism and Lorentz-violating lagrangians
NASA Astrophysics Data System (ADS)
Colladay, Don
2017-09-01
A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
DOE Office of Scientific and Technical Information (OSTI.GOV)
Bo, Wurigen; Shashkov, Mikhail
We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less
A Godunov-like point-centered essentially Lagrangian hydrodynamic approach
DOE Office of Scientific and Technical Information (OSTI.GOV)
Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.
We present an essentially Lagrangian hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedron meshes. The scheme reduces to a purely Lagrangian approach when the flow is linear or if the mesh size is equal to zero; as a result, we use the term essentially Lagrangian for the proposed approach. The motivation for developing a hydrodynamic method for tetrahedron meshes is because tetrahedron meshes have some advantages over other mesh topologies. Notable advantages include reduced complexity in generating conformal meshes, reduced complexity in mesh reconnection, and preserving tetrahedron cells with automatic mesh refinement. A challenge, however, is tetrahedron meshesmore » do not correctly deform with a lower order (i.e. piecewise constant) staggered-grid hydrodynamic scheme (SGH) or with a cell-centered hydrodynamic (CCH) scheme. The SGH and CCH approaches calculate the strain via the tetrahedron, which can cause artificial stiffness on large deformation problems. To resolve the stiffness problem, we adopt the point-centered hydrodynamic approach (PCH) and calculate the evolution of the flow via an integration path around the node. The PCH approach stores the conserved variables (mass, momentum, and total energy) at the node. The evolution equations for momentum and total energy are discretized using an edge-based finite element (FE) approach with linear basis functions. A multidirectional Riemann-like problem is introduced at the center of the tetrahedron to account for discontinuities in the flow such as a shock. Conservation is enforced at each tetrahedron center. The multidimensional Riemann-like problem used here is based on Lagrangian CCH work [8, 19, 37, 38, 44] and recent Lagrangian SGH work [33-35, 39, 45]. In addition, an approximate 1D Riemann problem is solved on each face of the nodal control volume to advect mass, momentum, and total energy. The 1D Riemann problem produces fluxes [18] that remove a volume error in the PCH
A Godunov-like point-centered essentially Lagrangian hydrodynamic approach
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
On Lagrangian residual currents with applications in south San Francisco Bay, California
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.
NASA Astrophysics Data System (ADS)
Mohrmann, J.; Ghate, V. P.; McCoy, I. L.; Bretherton, C. S.; Wood, R.; Minnis, P.; Palikonda, R.
2017-12-01
The Cloud System Evolution in the Trades (CSET) field campaign took place July/August 2015 to study the evolution of clouds, precipitation, and aerosols in the stratocumulus-to-cumulus (Sc-Cu) transition region of the northeast Pacific marine boundary layer (MBL). Aircraft observations sampled across a wide range of cloud and aerosol conditions. The sampling strategy, where MBL airmasses were sampled with the NSF/NCAR Gulfstream-V (HIAPER) and resampled then at their advected location two days later, resulted in a dataset of 14 paired flights suitable for Lagrangian analysis. This analysis shows that Lagrangian coherence of long-lived species (namely CO and O3) across 48 hours are high, but that of subcloud aerosol, MBL depth, and cloud properties is limited. Geostationary satellite retrievals are compared against aircraft observations; these are combined with reanalysis data and HYSPLIT trajectories to document the Lagrangian evolution of cloud fraction, cloud droplet number concentration, liquid water path, estimated inversion strength (EIS), and MBL depth, which are used to expand upon and validate the aircraft-based analysis. Many of the trajectories sampled by the aircraft show a clear Sc-Cu transition. Although satellite cloud fraction and EIS were found to be strongly spatiotemporally correlated, changes in MBL cloud fraction along trajectories did not correlate with any measure of EIS forcing.
Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids.
Aradi, Bálint; Niklasson, Anders M N; Frauenheim, Thomas
2015-07-14
A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born-Oppenheimer molecular dynamics. For systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can be applied to a broad range of problems in materials science, chemistry, and biology.
NASA Astrophysics Data System (ADS)
Yeh, Mei-Ling
We have performed a parallel decomposition of the fictitious Lagrangian method for molecular dynamics with tight-binding total energy expression into the hypercube computer. This is the first time in literature that the dynamical simulation of semiconducting systems containing more than 512 silicon atoms has become possible with the electrons treated as quantum particles. With the utilization of the Intel Paragon system, our timing analysis predicts that our code is expected to perform realistic simulations on very large systems consisting of thousands of atoms with time requirements of the order of tens of hours. Timing results and performance analysis of our parallel code are presented in terms of calculation time, communication time, and setup time. The accuracy of the fictitious Lagrangian method in molecular dynamics simulation is also investigated, especially the energy conservation of the total energy of ions. We find that the accuracy of the fictitious Lagrangian scheme in small silicon cluster and very large silicon system simulations is good for as long as the simulations proceed, even though we quench the electronic coordinates to the Born-Oppenheimer surface only in the beginning of the run. The kinetic energy of electrons does not increase as time goes on, and the energy conservation of the ionic subsystem remains very good. This means that, as far as the ionic subsystem is concerned, the electrons are on the average in the true quantum ground states. We also tie up some odds and ends regarding a few remaining questions about the fictitious Lagrangian method, such as the difference between the results obtained from the Gram-Schmidt and SHAKE method of orthonormalization, and differences between simulations where the electrons are quenched to the Born -Oppenheimer surface only once compared with periodic quenching.
Parent formulation at the Lagrangian level
NASA Astrophysics Data System (ADS)
Grigoriev, Maxim
2011-07-01
The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV-BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang-Mills theory, and gravity.
Lagrangian coherent structures are associated with fluctuations in airborne microbial populations
NASA Astrophysics Data System (ADS)
Tallapragada, P.; Ross, S. D.; Schmale, D. G.
2011-09-01
Many microorganisms are advected in the lower atmosphere from one habitat to another with scales of motion being hundreds to thousands of kilometers. The concentration of these microbes in the lower atmosphere at a single geographic location can show rapid temporal changes. We used autonomous unmanned aerial vehicles equipped with microbe-sampling devices to collect fungi in the genus Fusarium 100 m above ground level at a single sampling location in Blacksburg, Virginia, USA. Some Fusarium species are important plant and animal pathogens, others saprophytes, and still others are producers of dangerous toxins. We correlated punctuated changes in the concentration of Fusarium to the movement of atmospheric transport barriers identified as finite-time Lyapunov exponent-based Lagrangian coherent structures (LCSs). An analysis of the finite-time Lyapunov exponent field for periods surrounding 73 individual flight collections of Fusarium showed a relationship between punctuated changes in concentrations of Fusarium and the passage times of LCSs, particularly repelling LCSs. This work has implications for understanding the atmospheric transport of invasive microbial species into previously unexposed regions and may contribute to information systems for pest management and disease control in the future.
Assimilating Eulerian and Lagrangian data in traffic-flow models
NASA Astrophysics Data System (ADS)
Xia, Chao; Cochrane, Courtney; DeGuire, Joseph; Fan, Gaoyang; Holmes, Emma; McGuirl, Melissa; Murphy, Patrick; Palmer, Jenna; Carter, Paul; Slivinski, Laura; Sandstede, Björn
2017-05-01
Data assimilation of traffic flow remains a challenging problem. One difficulty is that data come from different sources ranging from stationary sensors and camera data to GPS and cell phone data from moving cars. Sensors and cameras give information about traffic density, while GPS data provide information about the positions and velocities of individual cars. Previous methods for assimilating Lagrangian data collected from individual cars relied on specific properties of the underlying computational model or its reformulation in Lagrangian coordinates. These approaches make it hard to assimilate both Eulerian density and Lagrangian positional data simultaneously. In this paper, we propose an alternative approach that allows us to assimilate both Eulerian and Lagrangian data. We show that the proposed algorithm is accurate and works well in different traffic scenarios and regardless of whether ensemble Kalman or particle filters are used. We also show that the algorithm is capable of estimating parameters and assimilating real traffic observations and synthetic observations obtained from microscopic models.
Lagrangian descriptors of driven chemical reaction manifolds.
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.
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.
Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow
NASA Astrophysics Data System (ADS)
Kajigaya, Toru; Kunikawa, Keita
2018-06-01
In this paper, we generalize several results for the Hamiltonian stability and the mean curvature flow of Lagrangian submanifolds in a Kähler-Einstein manifold to more general Kähler manifolds including a Fano manifold equipped with a Kähler form ω ∈ 2 πc1(M) by using the method proposed by Behrndt (2011). Namely, we first consider a weighted measure on a Lagrangian submanifold L in a Kähler manifold M and investigate the variational problem of L for the weighted volume functional. We call a stationary point of the weighted volume functional f-minimal, and define the notion of Hamiltonian f-stability as a local minimizer under Hamiltonian deformations. We show such examples naturally appear in a toric Fano manifold. Moreover, we consider the generalized Lagrangian mean curvature flow in a Fano manifold which is introduced by Behrndt and Smoczyk-Wang. We generalize the result of H. Li, and show that if the initial Lagrangian submanifold is a small Hamiltonian deformation of an f-minimal and Hamiltonian f-stable Lagrangian submanifold, then the generalized MCF converges exponentially fast to an f-minimal Lagrangian submanifold.
A macroscopic plasma Lagrangian and its application to wave interactions and resonances
NASA Technical Reports Server (NTRS)
Peng, Y. K. M.
1974-01-01
The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.
Orbital Maneuvers for Spacecrafts Travelling to/from the Lagrangian Points
NASA Astrophysics Data System (ADS)
Bertachini, A.
) Guess a final regularized time f and integrate the regularized equations of motion from 0 = 0 until f; iii) Check the final position rf obtained from the numerical integration with the prescribed final position and the final real time with the specified time of flight. If there is an agreement (difference less than a specified error allowed) the solution is found and the process can stop here. If there is no agreement, an increment in the initial guessed velocity Vi and in the guessed final regularized time is made and the process goes back to step i). The method used to find the increment in the guessed variables is the standard gradient method, as described in Press et. al., 1989. The routines available in this reference are also used in this research with minor modifications. After that this algorithm is implemented, the Lambert's three-body problem between the Earth and the Lagrangian points is solved for several values of the time of flight. Since the regularized system is used to solve this problem, there is no need to specify the final position of M3 as lying in an primary's parking orbit (to avoid the singularity). Then, to make a comparison with previous papers (Broucke, 1979 and Prado, 1996) the centre of the primary is used as the final position for M3. The results are organized in plots of the energy and the initial flight path angle (the control to be used) in the rotating frame against the time of flight. The definition of the angle is such that the zero is in the "x" axis, (pointing to the positive direction) and it increases in the counter-clock-wise sense. This problem, as well as the Lambert's original version, has two solutions for a given transfer time: one in the counter-clock-wise direction and one in the clock-wise direction in the inertial frame. In this paper, emphasis is given in finding the families with the smallest possible energy (and velocity), although many other families do exist. Broucke, R., (1979) Travelling Between the Lagrange
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.
Microscopic Lagrangian description of warm plasmas. IV - Macroscopic approximation
NASA Technical Reports Server (NTRS)
Kim, H.; Crawford, F. W.
1983-01-01
The averaged-Lagrangian method is applied to linear wave propagation and nonlinear three-wave interaction in a warm magnetoplasma, in the macroscopic approximation. The microscopic Lagrangian treated by Kim and Crawford (1977) and by Galloway and Crawford (1977) is first expanded to third order in perturbation. Velocity integration is then carried out, before applying Hamilton's principle to obtain a general description of wave propagation and coupling. The results are specialized to the case of interaction between two electron plasma waves and an Alfven wave. The method is shown to be more powerful than the alternative possibility of working from the beginning with a macroscopic Lagrangian density.
Extended Lagrangian formulation of charge-constrained tight-binding molecular dynamics.
Cawkwell, M J; Coe, J D; Yadav, S K; Liu, X-Y; Niklasson, A M N
2015-06-09
The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [Niklasson, Phys. Rev. Lett., 2008, 100, 123004] has been applied to a tight-binding model under the constraint of local charge neutrality to yield microcanonical trajectories with both precise, long-term energy conservation and a reduced number of self-consistent field optimizations at each time step. The extended Lagrangian molecular dynamics formalism restores time reversal symmetry in the propagation of the electronic degrees of freedom, and it enables the efficient and accurate self-consistent optimization of the chemical potential and atomwise potential energy shifts in the on-site elements of the tight-binding Hamiltonian that are required when enforcing local charge neutrality. These capabilities are illustrated with microcanonical molecular dynamics simulations of a small metallic cluster using an sd-valent tight-binding model for titanium. The effects of weak dissipation on the propagation of the auxiliary degrees of freedom for the chemical potential and on-site Hamiltonian matrix elements that is used to counteract the accumulation of numerical noise during trajectories was also investigated.
Functional integral for non-Lagrangian systems
NASA Astrophysics Data System (ADS)
Kochan, Denis
2010-02-01
A functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The approach, which we call “stringy quantization,” is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force -κq˙A. Results for A=1 are compared with those obtained in the approaches by Caldirola-Kanai, Bateman, and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.
Quantization of Non-Lagrangian Systems
NASA Astrophysics Data System (ADS)
Kochan, Denis
A novel method for quantization of non-Lagrangian (open) systems is proposed. It is argued that the essential object, which provides both classical and quantum evolution, is a certain canonical two-form defined in extended velocity space. In this setting classical dynamics is recovered from the stringy-type variational principle, which employs umbilical surfaces instead of histories of the system. Quantization is then accomplished in accordance with the introduced variational principle. The path integral for the transition probability amplitude (propagator) is rearranged to a surface functional integral. In the standard case of closed (Lagrangian) systems the presented method reduces to the standard Feynman's approach. The inverse problem of the calculus of variation, the problem of quantization ambiguity and the quantum mechanics in the presence of friction are analyzed in detail.
The S-Lagrangian and a theory of homeostasis in living systems
NASA Astrophysics Data System (ADS)
Sandler, U.; Tsitolovsky, L.
2017-04-01
A major paradox of living things is their ability to actively counteract degradation in a continuously changing environment or being injured through homeostatic protection. In this study, we propose a dynamic theory of homeostasis based on a generalized Lagrangian approach (S-Lagrangian), which can be equally applied to physical and nonphysical systems. Following discoverer of homeostasis Cannon (1935), we assume that homeostasis results from tendency of the organisms to decrease of the stress and avoid of death. We show that the universality of homeostasis is a consequence of analytical properties of the S-Lagrangian, while peculiarities of the biochemical and physiological mechanisms of homeostasis determine phenomenological parameters of the S-Lagrangian. Additionally, we reveal that plausible assumptions about S-Lagrangian features lead to good agreement between theoretical descriptions and observed homeostatic behavior. Here, we have focused on homeostasis of living systems, however, the proposed theory is also capable of being extended to social systems.
Forms of null Lagrangians in field theories of continuum mechanics
NASA Astrophysics Data System (ADS)
Kovalev, V. A.; Radaev, Yu. N.
2012-02-01
The divergence representation of a null Lagrangian that is regular in a star-shaped domain is used to obtain its general expression containing field gradients of order ≤ 1 in the case of spacetime of arbitrary dimension. It is shown that for a static three-component field in the three-dimensional space, a null Lagrangian can contain up to 15 independent elements in total. The general form of a null Lagrangian in the four-dimensional Minkowski spacetime is obtained (the number of physical field variables is assumed arbitrary). A complete theory of the null Lagrangian for the n-dimensional spacetime manifold (including the four-dimensional Minkowski spacetime as a special case) is given. Null Lagrangians are then used as a basis for solving an important variational problem of an integrating factor. This problem involves searching for factors that depend on the spacetime variables, field variables, and their gradients and, for a given system of partial differential equations, ensure the equality between the scalar product of a vector multiplier by the system vector and some divergence expression for arbitrary field variables and, hence, allow one to formulate a divergence conservation law on solutions to the system.
Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids
DOE Office of Scientific and Technical Information (OSTI.GOV)
Aradi, Bálint; Niklasson, Anders M. N.; Frauenheim, Thomas
A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born–Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can also be applied to a broad range of problems in materialsmore » science, chemistry, and biology.« less
Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids
Aradi, Bálint; Niklasson, Anders M. N.; Frauenheim, Thomas
2015-06-26
A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born–Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can also be applied to a broad range of problems in materialsmore » science, chemistry, and biology.« less
A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
NASA Astrophysics Data System (ADS)
Li, Wenliang
2018-04-01
We propose a framework for Lorentz-invariant Lagrangian field theories where Ostrogradsky's scalar ghosts could be absent. A key ingredient is the generalized Kronecker delta. The general Lagrangians are reformulated in the language of differential forms. The absence of higher order equations of motion for the scalar modes stems from the basic fact that every exact form is closed. The well-established Lagrangian theories for spin-0, spin-1, p-form, spin-2 fields have natural formulations in this framework. We also propose novel building blocks for Lagrangian field theories. Some of them are novel nonlinear derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar ghosts are absent in these fully nonlinear theories.
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.
Altimetric lagrangian advection to reconstruct Pacific Ocean fine scale surface tracer fields
NASA Astrophysics Data System (ADS)
Rogé, Marine; Morrow, Rosemary; Dencausse, Guillaume
2015-04-01
In past studies, lagrangian stirring of surface tracer fields by altimetric surface geostrophic currents has been performed in different mid to high-latitude regions, showing good results in reconstructing finer-scale tracer patterns. Here we apply the technique to three different regions in the eastern and western tropical Pacific, and in the subtropical southwest Pacific. Initial conditions are derived from weekly gridded temperature and salinity fields, based on hydrographic data and Argo. Validation of the improved fine-scale surface tracer fields is performed using satellite AMSRE SST data, and high-resolution ship thermosalinograph data. We test two kinds of lagrangian advection. The standard one-way advection is shown to introduce an increased tracer bias as the advection time increases. Indeed, since we only use passive stirring, a bias is introduced from the missing physics, such as air-sea fluxes or mixing. A second "backward-forward" advection technique is shown to reduce the seasonal bias, but more data is lost around coasts and islands, a strong handicap in the tropical Pacific with many small islands. In the subtropical Pacific Ocean, the mesoscale temperature and salinity fronts are well represented by the one-way advection over a 10-day advection time, including westward propagating features not apparent in the initial fields. In the tropics, the results are less clear. The validation is hampered by the complex vertical stratification, and the technique is limited by the lack of accurate surface currents for the stirring - the gridded altimetric fields poorly represent the meridional currents, and are not detecting the fast tropical instability waves, nor the wind-driven circulation. We suggest that the passive lateral stirring technique is efficient in regions with moderate the high mesoscale energy and correlated mesoscale surface temperature and surface height. In other regions, more complex dynamical processes may need to be included.
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 condensation microphysics with Twomey CCN activation
NASA Astrophysics Data System (ADS)
Grabowski, Wojciech W.; Dziekan, Piotr; Pawlowska, Hanna
2018-01-01
We report the development of a novel Lagrangian microphysics methodology for simulations of warm ice-free clouds. The approach applies the traditional Eulerian method for the momentum and continuous thermodynamic fields such as the temperature and water vapor mixing ratio, and uses Lagrangian super-droplets
to represent condensed phase such as cloud droplets and drizzle or rain drops. In other applications of the Lagrangian warm-rain microphysics, the super-droplets outside clouds represent unactivated cloud condensation nuclei (CCN) that become activated upon entering a cloud and can further grow through diffusional and collisional processes. The original methodology allows for the detailed study of not only effects of CCN on cloud microphysics and dynamics, but also CCN processing by a cloud. However, when cloud processing is not of interest, a simpler and computationally more efficient approach can be used with super-droplets forming only when CCN is activated and no super-droplet existing outside a cloud. This is possible by applying the Twomey activation scheme where the local supersaturation dictates the concentration of cloud droplets that need to be present inside a cloudy volume, as typically used in Eulerian bin microphysics schemes. Since a cloud volume is a small fraction of the computational domain volume, the Twomey super-droplets provide significant computational advantage when compared to the original super-droplet methodology. Additional advantage comes from significantly longer time steps that can be used when modeling of CCN deliquescence is avoided. Moreover, other formulation of the droplet activation can be applied in case of low vertical resolution of the host model, for instance, linking the concentration of activated cloud droplets to the local updraft speed. This paper discusses the development and testing of the Twomey super-droplet methodology, focusing on the activation and diffusional growth. Details of the activation
Lagrangian methods in nonlinear plasma wave interaction
NASA Technical Reports Server (NTRS)
Crawford, F. W.
1980-01-01
Analysis of nonlinear plasma wave interactions is usually very complicated, and simplifying mathematical approaches are highly desirable. The application of averaged-Lagrangian methods offers a considerable reduction in effort, with improved insight into synchronism and conservation (Manley-Rowe) relations. This chapter indicates how suitable Lagrangian densities have been defined, expanded, and manipulated to describe nonlinear wave-wave and wave-particle interactions in the microscopic, macroscopic and cold plasma models. Recently, further simplifications have been introduced by the use of techniques derived from Lie algebra. These and likely future developments are reviewed briefly.
Using Lagrangian Coherent Structures to understand coastal water quality
NASA Astrophysics Data System (ADS)
Fiorentino, L. A.; Olascoaga, M. J.; Reniers, A.; Feng, Z.; Beron-Vera, F. J.; MacMahan, J. H.
2012-09-01
The accumulation of pollutants near the shoreline can result in low quality coastal water with negative effects on human health. To understand the role of mixing by tidal flows in coastal water quality we study the nearshore Lagrangian circulation. Specifically, we reveal Lagrangian Coherent Structures (LCSs), i.e., distinguished material curves which shape global mixing patterns and thus act as skeletons of the Lagrangian circulation. This is done using the recently developed geodesic theory of transport barriers. Particular focus is placed on Hobie Beach, a recreational subtropical marine beach located in Virginia Key, Miami, Florida. According to studies of water quality, Hobie Beach is characterized by high microbial levels. Possible sources of pollution in Hobie Beach include human bather shedding, dog fecal matter, runoff, and sand efflux at high tides. Consistent with the patterns formed by satellite-tracked drifter trajectories, the LCSs extracted from simulated currents reveal a Lagrangian circulation favoring the retention near the shoreline of pollutants released along the shoreline, which can help explain the low quality water registered at Hobie Beach.
Integration over families of Lagrangian submanifolds in BV formalism
NASA Astrophysics Data System (ADS)
Mikhailov, Andrei
2018-03-01
Gauge fixing is interpreted in BV formalism as a choice of Lagrangian submanifold in an odd symplectic manifold (the BV phase space). A natural construction defines an integration procedure on families of Lagrangian submanifolds. In string perturbation theory, the moduli space integrals of higher genus amplitudes can be interpreted in this way. We discuss the role of gauge symmetries in this construction. We derive the conditions which should be imposed on gauge symmetries for the consistency of our integration procedure. We explain how these conditions behave under the deformations of the worldsheet theory. In particular, we show that integrated vertex operator is actually an inhomogeneous differential form on the space of Lagrangian submanifolds.
An updated Lagrangian particle hydrodynamics (ULPH) for Newtonian fluids
NASA Astrophysics Data System (ADS)
Tu, Qingsong; Li, Shaofan
2017-11-01
In this work, we have developed an updated Lagrangian particle hydrodynamics (ULPH) for Newtonian fluid. Unlike the smoothed particle hydrodynamics, the non-local particle hydrodynamics formulation proposed here is consistent and convergence. Unlike the state-based peridynamics, the discrete particle dynamics proposed here has no internal material bond between particles, and it is not formulated with respect to initial or a fixed referential configuration. In specific, we have shown that (1) the non-local update Lagrangian particle hydrodynamics formulation converges to the conventional local fluid mechanics formulation; (2) the non-local updated Lagrangian particle hydrodynamics can capture arbitrary flow discontinuities without any changes in the formulation, and (3) the proposed non-local particle hydrodynamics is computationally efficient and robust.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
A Kernel-based Lagrangian method for imperfectly-mixed chemical reactions
NASA Astrophysics Data System (ADS)
Schmidt, Michael J.; Pankavich, Stephen; Benson, David A.
2017-05-01
Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics-particularly for imperfectly-mixed systems. The number of particles is tied to the statistics of the initial concentration fields of the system at hand. Systems with shorter-range correlation and/or smaller concentration variance require more particles, potentially limiting the computational feasibility of the method. For the well-known problem of bimolecular reaction, we show that using kernel-based, rather than Dirac delta, particles can significantly reduce the required number of particles. We derive the fixed width of a Gaussian kernel for a given reduced number of particles that analytically eliminates the error between kernel and Dirac solutions at any specified time. We also show how to solve for the fixed kernel size by minimizing the squared differences between solutions over any given time interval. Numerical results show that the width of the kernel should be kept below about 12% of the domain size, and that the analytic equations used to derive kernel width suffer significantly from the neglect of higher-order moments. The simulations with a kernel width given by least squares minimization perform better than those made to match at one specific time. A heuristic time-variable kernel size, based on the previous results, performs on par with the least squares fixed kernel size.
Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R
2013-09-01
We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.
ATLAS - A new Lagrangian transport and mixing model with detailed stratospheric chemistry
NASA Astrophysics Data System (ADS)
Wohltmann, I.; Rex, M.; Lehmann, R.
2009-04-01
We present a new global Chemical Transport Model (CTM) with full stratospheric chemistry and Lagrangian transport and mixing called ATLAS. Lagrangian models have some crucial advantages over Eulerian grid-box based models, like no numerical diffusion, no limitation of the time step of the model by the CFL criterion, conservation of mixing ratios by design and easy parallelization of code. The transport module is based on a trajectory code developed at the Alfred Wegener Institute. The horizontal and vertical resolution, the vertical coordinate system (pressure, potential temperature, hybrid coordinate) and the time step of the model are flexible, so that the model can be used both for process studies and long-time runs over several decades. Mixing of the Lagrangian air parcels is parameterized based on the local shear and strain of the flow with a method similar to that used in the CLaMS model, but with some modifications like a triangulation that introduces no vertical layers. The stratospheric chemistry module was developed at the Institute and includes 49 species and 170 reactions and a detailed treatment of heterogenous chemistry on polar stratospheric clouds. We present an overview over the model architecture, the transport and mixing concept and some validation results. Comparison of model results with tracer data from flights of the ER2 aircraft in the stratospheric polar vortex in 1999/2000 which are able to resolve fine tracer filaments show that excellent agreement with observed tracer structures can be achieved with a suitable mixing parameterization.
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
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.
Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows
NASA Astrophysics Data System (ADS)
Gay-Balmaz, François; Holm, Darryl D.
2018-01-01
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.
Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows
NASA Astrophysics Data System (ADS)
Gay-Balmaz, François; Holm, Darryl D.
2018-06-01
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.
Lagrangian solution of supersonic real gas flows
NASA Technical Reports Server (NTRS)
Loh, Ching-Yuen; Liou, Meng-Sing
1993-01-01
The present extention of a Lagrangian approach of the Riemann solution procedure, which was originally proposed for perfect gases, to real gases, is nontrivial and requires the development of an exact real-gas Riemann solver for the Lagrangian form of the conservation laws. Calculations including complex wave interactions of various types were conducted to test the accuracy and robustness of the approach. Attention is given to the case of 2D oblique waves' capture, where a slip line is clearly in evidence; the real gas effect is demonstrated in the case of a generic engine nozzle.
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.
NASA Astrophysics Data System (ADS)
Le Borgne, T.; Kang, P. K.; Guihéneuf, N.; Shakas, A.; Bour, O.; Linde, N.; Dentz, M.
2015-12-01
Non-Fickian transport phenomena are observed in a wide range of scales across hydrological systems. They are generally manifested by a broad range of transit time distributions, as measured for instance in tracer breakthrough curves. However, similar transit time distributions may be caused by different origins, including broad velocity distributions, flow channeling or diffusive mass transfer [1,2]. The identification of these processes is critical for defining relevant transport models. How can we distinguish the different origins of non-Fickian transport in the field? In this presentation, we will review recent experimental developments to decipher the different causes of anomalous transport, based on tracer tests performed at different scales in cross borehole and push pull conditions, and time lapse hydrogeophysical imaging of tracer motion [3,4]. References:[1] de Anna-, P., T. Le Borgne, M. Dentz, A. M. Tartakovsky, D. Bolster, P. Davy (2013) Flow Intermittency, Dispersion and Correlated Continuous Time Random Walks in Porous Media, Phys. Rev. Lett., 110, 184502 [2] Le Borgne T., Dentz M., and Carrera J. (2008) Lagrangian Statistical Model for Transport in Highly Heterogeneous Velocity Fields. Phys. Rev. Lett. 101, 090601 [3] Kang, P. K., T. Le Borgne, M. Dentz, O. Bour, and R. Juanes (2015), Impact of velocity correlation and distribution on transport in fractured media : Field evidence and theoretical model, Water Resour. Res., 51, 940-959 [4] Dorn C., Linde N., Le Borgne T., O. Bour and L. Baron (2011) Single-hole GPR reflection imaging of solute transport in a granitic aquifer Geophys. Res. Lett. Vol.38, L08401
Lagrangian Approach to Study Catalytic Fluidized Bed Reactors
NASA Astrophysics Data System (ADS)
Madi, Hossein; Hossein Madi Team; Marcelo Kaufman Rechulski Collaboration; Christian Ludwig Collaboration; Tilman Schildhauer Collaboration
2013-03-01
Lagrangian approach of fluidized bed reactors is a method, which simulates the movement of catalyst particles (caused by the fluidization) by changing the gas composition around them. Application of such an investigation is in the analysis of the state of catalysts and surface reactions under quasi-operando conditions. The hydrodynamics of catalyst particles within a fluidized bed reactor was studied to improve a Lagrangian approach. A fluidized bed methanation employed in the production of Synthetic Natural Gas from wood was chosen as the case study. The Lagrangian perspective was modified and improved to include different particle circulation patterns, which were investigated through this study. Experiments were designed to evaluate the concepts of the model. The results indicate that the setup is able to perform the designed experiments and a good agreement between the simulation and the experimental results were observed. It has been shown that fluidized bed reactors, as opposed to fixed beds, can be used to avoid the deactivation of the methanation catalyst due to carbon deposits. Carbon deposition on the catalysts tested with the Lagrangian approach was investigated by temperature programmed oxidation (TPO) analysis of ex-situ catalyst samples. This investigation was done to identify the effects of particles velocity and their circulation patterns on the amount and type of deposited carbon on the catalyst surface. Ecole Polytechnique Federale de Lausanne(EPFL), Paul Scherrer Institute (PSI)
The Lagrangian-Hamiltonian formalism for higher order field theories
NASA Astrophysics Data System (ADS)
Vitagliano, Luca
2010-06-01
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.
Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems
NASA Astrophysics Data System (ADS)
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2011-09-01
The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.
Near-Surface Monsoonal Circulation of the Vietnam East Sea from Lagrangian Drifters
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
Unsteady force estimation using a Lagrangian drift-volume approach
NASA Astrophysics Data System (ADS)
McPhaden, Cameron J.; Rival, David E.
2018-04-01
A novel Lagrangian force estimation technique for unsteady fluid flows has been developed, using the concept of a Darwinian drift volume to measure unsteady forces on accelerating bodies. The construct of added mass in viscous flows, calculated from a series of drift volumes, is used to calculate the reaction force on an accelerating circular flat plate, containing highly-separated, vortical flow. The net displacement of fluid contained within the drift volumes is, through Darwin's drift-volume added-mass proposition, equal to the added mass of the plate and provides the reaction force of the fluid on the body. The resultant unsteady force estimates from the proposed technique are shown to align with the measured drag force associated with a rapid acceleration. The critical aspects of understanding unsteady flows, relating to peak and time-resolved forces, often lie within the acceleration phase of the motions, which are well-captured by the drift-volume approach. Therefore, this Lagrangian added-mass estimation technique opens the door to fluid-dynamic analyses in areas that, until now, were inaccessible by conventional means.
Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories
DOE Office of Scientific and Technical Information (OSTI.GOV)
Tronko, Natalia; Brizard, Alain J.
A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint onmore » the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.« less
A new Lagrangian method for real gases at supersonic speed
NASA Technical Reports Server (NTRS)
Loh, C. Y.; Liou, Meng-Sing
1992-01-01
With the renewed interest in high speed flights, the real gas effect is of theoretical as well as practical importance. In the past decade, upwind splittings or Godunov-type Riemann solutions have received tremendous attention and as a result significant progress has been made both in the ideal and non-ideal gas. In this paper, we propose a new approach that is formulated using the Lagrangian description, for the calculation of supersonic/hypersonic real gas inviscid flows. This new formulation avoids the grid generation step which is automatically obtained as the solution procedure marches in the 'time-like' direction. As a result, no remapping is required and the accuracy is faithfully maintained in the Lagrangian level. In this paper, we give numerical results for a variety of real gas problems consisting of essential elements in high speed flows, such as shock waves, expansion waves, slip surfaces and their interactions. Finally, calculations for flows in a generic inlet and nozzle are presented.
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean.
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.
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 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.
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.
Eulerian and Lagrangian approaches to multidimensional condensation and collection
NASA Astrophysics Data System (ADS)
Li, Xiang-Yu; Brandenburg, A.; Haugen, N. E. L.; Svensson, G.
2017-06-01
Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow or just gravitational acceleration without gas flow. Good agreement between the different schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. The Lagrangian superparticle schemes are found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results. For the Eulerian scheme, gravitational collection is rather sensitive to the mass bin resolution, but not so in the case with turbulence.
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.
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
Stability analysis of Eulerian-Lagrangian methods for the one-dimensional shallow-water equations
Casulli, V.; Cheng, R.T.
1990-01-01
In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined Eulerian-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit Eulerian-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the Eulerian-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses. ?? 1990.
Users manual for a one-dimensional Lagrangian transport model
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)
A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.
1989-01-01
A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.
Using hyperbolic Lagrangian coherent structures to investigate vortices in bioinspired fluid flows
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
Mixing model with multi-particle interactions for Lagrangian simulations of turbulent mixing
NASA Astrophysics Data System (ADS)
Watanabe, T.; Nagata, K.
2016-08-01
We report on the numerical study of the mixing volume model (MVM) for molecular diffusion in Lagrangian simulations of turbulent mixing problems. The MVM is based on the multi-particle interaction in a finite volume (mixing volume). A priori test of the MVM, based on the direct numerical simulations of planar jets, is conducted in the turbulent region and the interfacial layer between the turbulent and non-turbulent fluids. The results show that the MVM predicts well the mean effects of the molecular diffusion under various numerical and flow parameters. The number of the mixing particles should be large for predicting a value of the molecular diffusion term positively correlated to the exact value. The size of the mixing volume relative to the Kolmogorov scale η is important in the performance of the MVM. The scalar transfer across the turbulent/non-turbulent interface is well captured by the MVM especially with the small mixing volume. Furthermore, the MVM with multiple mixing particles is tested in the hybrid implicit large-eddy-simulation/Lagrangian-particle-simulation (LES-LPS) of the planar jet with the characteristic length of the mixing volume of O(100η). Despite the large mixing volume, the MVM works well and decays the scalar variance in a rate close to the reference LES. The statistics in the LPS are very robust to the number of the particles used in the simulations and the computational grid size of the LES. Both in the turbulent core region and the intermittent region, the LPS predicts a scalar field well correlated to the LES.
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.
Evaluation of wastewater contaminant transport in surface waters using verified Lagrangian sampling.
Antweiler, Ronald C; Writer, Jeffrey H; Murphy, Sheila F
2014-02-01
Contaminants released from wastewater treatment plants can persist in surface waters for substantial distances. Much research has gone into evaluating the fate and transport of these contaminants, but this work has often assumed constant flow from wastewater treatment plants. However, effluent discharge commonly varies widely over a 24-hour period, and this variation controls contaminant loading and can profoundly influence interpretations of environmental data. We show that methodologies relying on the normalization of downstream data to conservative elements can give spurious results, and should not be used unless it can be verified that the same parcel of water was sampled. Lagrangian sampling, which in theory samples the same water parcel as it moves downstream (the Lagrangian parcel), links hydrologic and chemical transformation processes so that the in-stream fate of wastewater contaminants can be quantitatively evaluated. However, precise Lagrangian sampling is difficult, and small deviations - such as missing the Lagrangian parcel by less than 1h - can cause large differences in measured concentrations of all dissolved compounds at downstream sites, leading to erroneous conclusions regarding in-stream processes controlling the fate and transport of wastewater contaminants. Therefore, we have developed a method termed "verified Lagrangian" sampling, which can be used to determine if the Lagrangian parcel was actually sampled, and if it was not, a means for correcting the data to reflect the concentrations which would have been obtained had the Lagrangian parcel been sampled. To apply the method, it is necessary to have concentration data for a number of conservative constituents from the upstream, effluent, and downstream sites, along with upstream and effluent concentrations that are constant over the short-term (typically 2-4h). These corrections can subsequently be applied to all data, including non-conservative constituents. Finally, we show how data
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).
A Lagrangian View of Stratospheric Trace Gas Distributions
NASA Technical Reports Server (NTRS)
Schoeberl, M. R.; Sparling, L.; Dessler, A.; Jackman, C. H.; Fleming, E. L.
1998-01-01
As a result of photochemistry, some relationship between the stratospheric age-of-air and the amount of tracer contained within an air sample is expected. The existence of such a relationship allows inferences about transport history to be made from observations of chemical tracers. This paper lays down the conceptual foundations for the relationship between age and tracer amount, developed within a Lagrangian framework. In general, the photochemical loss depends not only on the age of the parcel but also on its path. We show that under the "average path approximation" that the path variations are less important than parcel age. The average path approximation then allows us to develop a formal relationship between the age spectrum and the tracer spectrum. Using the relation between the tracer and age spectra, tracer-tracer correlations can be interpreted as resulting from mixing which connects parts of the single path photochemistry curve, which is formed purely from the action of photochemistry on an irreducible parcel. This geometric interpretation of mixing gives rise to constraints on trace gas correlations, and explains why some observations are do not fall on rapid mixing curves. This effect is seen in the ATMOS observations.
Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.
Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun
2013-01-01
An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.
Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations
Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun
2013-01-01
An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids. PMID:24235888
The effective chiral Lagrangian from the theta term
DOE Office of Scientific and Technical Information (OSTI.GOV)
Mereghetti, E., E-mail: emanuele@physics.arizona.ed; Hockings, W.H., E-mail: whockings@bmc.ed; Kolck, U. van, E-mail: vankolck@physics.arizona.ed
2010-11-15
We construct the effective chiral Lagrangian involving hadronic and electromagnetic interactions originating from the QCD {theta}-bar term. We impose vacuum alignment at both quark and hadronic levels, including field redefinitions to eliminate pion tadpoles. We show that leading time-reversal-violating (TV) hadronic interactions are related to isospin-violating interactions that can in principle be determined from charge-symmetry-breaking experiments. We discuss the complications that arise from TV electromagnetic interactions. Some implications of the expected sizes of various pion-nucleon TV interactions are presented, and the pion-nucleon form factor is used as an example.
Programmers manual for a one-dimensional Lagrangian transport model
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)
NASA Astrophysics Data System (ADS)
Kreymer, E. L.
2018-06-01
The model of Euclidean space with imaginary time used in sub-hadron physics uses only part of it since this part is isomorphic to Minkowski space and has the velocity limit 0 ≤ ||v Ei|| ≤ 1. The model of four-dimensional Euclidean space with real time (E space), in which 0 ≤ ||v E|| ≤ ∞ is investigated. The vectors of this space have E-invariants, equal or analogous to the invariants of Minkowski space. All relations between physical quantities in E-space, after they are mapped into Minkowski space, satisfy the principles of SRT and are Lorentz-invariant, and the velocity of light corresponds to infinite velocity. Results obtained in the model are different from the physical laws in Minkowski space. Thus, from the model of the Lagrangian mechanics of quarks in a centrally symmetric attractive potential it follows that the energy-mass of a quark decreases with increase of the velocity and is equal to zero for v = ∞. This made it possible to establish the conditions of emission and absorption of gluons by quarks. The effect of emission of gluons by high-energy quarks was discovered experimentally significantly earlier. The model describes for the first time the dynamic coupling of the masses of constituent and current quarks and reveals new possibilities in the study of intrahardon space. The classical trajectory of the oscillation of quarks in protons is described.
Enhancements to the Branched Lagrangian Transport Modeling System
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.
NASA Astrophysics Data System (ADS)
Gotovac, Hrvoje; Srzic, Veljko
2014-05-01
Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large
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.
Identifying Lagrangian fronts with favourable fishery conditions
NASA Astrophysics Data System (ADS)
Prants, S. V.; Budyansky, M. V.; Uleysky, M. Yu.
2014-08-01
Lagrangian fronts (LFs) in the ocean are defined as boundaries between surface waters with strongly different Lagrangian properties. They can be accurately detected in a given velocity field by computing synoptic maps for displacements of synthetic tracers and other Lagrangian indicators. We use Pacific saury catch and location data for a number of commercial fishery seasons in the region of the northwest Pacific with one of the richest fishery in the world. It is shown statistically that the saury fishing grounds with maximal catches are not randomly distributed over the region but located mainly along the sharp LFs where productive cold waters of the Oyashio Current, warmer waters of the southern branch of the Soya Current, and waters of warm-core Kuroshio rings converge. Computation of those fronts in altimetric geostrophic velocity fields both in the years with the First and Second Oyashio Intrusions shows that in spite of different oceanographic conditions LF locations may serve as good indicators of potential fishing grounds. Possible biophysical reasons for saury aggregation near sharp LFs are discussed. We propose a mechanism for effective export of nutrient rich waters based on stretching of material lines in the vicinity of hyperbolic objects in the ocean. The developed method, based on identifying LFs in any velocity fields, is quite general and may be applied to find potential fishing grounds for the other pelagic fish.
NASA Astrophysics Data System (ADS)
Qin, Xuerong; van Sebille, Erik; Sen Gupta, Alexander
2014-04-01
Lagrangian particle tracking within ocean models is an important tool for the examination of ocean circulation, ventilation timescales and connectivity and is increasingly being used to understand ocean biogeochemistry. Lagrangian trajectories are obtained by advecting particles within velocity fields derived from hydrodynamic ocean models. For studies of ocean flows on scales ranging from mesoscale up to basin scales, the temporal resolution of the velocity fields should ideally not be more than a few days to capture the high frequency variability that is inherent in mesoscale features. However, in reality, the model output is often archived at much lower temporal resolutions. Here, we quantify the differences in the Lagrangian particle trajectories embedded in velocity fields of varying temporal resolution. Particles are advected from 3-day to 30-day averaged fields in a high-resolution global ocean circulation model. We also investigate whether adding lateral diffusion to the particle movement can compensate for the reduced temporal resolution. Trajectory errors reveal the expected degradation of accuracy in the trajectory positions when decreasing the temporal resolution of the velocity field. Divergence timescales associated with averaging velocity fields up to 30 days are faster than the intrinsic dispersion of the velocity fields but slower than the dispersion caused by the interannual variability of the velocity fields. In experiments focusing on the connectivity along major currents, including western boundary currents, the volume transport carried between two strategically placed sections tends to increase with increased temporal averaging. Simultaneously, the average travel times tend to decrease. Based on these two bulk measured diagnostics, Lagrangian experiments that use temporal averaging of up to nine days show no significant degradation in the flow characteristics for a set of six currents investigated in more detail. The addition of random
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.
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.
An airborne perfluorocarbon tracer system and its first application for a Lagrangian experiment
NASA Astrophysics Data System (ADS)
Ren, Y.; Baumann, R.; Schlager, H.
2015-01-01
A perfluorocarbon tracer system (PERTRAS), specifically designed for Lagrangian aircraft experiments, has been developed by the Deutsches Zentrum für Luft- und Raumfahrt (German Aerospace Center, DLR). It consists of three main parts: a tracer release unit (RU), an adsorption tube sampler (ATS), and a tracer analytical system. The RU was designed for airborne tracer release experiments; meanwhile, it can be used on various platforms for different experimental purposes (here research vessel). PERTRAS was for the first time applied in the field campaign Stratospheric ozone: Halogen Impacts in a Varying Atmosphere (SHIVA) in November 2011. An amount of 8.8 kg perfluoromethylcyclopentane (PMCP) was released aboard the research vessel Sonne (RV Sonne) near the operational site of this campaign, Miri, Malaysia, on 21 November. The tracer samples collected using the ATS onboard the DLR research aircraft Falcon were analyzed in the laboratory using a thermal desorber-gas chromatography-mass spectrometry (TD-GC-MS) system. Guided by forecasts calculated with the Lagrangian model Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT), 64 tracer samples were collected onboard the Falcon approximately 5 and 25 h after the release, mostly with a time resolution of 1 min. Enhanced PMCP concentrations relative to ambient PMCP background values (mean: 6.62 fmol mol-1) were detected during three intersects of the fresh tracer plume (age 5 h), with a maximum value of 301.33 fmol mol-1. This indicates that the fresh tracer plume was successfully intercepted at the forecast position. During the second flight, 25 h after the release, the center of tracer plume was not detected by the sampling system due to a faster advection of the plume than forecast. The newly developed PERTRAS system has been successfully deployed for the first time. The instrumental setup and comparisons between the measurements and HYSPLIT simulations are presented in this study.
An airborne perfluorocarbon tracer system and its first application for a Lagrangian experiment
NASA Astrophysics Data System (ADS)
Ren, Y.; Baumann, R.; Schlager, H.
2014-07-01
A perfluorocarbon tracer system (PERTRAS), specifically designed for Lagrangian aircraft experiments, has been developed by the Deutsches Zentrum für Luft- und Raumfahrt (German Aerospace Center, DLR). It consists of three main parts: a tracer release unit (RU), an adsorption tube sampler (ATS) and a tracer analytical system. The RU was designed for airborne tracer release experiments; meanwhile, it can be used on various platforms for different experimental purpose (here research vessel). PERTRAS was for the first time applied in the field campaign Stratospheric ozone: halogen Impacts in a Varying Atmosphere (SHIVA) in November 2011. An amount of 8.8 kg perfluoromethylcyclopentane (PMCP) was released aboard the research vessel Sonne (RV Sonne) near the operational site of this campaign, Miri, Malaysia, on 21 November. The tracer samples collected using the ATS on board the DLR research aircraft Falcon were analyzed in the laboratory using a thermal desorber/gas chromatography/mass spectrometry (TD/GC/MS) system. Guided by forecasts calculated with the Lagrangian model, Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT), 64 tracer samples were collected onboard the Falcon approximately 5 and 25 h after the release, respectively, mostly with a time resolution of 1 min. Enhanced PMCP concentrations relative to ambient PMCP background values (mean: 6.62 fmol mol-1) were detected during three intersects of the fresh tracer plume (age 5 h), with a maximum value of 301.33 fmol mol-1. This indicates that the fresh tracer plume was successfully intercepted at the forecasted position. During the second flight, 25 h after the release, the center of tracer plume was not detected by the sampling system due to a faster advection of the plume than forecasted. The newly developed PERTRAS system has been successfully deployed for the first time. The instrumental set-up and comparisons between the measurements and HYSPLIT simulations are presented in this study.
Differential geometry based solvation model II: Lagrangian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2011-12-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of
Differential geometry based solvation model II: Lagrangian formulation
Chen, Zhan; Baker, Nathan A.; Wei, G. W.
2010-01-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation model. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for
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.
The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows
NASA Technical Reports Server (NTRS)
Lufkin, Eric A.; Hawley, John F.
1993-01-01
We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.
Mixing model with multi-particle interactions for Lagrangian simulations of turbulent mixing
DOE Office of Scientific and Technical Information (OSTI.GOV)
Watanabe, T., E-mail: watanabe.tomoaki@c.nagoya-u.jp; Nagata, K.
We report on the numerical study of the mixing volume model (MVM) for molecular diffusion in Lagrangian simulations of turbulent mixing problems. The MVM is based on the multi-particle interaction in a finite volume (mixing volume). A priori test of the MVM, based on the direct numerical simulations of planar jets, is conducted in the turbulent region and the interfacial layer between the turbulent and non-turbulent fluids. The results show that the MVM predicts well the mean effects of the molecular diffusion under various numerical and flow parameters. The number of the mixing particles should be large for predicting amore » value of the molecular diffusion term positively correlated to the exact value. The size of the mixing volume relative to the Kolmogorov scale η is important in the performance of the MVM. The scalar transfer across the turbulent/non-turbulent interface is well captured by the MVM especially with the small mixing volume. Furthermore, the MVM with multiple mixing particles is tested in the hybrid implicit large-eddy-simulation/Lagrangian-particle-simulation (LES–LPS) of the planar jet with the characteristic length of the mixing volume of O(100η). Despite the large mixing volume, the MVM works well and decays the scalar variance in a rate close to the reference LES. The statistics in the LPS are very robust to the number of the particles used in the simulations and the computational grid size of the LES. Both in the turbulent core region and the intermittent region, the LPS predicts a scalar field well correlated to the LES.« less
Koracin, Darko; Vellore, Ramesh; Lowenthal, Douglas H; Watson, John G; Koracin, Julide; McCord, Travis; DuBois, David W; Chen, L W Antony; Kumar, Naresh; Knipping, Eladio M; Wheeler, Neil J M; Craig, Kenneth; Reid, Stephen
2011-06-01
The main objective of this study was to investigate the capabilities of the receptor-oriented inverse mode Lagrangian Stochastic Particle Dispersion Model (LSPDM) with the 12-km resolution Mesoscale Model 5 (MM5) wind field input for the assessment of source identification from seven regions impacting two receptors located in the eastern United States. The LSPDM analysis was compared with a standard version of the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) single-particle backward-trajectory analysis using inputs from MM5 and the Eta Data Assimilation System (EDAS) with horizontal grid resolutions of 12 and 80 km, respectively. The analysis included four 7-day summertime events in 2002; residence times in the modeling domain were computed from the inverse LSPDM runs and HYPSLIT-simulated backward trajectories started from receptor-source heights of 100, 500, 1000, 1500, and 3000 m. Statistics were derived using normalized values of LSPDM- and HYSPLIT-predicted residence times versus Community Multiscale Air Quality model-predicted sulfate concentrations used as baseline information. From 40 cases considered, the LSPDM identified first- and second-ranked emission region influences in 37 cases, whereas HYSPLIT-MM5 (HYSPLIT-EDAS) identified the sources in 21 (16) cases. The LSPDM produced a higher overall correlation coefficient (0.89) compared with HYSPLIT (0.55-0.62). The improvement of using the LSPDM is also seen in the overall normalized root mean square error values of 0.17 for LSPDM compared with 0.30-0.32 for HYSPLIT. The HYSPLIT backward trajectories generally tend to underestimate near-receptor sources because of a lack of stochastic dispersion of the backward trajectories and to overestimate distant sources because of a lack of treatment of dispersion. Additionally, the HYSPLIT backward trajectories showed a lack of consistency in the results obtained from different single vertical levels for starting the backward trajectories. To
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 transport in a class of three-dimensional buoyancy-driven flows
NASA Astrophysics Data System (ADS)
Contreras, Sebastian; Speetjens, Michel; Clercx, Herman
2017-11-01
The study concerns the Lagrangian dynamics of three-dimensional (3D) buoyancy-driven cavity flows under steady and laminar conditions due to a global temperature gradient imposed via an opposite hot and cold sidewall. This serves as archetypal configuration for natural-convection flows in which gravity is perpendicular to the global temperature gradient. Limited insight into the Lagrangian properties of this class of flows motivates this study. The 3D Lagrangian dynamics are investigated in terms of the generic structure of the Lagrangian flow topology that is described in terms of the Grashof number (Gr) and the Prandtl number (Pr). Gr is the principal control parameter for the flow topology: vanishing Gr yields a state of closed streamlines (integrable state); increasing Gr causes the formation of toroidal coherent structures embedded in chaotic streamlines governed by Hamiltonian mechanisms. Fluid inertia prevails for ``smaller'' Gr. A buoyancy-induced bifurcation of the flow topology occurs for ``larger'' Gr and underlies the emergence of ``secondary rolls'' and secondary tori for ``larger'' Pr. Stagnation points and corresponding manifold interactions are key to the dynamics. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).
ALMA Correlator Real-Time Data Processor
NASA Astrophysics Data System (ADS)
Pisano, J.; Amestica, R.; Perez, J.
2005-10-01
The design of a real-time Linux application utilizing Real-Time Application Interface (RTAI) to process real-time data from the radio astronomy correlator for the Atacama Large Millimeter Array (ALMA) is described. The correlator is a custom-built digital signal processor which computes the cross-correlation function of two digitized signal streams. ALMA will have 64 antennas with 2080 signal streams each with a sample rate of 4 giga-samples per second. The correlator's aggregate data output will be 1 gigabyte per second. The software is defined by hard deadlines with high input and processing data rates, while requiring interfaces to non real-time external computers. The designed computer system - the Correlator Data Processor or CDP, consists of a cluster of 17 SMP computers, 16 of which are compute nodes plus a master controller node all running real-time Linux kernels. Each compute node uses an RTAI kernel module to interface to a 32-bit parallel interface which accepts raw data at 64 megabytes per second in 1 megabyte chunks every 16 milliseconds. These data are transferred to tasks running on multiple CPUs in hard real-time using RTAI's LXRT facility to perform quantization corrections, data windowing, FFTs, and phase corrections for a processing rate of approximately 1 GFLOPS. Highly accurate timing signals are distributed to all seventeen computer nodes in order to synchronize them to other time-dependent devices in the observatory array. RTAI kernel tasks interface to the timing signals providing sub-millisecond timing resolution. The CDP interfaces, via the master node, to other computer systems on an external intra-net for command and control, data storage, and further data (image) processing. The master node accesses these external systems utilizing ALMA Common Software (ACS), a CORBA-based client-server software infrastructure providing logging, monitoring, data delivery, and intra-computer function invocation. The software is being developed in tandem
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.
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
Lagrangian statistics across the turbulent-nonturbulent interface in a turbulent plane jet.
Taveira, Rodrigo R; Diogo, José S; Lopes, Diogo C; da Silva, Carlos B
2013-10-01
Lagrangian statistics from millions of particles are used to study the turbulent entrainment mechanism in a direct numerical simulation of a turbulent plane jet at Re(λ) ≈ 110. The particles (tracers) are initially seeded at the irrotational region of the jet near the turbulent shear layer and are followed as they are drawn into the turbulent region across the turbulent-nonturbulent interface (TNTI), allowing the study of the enstrophy buildup and thereby characterizing the turbulent entrainment mechanism in the jet. The use of Lagrangian statistics following fluid particles gives a more correct description of the entrainment mechanism than in previous works since the statistics in relation to the TNTI position involve data from the trajectories of the entraining fluid particles. The Lagrangian statistics for the particles show the existence of a velocity jump and a characteristic vorticity jump (with a thickness which is one order of magnitude greater than the Kolmogorov microscale), in agreement with previous results using Eulerian statistics. The particles initially acquire enstrophy by viscous diffusion and later by enstrophy production, which becomes "active" only deep inside the turbulent region. Both enstrophy diffusion and production near the TNTI differ substantially from inside the turbulent region. Only about 1% of all particles find their way into pockets of irrotational flow engulfed into the turbulent shear layer region, indicating that "engulfment" is not significant for the present flow, indirectly suggesting that the entrainment is largely due to "nibbling" small-scale mechanisms acting along the entire TNTI surface. Probability density functions of particle positions suggests that the particles spend more time crossing the region near the TNTI than traveling inside the turbulent region, consistent with the particles moving tangent to the interface around the time they cross it.
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.
Junginger, Andrej; Duvenbeck, Lennart; Feldmaier, Matthias; Main, Jörg; Wunner, Günter; Hernandez, Rigoberto
2017-08-14
In chemical or physical reaction dynamics, it is essential to distinguish precisely between reactants and products for all times. This task is especially demanding in time-dependent or driven systems because therein the dividing surface (DS) between these states often exhibits a nontrivial time-dependence. The so-called transition state (TS) trajectory has been seen to define a DS which is free of recrossings in a large number of one-dimensional reactions across time-dependent barriers and thus, allows one to determine exact reaction rates. A fundamental challenge to applying this method is the construction of the TS trajectory itself. The minimization of Lagrangian descriptors (LDs) provides a general and powerful scheme to obtain that trajectory even when perturbation theory fails. Both approaches encounter possible breakdowns when the overall potential is bounded, admitting the possibility of returns to the barrier long after the trajectories have reached the product or reactant wells. Such global dynamics cannot be captured by perturbation theory. Meanwhile, in the LD-DS approach, it leads to the emergence of additional local minima which make it difficult to extract the optimal branch associated with the desired TS trajectory. In this work, we illustrate this behavior for a time-dependent double-well potential revealing a self-similar structure of the LD, and we demonstrate how the reflections and side-minima can be addressed by an appropriate modification of the LD associated with the direct rate across the barrier.
Nonpolynomial Lagrangian approach to regular black holes
NASA Astrophysics Data System (ADS)
Colléaux, Aimeric; Chinaglia, Stefano; Zerbini, Sergio
We present a review on Lagrangian models admitting spherically symmetric regular black holes (RBHs), and cosmological bounce solutions. Nonlinear electrodynamics, nonpolynomial gravity, and fluid approaches are explained in details. They consist respectively in a gauge invariant generalization of the Maxwell-Lagrangian, in modifications of the Einstein-Hilbert action via nonpolynomial curvature invariants, and finally in the reconstruction of density profiles able to cure the central singularity of black holes. The nonpolynomial gravity curvature invariants have the special property to be second-order and polynomial in the metric field, in spherically symmetric spacetimes. Along the way, other models and results are discussed, and some general properties that RBHs should satisfy are mentioned. A covariant Sakharov criterion for the absence of singularities in dynamical spherically symmetric spacetimes is also proposed and checked for some examples of such regular metric fields.
The augmented Lagrangian method for parameter estimation in elliptic systems
NASA Technical Reports Server (NTRS)
Ito, Kazufumi; Kunisch, Karl
1990-01-01
In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.
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.
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.
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
A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry
NASA Astrophysics Data System (ADS)
Jaouen, Stéphane
2007-07-01
In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.
Evaluation of wastewater contaminant transport in surface waters using verified Lagrangian sampling
Antweiler, Ronald C.; Writer, Jeffrey H.; Murphy, Sheila F.
2014-01-01
Contaminants released from wastewater treatment plants can persist in surface waters for substantial distances. Much research has gone into evaluating the fate and transport of these contaminants, but this work has often assumed constant flow from wastewater treatment plants. However, effluent discharge commonly varies widely over a 24-hour period, and this variation controls contaminant loading and can profoundly influence interpretations of environmental data. We show that methodologies relying on the normalization of downstream data to conservative elements can give spurious results, and should not be used unless it can be verified that the same parcel of water was sampled. Lagrangian sampling, which in theory samples the same water parcel as it moves downstream (the Lagrangian parcel), links hydrologic and chemical transformation processes so that the in-stream fate of wastewater contaminants can be quantitatively evaluated. However, precise Lagrangian sampling is difficult, and small deviations – such as missing the Lagrangian parcel by less than 1 h – can cause large differences in measured concentrations of all dissolved compounds at downstream sites, leading to erroneous conclusions regarding in-stream processes controlling the fate and transport of wastewater contaminants. Therefore, we have developed a method termed “verified Lagrangian” sampling, which can be used to determine if the Lagrangian parcel was actually sampled, and if it was not, a means for correcting the data to reflect the concentrations which would have been obtained had the Lagrangian parcel been sampled. To apply the method, it is necessary to have concentration data for a number of conservative constituents from the upstream, effluent, and downstream sites, along with upstream and effluent concentrations that are constant over the short-term (typically 2–4 h). These corrections can subsequently be applied to all data, including non-conservative constituents. Finally, we
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.
Joly, Florian; Soulez, Gilles; Garcia, Damien; Lessard, Simon; Kauffmann, Claude
2018-01-01
Abdominal aortic aneurysms (AAA) are localized, commonly-occurring dilations of the aorta. When equilibrium between blood pressure (loading) and wall mechanical resistance is lost, rupture ensues, and patient death follows, if not treated immediately. Experimental and numerical analyses of flow patterns in arteries show direct correlations between wall shear stress and wall mechano-adaptation with the development of zones prone to thrombus formation. For further insights into AAA flow topology/growth interaction, a workout of patient-specific computational flow dynamics (CFD) is proposed to compute finite-time Lyapunov exponents and extract Lagrangian-coherent structures (LCS). This computational model was first compared with 4-D phase-contrast magnetic resonance imaging (MRI) in 5 patients. To better understand the impact of flow topology and transport on AAA growth, hyperbolic, repelling LCS were computed in 1 patient during 8-year follow-up, including 9 volumetric morphologic AAA measures by computed tomography-angiography (CTA). LCS defined barriers to Lagrangian jet cores entering AAA. Domains enclosed between LCS and the aortic wall were considered to be stagnation zones. Their evolution was studied during AAA growth. Good correlation - 2-D cross-correlation coefficients of 0.65, 0.86 and 0.082 (min, max, SD) - was obtained between numerical simulations and 4-D MRI acquisitions in 6 specific cross-sections from 4 patients. In follow-up study, LCS divided AAA lumens into 3 dynamically-isolated zones: 2 stagnation volumes lying in dilated portions of the AAA, and circulating volume connecting the inlet to the outlet. The volume of each zone was tracked over time. Although circulating volume remained unchanged during 8-year follow-up, the AAA lumen and main stagnation zones grew significantly (8 cm 3 /year and 6 cm 3 /year, respectively). This study reveals that transient transport topology can be quantified in patient-specific AAA during disease progression
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.
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)
Time-localized wavelet multiple regression and correlation
NASA Astrophysics Data System (ADS)
Fernández-Macho, Javier
2018-02-01
This paper extends wavelet methodology to handle comovement dynamics of multivariate time series via moving weighted regression on wavelet coefficients. The concept of wavelet local multiple correlation is used to produce one single set of multiscale correlations along time, in contrast with the large number of wavelet correlation maps that need to be compared when using standard pairwise wavelet correlations with rolling windows. Also, the spectral properties of weight functions are investigated and it is argued that some common time windows, such as the usual rectangular rolling window, are not satisfactory on these grounds. The method is illustrated with a multiscale analysis of the comovements of Eurozone stock markets during this century. It is shown how the evolution of the correlation structure in these markets has been far from homogeneous both along time and across timescales featuring an acute divide across timescales at about the quarterly scale. At longer scales, evidence from the long-term correlation structure can be interpreted as stable perfect integration among Euro stock markets. On the other hand, at intramonth and intraweek scales, the short-term correlation structure has been clearly evolving along time, experiencing a sharp increase during financial crises which may be interpreted as evidence of financial 'contagion'.
Dynamics of Multibody Systems Near Lagrangian Points
NASA Astrophysics Data System (ADS)
Wong, Brian
This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the Lagrangian points of a Circular Restricted Three-Body System. The spacecraft system is arranged in a wheel-spoke configuration with smaller and less massive satellites connected to a central hub using truss/beams or tether connectors. The kinematics of the system is first defined, and the kinetic, gravitational potential energy and elastic potential energy of the system are derived. The Assumed Modes Method is used to discretize the continuous variables of the system, and a general set of ordinary differential equations describing the dynamics of the connectors and the central hub are obtained using the Lagrangian method. The flexible body dynamics of the tethered and truss connected systems are examined using numerical simulations. The results show that these systems experienced only small elastic deflections when they are naturally librating or rotating at moderate angular velocities, and these deflections have relatively small effect on the attitude dynamics of the systems. Based on these results, it is determined that the connectors can be modeled as rigid when only the attitude dynamics of the system is of interest. The equations of motion of rigid satellites stationed at the Lagrangian points are linearized, and the stability conditions of the satellite are obtained from the linear equations. The required conditions are shown to be similar to those of geocentric satellites. Study of the linear equations also revealed the resonant conditions of rigid Lagrangian point satellites, when a librational natural frequency of the satellite matches the frequency of its station-keeping orbit leading to large attitude motions. For tethered satellites, the linear analysis shows that the tethers are in stable equilibrium when they lie along a line joining the two primary celestial bodies of the Three-Body System. Numerical simulations are used to study the long term
Geometric Lagrangian approach to the physical degree of freedom count in field theory
NASA Astrophysics Data System (ADS)
Díaz, Bogar; Montesinos, Merced
2018-05-01
To circumvent some technical difficulties faced by the geometric Lagrangian approach to the physical degree of freedom count presented in the work of Díaz, Higuita, and Montesinos [J. Math. Phys. 55, 122901 (2014)] that prevent its direct implementation to field theory, in this paper, we slightly modify the geometric Lagrangian approach in such a way that its resulting version works perfectly for field theory (and for particle systems, of course). As in previous work, the current approach also allows us to directly get the Lagrangian constraints, a new Lagrangian formula for the counting of the number of physical degrees of freedom, the gauge transformations, and the number of first- and second-class constraints for any action principle based on a Lagrangian depending on the fields and their first derivatives without performing any Dirac's canonical analysis. An advantage of this approach over the previous work is that it also allows us to handle the reducibility of the constraints and to get the off-shell gauge transformations. The theoretical framework is illustrated in 3-dimensional generalized general relativity (Palatini and Witten's exotic actions), Chern-Simons theory, 4-dimensional BF theory, and 4-dimensional general relativity given by Palatini's action with a cosmological constant.
Macroscopic Lagrangian description of warm plasmas. II Nonlinear wave interactions
NASA Technical Reports Server (NTRS)
Kim, H.; Crawford, F. W.
1983-01-01
A macroscopic Lagrangian is simplified to the adiabatic limit and expanded about equilibrium, to third order in perturbation, for three illustrative cases: one-dimensional compression parallel to the static magnetic field, two-dimensional compression perpendicular to the static magnetic field, and three-dimensional compression. As examples of the averaged-Lagrangian method applied to nonlinear wave interactions, coupling coefficients are derived for interactions between two electron plasma waves and an ion acoustic wave, and between an ordinary wave, an electron plasma wave, and an ion acoustic wave.
NASA Astrophysics Data System (ADS)
BozorgMagham, Amir E.; Ross, Shane D.; Schmale, David G.
2013-09-01
The language of Lagrangian coherent structures (LCSs) provides a new means for studying transport and mixing of passive particles advected by an atmospheric flow field. Recent observations suggest that LCSs govern the large-scale atmospheric motion of airborne microorganisms, paving the way for more efficient models and management strategies for the spread of infectious diseases affecting plants, domestic animals, and humans. In addition, having reliable predictions of the timing of hyperbolic LCSs may contribute to improved aerobiological sampling of microorganisms with unmanned aerial vehicles and LCS-based early warning systems. Chaotic atmospheric dynamics lead to unavoidable forecasting errors in the wind velocity field, which compounds errors in LCS forecasting. In this study, we reveal the cumulative effects of errors of (short-term) wind field forecasts on the finite-time Lyapunov exponent (FTLE) fields and the associated LCSs when realistic forecast plans impose certain limits on the forecasting parameters. Objectives of this paper are to (a) quantify the accuracy of prediction of FTLE-LCS features and (b) determine the sensitivity of such predictions to forecasting parameters. Results indicate that forecasts of attracting LCSs exhibit less divergence from the archive-based LCSs than the repelling features. This result is important since attracting LCSs are the backbone of long-lived features in moving fluids. We also show under what circumstances one can trust the forecast results if one merely wants to know if an LCS passed over a region and does not need to precisely know the passage time.
A non-conventional discontinuous Lagrangian for viscous flow
Marner, F.
2017-01-01
Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided. PMID:28386415
A non-conventional discontinuous Lagrangian for viscous flow.
Scholle, M; Marner, F
2017-02-01
Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier-Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier-Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.
Bikondoa, Oier
2017-04-01
Multi-time correlation functions are especially well suited to study non-equilibrium processes. In particular, two-time correlation functions are widely used in X-ray photon correlation experiments on systems out of equilibrium. One-time correlations are often extracted from two-time correlation functions at different sample ages. However, this way of analysing two-time correlation functions is not unique. Here, two methods to analyse two-time correlation functions are scrutinized, and three illustrative examples are used to discuss the implications for the evaluation of the correlation times and functional shape of the correlations.
A Lagrangian discontinuous Galerkin hydrodynamic method
DOE Office of Scientific and Technical Information (OSTI.GOV)
Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.
Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less
A Lagrangian discontinuous Galerkin hydrodynamic method
Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.
2017-12-11
Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less
Lagrangian methods in the analysis of nonlinear wave interactions in plasma
NASA Technical Reports Server (NTRS)
Galloway, J. J.
1972-01-01
An averaged-Lagrangian method is developed for obtaining the equations which describe the nonlinear interactions of the wave (oscillatory) and background (nonoscillatory) components which comprise a continuous medium. The method applies to monochromatic waves in any continuous medium that can be described by a Lagrangian density, but is demonstrated in the context of plasma physics. The theory is presented in a more general and unified form by way of a new averaged-Lagrangian formalism which simplifies the perturbation ordering procedure. Earlier theory is extended to deal with a medium distributed in velocity space and to account for the interaction of the background with the waves. The analytic steps are systematized, so as to maximize calculational efficiency. An assessment of the applicability and limitations of the method shows that it has some definite advantages over other approaches in efficiency and versatility.
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
Lagrangian chaos in three- dimensional steady buoyancy-driven flows
NASA Astrophysics Data System (ADS)
Contreras, Sebastian; Speetjens, Michel; Clercx, Herman
2016-11-01
Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside a cubic cavity differentially-heated from the side. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. The Lagrangian dynamics are controlled by the Péclet number (Pe) and the Prandtl number (Pr). Pe controls the behaviour qualitatively in that growing Pe progressively perturbs the integable state (Pe =0), thus paving the way to chaotic dynamics. Pr plays an entirely quantitative role in that Pr<1 and Pr>1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).
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
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.
Power corrections to the HTL effective Lagrangian of QED
NASA Astrophysics Data System (ADS)
Carignano, Stefano; Manuel, Cristina; Soto, Joan
2018-05-01
We present compact expressions for the power corrections to the hard thermal loop (HTL) Lagrangian of QED in d space dimensions. These are corrections of order (L / T) 2, valid for momenta L ≪ T, where T is the temperature. In the limit d → 3 we achieve a consistent regularization of both infrared and ultraviolet divergences, which respects the gauge symmetry of the theory. Dimensional regularization also allows us to witness subtle cancellations of infrared divergences. We also discuss how to generalize our results in the presence of a chemical potential, so as to obtain the power corrections to the hard dense loop (HDL) Lagrangian.
Lagrangian Coherent Structures, Hyperbolicity, and Lyapunov Exponents
NASA Astrophysics Data System (ADS)
Haller, George
2010-05-01
We review the fundamental physical motivation behind the definition of Lagrangian Coherent Structures (LCS) and show how it leads to the concept of finite-time hyperbolicity in non-autonomous dynamical systems. Using this concept of hyperbolicity, we obtain a self-consistent criterion for the existence of attracting and repelling material surfaces in unsteady fluid flows, such as those in the atmosphere and the ocean. The existence of LCS is often postulated in terms of features of the Finite-Time Lyapunov Exponent (FTLE) field associated with the system. As simple examples show, however, the FTLE field does not necessarily highlight LCS, or may ighlight structures that are not LCS. Under appropriate nondegeneracy conditions, we show that ridges of the FTLE field indeed coincide with LCS in volume-preserving flows. For general flows, we obtain a more general scalar field whose ridges correspond to LCS. We finally review recent applications of LCS techniques to flight safety analysis at Hong Kong International Airport.
Effect of VSR invariant Chern-Simons Lagrangian on photon polarization
DOE Office of Scientific and Technical Information (OSTI.GOV)
Nayak, Alekha C.; Verma, Ravindra K.; Jain, Pankaj, E-mail: acnayak@iitk.ac.in, E-mail: ravindkv@iitk.ac.in, E-mail: pkjain@iitk.ac.in
2015-07-01
We propose a generalization of the Chern-Simons (CS) Lagrangian which is invariant under the SIM(2) transformations but not under the full Lorentz group. The generalized lagrangian is also invariant under a SIM(2) gauge transformation. We study the effect of such a term on radiation propagating over cosmological distances. We find that the dominant effect of this term is to produce circular polarization as radiation propagates through space. We use the circular polarization data from distant radio sources in order to impose a limit on this term.
Effect of VSR invariant Chern-Simons Lagrangian on photon polarization
DOE Office of Scientific and Technical Information (OSTI.GOV)
Nayak, Alekha C.; Verma, Ravindra K.; Jain, Pankaj
We propose a generalization of the Chern-Simons (CS) Lagrangian which is invariant under the SIM(2) transformations but not under the full Lorentz group. The generalized lagrangian is also invariant under a SIM(2) gauge transformation. We study the effect of such a term on radiation propagating over cosmological distances. We find that the dominant effect of this term is to produce circular polarization as radiation propagates through space. We use the circular polarization data from distant radio sources in order to impose a limit on this term.
Electron correlation in real time.
Sansone, Giuseppe; Pfeifer, Thomas; Simeonidis, Konstantinos; Kuleff, Alexander I
2012-02-01
Electron correlation, caused by the interaction among electrons in a multielectron system, manifests itself in all states of matter. A complete theoretical description of interacting electrons is challenging; different approximations have been developed to describe the fundamental aspects of the correlation that drives the evolution of simple (few-electron systems in atoms/molecules) as well as complex (multielectron wave functions in atoms, molecules, and solids) systems. Electron correlation plays a key role in the relaxation mechanisms that characterize excited states of neutral or ionized atoms and molecules populated by absorption of extreme ultraviolet (XUV) or X-ray radiation. The dynamics of these states can lead to different processes such as Fano resonance and Auger decay in atoms or interatomic Coulombic decay or charge migration in molecules and clusters. Many of these relaxation mechanisms are ubiquitous in nature and characterize the interaction of complex systems, such as biomolecules, adsorbates on surfaces, and hydrogen-bonded clusters, with XUV light. These mechanisms evolve typically on the femtosecond (1 fs=10(-15) s) or sub-femtosecond timescale. The experimental availability of few-femtosecond and attosecond (1 as=10(-18) s) XUV pulses achieved in the last 10 years offers, for the first time, the opportunity to excite and probe in time these dynamics giving the possibility to trace and control multielectron processes. The generation of ultrashort XUV radiation has triggered the development and application of spectroscopy techniques that can achieve time resolution well into the attosecond domain, thereby offering information on the correlated electronic motion and on the correlation between electron and nuclear motion. A deeper understanding of how electron correlation works could have a large impact in several research fields, such as biochemistry and biology, and trigger important developments in the design and optimization of electronic
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.
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.
On the Lagrangian description of unsteady boundary-layer separation. II - The spinning sphere
NASA Technical Reports Server (NTRS)
Van Dommelen, Leon L.
1990-01-01
A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A Lagrangian numerical scheme is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian computations broke down at the first occurrence of separation, it is found that the Lagrangian computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time.
The Monotonic Lagrangian Grid for Rapid Air-Traffic Evaluation
NASA Technical Reports Server (NTRS)
Kaplan, Carolyn; Dahm, Johann; Oran, Elaine; Alexandrov, Natalia; Boris, Jay
2010-01-01
The Air Traffic Monotonic Lagrangian Grid (ATMLG) is presented as a tool to evaluate new air traffic system concepts. The model, based on an algorithm called the Monotonic Lagrangian Grid (MLG), can quickly sort, track, and update positions of many aircraft, both on the ground (at airports) and in the air. The underlying data structure is based on the MLG, which is used for sorting and ordering positions and other data needed to describe N moving bodies and their interactions. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. Recent upgrades to ATMLG include adding blank place-holders within the MLG data structure, which makes it possible to dynamically change the MLG size and also improves the quality of the MLG grid. Additional upgrades include adding FAA flight plan data, such as way-points and arrival and departure times from the Enhanced Traffic Management System (ETMS), and combining the MLG with the state-of-the-art strategic and tactical conflict detection and resolution algorithms from the NASA-developed Stratway software. In this paper, we present results from our early efforts to couple ATMLG with the Stratway software, and we demonstrate that it can be used to quickly simulate air traffic flow for a very large ETMS dataset.
Lagrangian 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
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.
Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
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
Phase correlation of foreign exchange time series
NASA Astrophysics Data System (ADS)
Wu, Ming-Chya
2007-03-01
Correlation of foreign exchange rates in currency markets is investigated based on the empirical data of USD/DEM and USD/JPY exchange rates for a period from February 1 1986 to December 31 1996. The return of exchange time series is first decomposed into a number of intrinsic mode functions (IMFs) by the empirical mode decomposition method. The instantaneous phases of the resultant IMFs calculated by the Hilbert transform are then used to characterize the behaviors of pricing transmissions, and the correlation is probed by measuring the phase differences between two IMFs in the same order. From the distribution of phase differences, our results show explicitly that the correlations are stronger in daily time scale than in longer time scales. The demonstration for the correlations in periods of 1986-1989 and 1990-1993 indicates two exchange rates in the former period were more correlated than in the latter period. The result is consistent with the observations from the cross-correlation calculation.
Examination of Eulerian and Lagrangian Coordinate Systems.
ERIC Educational Resources Information Center
Remillard, Wilfred J.
1978-01-01
Studies the relationship between Eulerian and Lagrangian coordinate systems with the help of computer plots of variables such as density and particle displacement. Gives examples which illustrate the differences in the shape of a traveling wave as seen by observers in the two systems. (Author/GA)
DOE Office of Scientific and Technical Information (OSTI.GOV)
Zaveri, Rahul A.; Berkowitz, Carl M.; Hubbe, John M.
2004-10-04
Heterogeneous chemical processes involving trace gases and aerosols are poorly understood and are expected to play an important role at night. As part of the 2002 New England Air Quality Study (NEAQS), the Nighttime Aerosol/Oxidant Plume Experiment (NAOPEX) was designed to study the chemical evolution and interaction of ambient urban aerosols and trace gases in the absence of photochemistry. Lagrangian measurements of trace gases (O3, NOx, NOy, VOCs, CO) and aerosols (size distribution and composition) were made with the Department of Energy’s (DOE) G-1 aircraft in the nocturnal residual layer downwind of greater Boston area. On clear nights with offshoremore » flow, a superpressure, constant-volume balloon (tetroon) was launched from a coastal site into the Boston plume around sunset to serve as a Lagrangian marker of urban air parcels as they moved out over the Atlantic Ocean. The tetroon carried an instrument payload of about 2.5 kg that included a GPS receiver, radiosonde and ozonesonde. Latitude, longitude, altitude, temperature, pressure, relative humidity and ozone concentration data were transmitted in real-time to a receiver on the ground as well as one onboard the G-1 aircraft. About an hour after the launch, when the tetroon was outside the restricted Class-B airspace, the G-1 aircraft made the first flight to make more comprehensive measurements in the vicinity of the tetroon. About five hours after the launch, the G-1 made a second flight to make another set of measurements near the tetroon. Here, we report on the two flights made between 20:00 EST July 30 and 02:00 EST July 31. Analyses of the Lagrangian aerosol and trace gases dataset suggest evidence of heterogeneous activity and aging of aerosols. Vertical profiles of Ozone + NOy concentrations in the vicinity of the tetroon were found to be anti-correlated with aerosol number density, and the slope of the linear regression fit decreased as a function of time. These changes could be explained
Eulerian-Lagrangian Simulations of Transonic Flutter Instabilities
NASA Technical Reports Server (NTRS)
Bendiksen, Oddvar O.
1994-01-01
This paper presents an overview of recent applications of Eulerian-Lagrangian computational schemes in simulating transonic flutter instabilities. This approach, the fluid-structure system is treated as a single continuum dynamics problem, by switching from an Eulerian to a Lagrangian formulation at the fluid-structure boundary. This computational approach effectively eliminates the phase integration errors associated with previous methods, where the fluid and structure are integrated sequentially using different schemes. The formulation is based on Hamilton's Principle in mixed coordinates, and both finite volume and finite element discretization schemes are considered. Results from numerical simulations of transonic flutter instabilities are presented for isolated wings, thin panels, and turbomachinery blades. The results suggest that the method is capable of reproducing the energy exchange between the fluid and the structure with significantly less error than existing methods. Localized flutter modes and panel flutter modes involving traveling waves can also be simulated effectively with no a priori knowledge of the type of instability involved.
NASA Astrophysics Data System (ADS)
Einkemmer, Lukas
2016-05-01
The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-Lagrangian schemes (which are usually based on polynomial or spline interpolation). In this paper, we consider a parallel implementation of a semi-Lagrangian discontinuous Galerkin method for distributed memory systems (so-called clusters). Both strong and weak scaling studies are performed on the Vienna Scientific Cluster 2 (VSC-2). In the case of weak scaling we observe a parallel efficiency above 0.8 for both two and four dimensional problems and up to 8192 cores. Strong scaling results show good scalability to at least 512 cores (we consider problems that can be run on a single processor in reasonable time). In addition, we study the scaling of a two dimensional Vlasov-Poisson solver that is implemented using the framework provided. All of the simulations are conducted in the context of worst case communication overhead; i.e., in a setting where the CFL (Courant-Friedrichs-Lewy) number increases linearly with the problem size. The framework introduced in this paper facilitates a dimension independent implementation of scientific codes (based on C++ templates) using both an MPI and a hybrid approach to parallelization. We describe the essential ingredients of our implementation.
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.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Caramana, E.J.; Shashkov, M.J.
1997-12-31
The bane of Lagrangian hydrodynamics calculations is premature breakdown of the grid topology that results in severe degradation of accuracy and run termination often long before the assumption of Lagrangian zonal mass ceased to be valid. At short spatial grid scales this is usually referred to by the terms hourglass mode or keystone motion associated in particular with underconstrained grids such as quadrilaterals and hexahedrons in two and three dimensions, respectively. At longer spatial scales relative to the grid spacing there is what is referred to ubiquitously as spurious vorticity, or the long-thin zone problem. In both cases the resultmore » is anomalous grid distortion and tangling that has nothing to do with the actual solution, as would be the case for turbulent flow. In this work the authors show how such motions can be eliminated by the proper use of subzonal Lagrangian masses, and associated densities and pressures. These subzonal masses arise in a natural way from the fact that they require the mass associated with the nodal grid point to be constant in time. This is addition to the usual assumption of constant, Lagrangian zonal mass in staggered grid hydrodynamics scheme. The authors show that with proper discretization of subzonal forces resulting from subzonal pressures, hourglass motion and spurious vorticity can be eliminated for a very large range of problems. Finally the authors are presenting results of calculations of many test problems.« less
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
On the lagrangian 1-form structure of the hyperbolic calogero-moser system
NASA Astrophysics Data System (ADS)
Jairuk, Umpon; Tanasittikosol, Monsit; Yoo-Kong, Sikarin
2017-06-01
In this work, we present the Lagrangian 1-form structure of the hyperbolic Calogero-Moser system in both discrete-time level and continuous-time level. The discrete-time hyperbolic Calogero-Moser system is obtained by considering pole reduction of the semi-discrete Kadomtsev-Petviashvili (KP) equation. Furthermore, it is shown that the hyperbolic Calogero-Moser system possesses the key relation, known as the discrete-time closure relation. This relation is a consequence of the compatibility property of the temporal Lax matrices. The continuous-time hierarchy of the hyperbolic Calogero-Moser system is obtained by taking two successive continuum limits, namely, the skewed limit and full limit. With these successive limits, the continuous-time closure relation is also obtained and is shown to hold at the continuous level.
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.
Sigma decomposition: the CP-odd Lagrangian
NASA Astrophysics Data System (ADS)
Hierro, I. M.; Merlo, L.; Rigolin, S.
2016-04-01
In Alonso et al., JHEP 12 (2014) 034, the CP-even sector of the effective chiral Lagrangian for a generic composite Higgs model with a symmetric coset has been constructed, up to four momenta. In this paper, the CP-odd couplings are studied within the same context. If only the Standard Model bosonic sources of custodial symmetry breaking are considered, then at most six independent operators form a basis. One of them is the weak- θ term linked to non-perturbative sources of CP violation, while the others describe CP-odd perturbative couplings between the Standard Model gauge bosons and an Higgs-like scalar belonging to the Goldstone boson sector. The procedure is then applied to three distinct exemplifying frameworks: the original SU(5)/SO(5) Georgi-Kaplan model, the minimal custodial-preserving SO(5)/SO(4) model and the minimal SU(3)/(SU(2) × U(1)) model, which intrinsically breaks custodial symmetry. Moreover, the projection of the high-energy electroweak effective theory to the low-energy chiral effective Lagrangian for a dynamical Higgs is performed, uncovering strong relations between the operator coefficients and pinpointing the differences with the elementary Higgs scenario.
Matter Lagrangian of particles and fluids
NASA Astrophysics Data System (ADS)
Avelino, P. P.; Sousa, L.
2018-03-01
We consider a model where particles are described as localized concentrations of energy, with fixed rest mass and structure, which are not significantly affected by their self-induced gravitational field. We show that the volume average of the on-shell matter Lagrangian Lm describing such particles, in the proper frame, is equal to the volume average of the trace T of the energy-momentum tensor in the same frame, independently of the particle's structure and constitution. Since both Lm and T are scalars, and thus independent of the reference frame, this result is also applicable to collections of moving particles and, in particular, to those which can be described by a perfect fluid. Our results are expected to be particularly relevant in the case of modified theories of gravity with nonminimal coupling to matter where the matter Lagrangian appears explicitly in the equations of motion of the gravitational and matter fields, such as f (R ,Lm) and f (R ,T ) gravity. In particular, they indicate that, in this context, f (R ,Lm) theories may be regarded as a subclass of f (R ,T ) gravity.
Stochastic dynamics of time correlation in complex systems with discrete time
NASA Astrophysics Data System (ADS)
Yulmetyev, Renat; Hänggi, Peter; Gafarov, Fail
2000-11-01
In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy Si(t) where i=0,1,2,3,..., as an information measure of stochastic dynamics of time correlation (i=0) and time memory (i=1,2,3,...). The set of functions Si(t) constitute the quantitative measure of time correlation disorder (i=0) and time memory disorder (i=1,2,3,...) in complex system. The theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states. We examine two stochastic processes involving the creation and annihilation of time correlation (or time memory) in details. We carry out the analysis of vectors' dynamics employing finite-difference equations for random variables and the evolution operator describing their natural motion. The existence of TCF results in the construction of the set of projection operators by the usage of scalar product operation. Harnessing the infinite set of orthogonal dynamic random variables on a basis of Gram-Shmidt orthogonalization procedure tends to creation of infinite chain of finite-difference non-Markov kinetic equations for discrete TCFs and memory functions (MFs). The solution of the equations above thereof brings to the recurrence relations between the TCF and MF of senior and junior orders. This offers new opportunities for detecting the frequency spectra of power of entropy function Si(t) for time correlation (i=0) and time memory (i=1,2,3,...). The results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems. Application of this technique on the analysis of stochastic dynamics of RR intervals from human ECG's shows convincing evidence for
Lagrangian modeling of global atmospheric methane (1990-2012)
NASA Astrophysics Data System (ADS)
Arfeuille, Florian; Henne, Stephan; Brunner, Dominik
2016-04-01
In the MAIOLICA-II project, the lagrangian particle model FLEXPART is used to simulate the global atmospheric methane over the 1990-2012 period. In this lagrangian framework, 3 million particles are permanently transported based on winds from ERA-interim. The history of individual particles can be followed allowing for a comprehensive analysis of transport pathways and timescales. The link between sources (emissions) and receptors (measurement stations) is then established in a straightforward manner, a prerequisite for source inversion problems. FLEXPART was extended to incorporate the methane loss by reaction with OH, soil uptake and stratospheric loss reactions with prescribed Cl and O(1d) radicals. Sources are separated into 245 different tracers, depending on source origin (anthropogenic, wetlands, rice, biomass burning, termites, wild animals, oceans, volcanoes), region of emission, and time since emission (5 age classes). The inversion method applied is a fixed-lag Kalman smoother similar to that described in Bruhwiler et al. [2005]. Results from the FLEXPART global methane simulation and from the subsequent inversion will be presented. Results notably suggest: - A reduction in methane growth rates due to diminished wetland emissions and anthropogenic European emission in 1990-1993. - A second decrease in 1995-1996 is also mainly attributed to these two emission categories. - A reduced increase in Chinese anthropogenic emissions after 2003 compared to EDGAR inventories. - Large South American wetlands emissions during the entire period. Bruhwiler, L. M. P., Michalak, A. M., Peters, W., Baker, D. F. & Tans, P. 2005: An improved Kalman smoother fore atmospheric inversions, Atmos Chem Phys, 5, 2691-2702.
Response time correlations for platinum resistance thermometers
NASA Technical Reports Server (NTRS)
Pandey, D. K.; Ash, R. L.; Dillon-Townes, L. A.
1985-01-01
The 'plunge method' recommended by ASTM has been used to determine the time constant of 100-ohm platinum resistance thermometers (PRT) considered for use in the National Transonic Facility. It is shown that the response time of ventilated PRT can be correlated with the reciprocal of the heat transfer coefficient in a given field. Universal correlations are established for the 100- and 1000-ohm PRT with uncertainties of 20 and 30 percent, respectively. The correlations are found to be consistent with the uncertainty involved in heat transfer correlations available in the literature and are recommended for use in flowing liquids and gases.
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
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
Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices.
Huhn, F; van Rees, W M; Gazzola, M; Rossinelli, D; Haller, G; Koumoutsakos, P
2015-08-01
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
Evaluation of the Monotonic Lagrangian Grid and Lat-Long Grid for Air Traffic Management
NASA Technical Reports Server (NTRS)
Kaplan, Carolyn; Dahm, Johann; Oran, Elaine; Alexandrov, Natalia; Boris, Jay
2011-01-01
The Air Traffic Monotonic Lagrangian Grid (ATMLG) is used to simulate a 24 hour period of air traffic flow in the National Airspace System (NAS). During this time period, there are 41,594 flights over the United States, and the flight plan information (departure and arrival airports and times, and waypoints along the way) are obtained from an Federal Aviation Administration (FAA) Enhanced Traffic Management System (ETMS) dataset. Two simulation procedures are tested and compared: one based on the Monotonic Lagrangian Grid (MLG), and the other based on the stationary Latitude-Longitude (Lat- Long) grid. Simulating one full day of air traffic over the United States required the following amounts of CPU time on a single processor of an SGI Altix: 88 s for the MLG method, and 163 s for the Lat-Long grid method. We present a discussion of the amount of CPU time required for each of the simulation processes (updating aircraft trajectories, sorting, conflict detection and resolution, etc.), and show that the main advantage of the MLG method is that it is a general sorting algorithm that can sort on multiple properties. We discuss how many MLG neighbors must be considered in the separation assurance procedure in order to ensure a five-mile separation buffer between aircraft, and we investigate the effect of removing waypoints from aircraft trajectories. When aircraft choose their own trajectory, there are more flights with shorter duration times and fewer CD&R maneuvers, resulting in significant fuel savings.
Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach
NASA Astrophysics Data System (ADS)
Comolli, Alessandro; Dentz, Marco
2017-09-01
We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy's law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in
L-GRAAL: Lagrangian graphlet-based network aligner.
Malod-Dognin, Noël; Pržulj, Nataša
2015-07-01
Discovering and understanding patterns in networks of protein-protein interactions (PPIs) is a central problem in systems biology. Alignments between these networks aid functional understanding as they uncover important information, such as evolutionary conserved pathways, protein complexes and functional orthologs. A few methods have been proposed for global PPI network alignments, but because of NP-completeness of underlying sub-graph isomorphism problem, producing topologically and biologically accurate alignments remains a challenge. We introduce a novel global network alignment tool, Lagrangian GRAphlet-based ALigner (L-GRAAL), which directly optimizes both the protein and the interaction functional conservations, using a novel alignment search heuristic based on integer programming and Lagrangian relaxation. We compare L-GRAAL with the state-of-the-art network aligners on the largest available PPI networks from BioGRID and observe that L-GRAAL uncovers the largest common sub-graphs between the networks, as measured by edge-correctness and symmetric sub-structures scores, which allow transferring more functional information across networks. We assess the biological quality of the protein mappings using the semantic similarity of their Gene Ontology annotations and observe that L-GRAAL best uncovers functionally conserved proteins. Furthermore, we introduce for the first time a measure of the semantic similarity of the mapped interactions and show that L-GRAAL also uncovers best functionally conserved interactions. In addition, we illustrate on the PPI networks of baker's yeast and human the ability of L-GRAAL to predict new PPIs. Finally, L-GRAAL's results are the first to show that topological information is more important than sequence information for uncovering functionally conserved interactions. L-GRAAL is coded in C++. Software is available at: http://bio-nets.doc.ic.ac.uk/L-GRAAL/. n.malod-dognin@imperial.ac.uk Supplementary data are available at
Gopi, Varun P; Palanisamy, P; Wahid, Khan A; Babyn, Paul; Cooper, David
2013-01-01
Micro-computed tomography (micro-CT) plays an important role in pre-clinical imaging. The radiation from micro-CT can result in excess radiation exposure to the specimen under test, hence the reduction of radiation from micro-CT is essential. The proposed research focused on analyzing and testing an alternating direction augmented Lagrangian (ADAL) algorithm to recover images from random projections using total variation (TV) regularization. The use of TV regularization in compressed sensing problems makes the recovered image quality sharper by preserving the edges or boundaries more accurately. In this work TV regularization problem is addressed by ADAL which is a variant of the classic augmented Lagrangian method for structured optimization. The per-iteration computational complexity of the algorithm is two fast Fourier transforms, two matrix vector multiplications and a linear time shrinkage operation. Comparison of experimental results indicate that the proposed algorithm is stable, efficient and competitive with the existing algorithms for solving TV regularization problems. Copyright © 2013 Elsevier Ltd. All rights reserved.
Experimental design for drifting buoy Lagrangian test
NASA Technical Reports Server (NTRS)
Saunders, P. M.
1975-01-01
A test of instrumentation fabricated to measure the performance of a free drifting buoy as a (Lagrangian) current meter is described. Specifically it is proposed to distinguish between the trajectory of a drogued buoy and the trajectory of the water at the level of the drogue by measuring the flow relative to the drogue.
Lagrangian particle method for compressible fluid dynamics
NASA Astrophysics Data System (ADS)
Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang
2018-06-01
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface/multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic-elliptic systems. Numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.
Lagrangian Timescales of Southern Ocean Upwelling in a Hierarchy of Model Resolutions
NASA Astrophysics Data System (ADS)
Drake, Henri F.; Morrison, Adele K.; Griffies, Stephen M.; Sarmiento, Jorge L.; Weijer, Wilbert; Gray, Alison R.
2018-01-01
In this paper we study upwelling pathways and timescales of Circumpolar Deep Water (CDW) in a hierarchy of models using a Lagrangian particle tracking method. Lagrangian timescales of CDW upwelling decrease from 87 years to 31 years to 17 years as the ocean resolution is refined from 1° to 0.25° to 0.1°. We attribute some of the differences in timescale to the strength of the eddy fields, as demonstrated by temporally degrading high-resolution model velocity fields. Consistent with the timescale dependence, we find that an average Lagrangian particle completes 3.2 circumpolar loops in the 1° model in comparison to 0.9 loops in the 0.1° model. These differences suggest that advective timescales and thus interbasin merging of upwelling CDW may be overestimated by coarse-resolution models, potentially affecting the skill of centennial scale climate change projections.
Effective Lagrangians and Current Algebra in Three Dimensions
NASA Astrophysics Data System (ADS)
Ferretti, Gabriele
In this thesis we study three dimensional field theories that arise as effective Lagrangians of quantum chromodynamics in Minkowski space with signature (2,1) (QCD3). In the first chapter, we explain the method of effective Langrangians and the relevance of current algebra techniques to field theory. We also provide the physical motivations for the study of QCD3 as a toy model for confinement and as a theory of quantum antiferromagnets (QAF). In chapter two, we derive the relevant effective Lagrangian by studying the low energy behavior of QCD3, paying particular attention to how the global symmetries are realized at the quantum level. In chapter three, we show how baryons arise as topological solitons of the effective Lagrangian and also show that their statistics depends on the number of colors as predicted by the quark model. We calculate mass splitting and magnetic moments of the soliton and find logarithmic corrections to the naive quark model predictions. In chapter four, we drive the current algebra of the theory. We find that the current algebra is a co -homologically non-trivial generalization of Kac-Moody algebras to three dimensions. This fact may provide a new, non -perturbative way to quantize the theory. In chapter five, we discuss the renormalizability of the model in the large-N expansion. We prove the validity of the non-renormalization theorem and compute the critical exponents in a specific limiting case, the CP^ {N-1} model with a Chern-Simons term. Finally, chapter six contains some brief concluding remarks.
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
Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates
Cheng, Ralph T.; Casulli, Vincenzo; Milford, S. Nevil
1984-01-01
The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order Lagrangian polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.
The general form of the coupled Horndeski Lagrangian that allows cosmological scaling solutions
DOE Office of Scientific and Technical Information (OSTI.GOV)
Gomes, Adalto R.; Amendola, Luca, E-mail: argomes.ufma@gmail.com, E-mail: l.amendola@thphys.uni-heidelberg.de
We consider the general scalar field Horndeski Lagrangian coupled to dark matter. Within this class of models, we present two results that are independent of the particular form of the model. First, we show that in a Friedmann-Robertson-Walker metric the Horndeski Lagrangian coincides with the pressure of the scalar field. Second, we employ the previous result to identify the most general form of the Lagrangian that allows for cosmological scaling solutions, i.e. solutions where the ratio of dark matter to field density and the equation of state remain constant. Scaling solutions of this kind may help solving the coincidence problemmore » since in this case the presently observed ratio of matter to dark energy does not depend on initial conditions, but rather on the theoretical parameters.« less
NASA Astrophysics Data System (ADS)
Bodenschatz, Eberhard
2014-11-01
In my talk I shall present results from particle tracking experiments in turbulence. After a short review of the history of the field, I shall summarize the most recent technological advances that range form low and high-density particle tracking to direct measurements of the Lagrangian evolution of vorticity. I shall embark on a journey that describes the discoveries made possible by this new technology in the last 15 years. I present results that challenge our understanding of turbulence and show how Lagrangian particle tracking can help us ask questions on turbulent flows that so far were hidden. I shall show how Lagrangian particle tracking may provide important insights into the reversibility of turbulent flows, on vorticity generation, the energy cascade and turbulent mixing. I shall describe the consequences of inertial particle transport on rain formation and end with an outlook on how Lagrangian particle tracking experiments on non-stationary flows in real-world situations may provide high quality data that can support real world engineering problems. I am very thankful for the support by Cornell University, the National Science Foundation, the Research Corporation, the Alfred P. Sloan Foundation, the Kavli Institute for Theoretical Physics, the German Research Foundation, the European Union and the Max Planck Society. I very gratefully acknowledge the excellent partnership with many colleagues in the field of fluid mechanics and turbulence.
Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H
2015-10-01
Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.
A Compact Bulk Acousto-Optic Time Integrating Correlator.
1984-11-01
AD-A156 668 A COMPACT BULK ACOUSTO - OPTIC TIME INTEGRATING 1/1 CORRELATOR(U) ELECTRONICS RESEARCH LAB ADELAIDE (AUSTRALIA) D A FOGG NOV 84 ERL-9323-TR...DEFENCE RESEARCH CENTRE SALISBURY SOUTH AUSTRALIA TECHNICAL REPORT ER L-0323-TR A COMPACT BULK ACOUSTO - OPTIC TIME INTEGRATING CORRELATOR D.A.B. FOGG...LABORATORY TECHNICAL REPORT ERL-0323-TR A COMPACT BULK ACOUSTO - OPTIC TIME INTEGRATING CORRELATOR D.A.B. Fogg SUMMARY This report describes the design and
Second order upwind Lagrangian particle method for Euler equations
Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin
2016-06-01
A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less
Second order upwind Lagrangian particle method for Euler equations
DOE Office of Scientific and Technical Information (OSTI.GOV)
Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin
A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less
Healy, R.W.; Russell, T.F.
1993-01-01
A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.
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
A new Lagrangian method for three-dimensional steady supersonic flows
NASA Technical Reports Server (NTRS)
Loh, Ching-Yuen; Liou, Meng-Sing
1993-01-01
In this report, the new Lagrangian method introduced by Loh and Hui is extended for three-dimensional, steady supersonic flow computation. The derivation of the conservation form and the solution of the local Riemann solver using the Godunov and the high-resolution TVD (total variation diminished) scheme is presented. This new approach is accurate and robust, capable of handling complicated geometry and interactions between discontinuous waves. Test problems show that the extended Lagrangian method retains all the advantages of the two-dimensional method (e.g., crisp resolution of a slip-surface (contact discontinuity) and automatic grid generation). In this report, we also suggest a novel three dimensional Riemann problem in which interesting and intricate flow features are present.
Effective Lagrangian in nonlinear electrodynamics and its properties of causality and unitarity
DOE Office of Scientific and Technical Information (OSTI.GOV)
Shabad, Anatoly E.; Usov, Vladimir V.
2011-05-15
In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed the speed of light in the vacuum c=1, and the unitarity principle as the requirement that the residue of the propagator should be nonnegative, we establish the positive convexity of the effective Lagrangian on the class of constant fields, also the positivity of all characteristic dielectric and magnetic permittivity constants that are derivatives of the effective Lagrangian with respect to the field invariants. Violation of the general principles by the one-loop approximation in QED atmore » exponentially large magnetic field is analyzed, resulting in complex energy ghosts that signal the instability of the magnetized vacuum. Superluminal excitations (tachyons) appear, too, but for the magnetic field exceeding its instability threshold. Also other popular Lagrangians are tested to establish that the ones leading to spontaneous vacuum magnetization possess wrong convexity.« less
A Satellite-Based Lagrangian View on Phytoplankton Dynamics.
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.
Multiphase Interface Tracking with Fast Semi-Lagrangian Contouring.
Li, Xiaosheng; He, Xiaowei; Liu, Xuehui; Zhang, Jian J; Liu, Baoquan; Wu, Enhua
2016-08-01
We propose a semi-Lagrangian method for multiphase interface tracking. In contrast to previous methods, our method maintains an explicit polygonal mesh, which is reconstructed from an unsigned distance function and an indicator function, to track the interface of arbitrary number of phases. The surface mesh is reconstructed at each step using an efficient multiphase polygonization procedure with precomputed stencils while the distance and indicator function are updated with an accurate semi-Lagrangian path tracing from the meshes of the last step. Furthermore, we provide an adaptive data structure, multiphase distance tree, to accelerate the updating of both the distance function and the indicator function. In addition, the adaptive structure also enables us to contour the distance tree accurately with simple bisection techniques. The major advantage of our method is that it can easily handle topological changes without ambiguities and preserve both the sharp features and the volume well. We will evaluate its efficiency, accuracy and robustness in the results part with several examples.
Unambiguous formalism for higher order Lagrangian field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris
2009-11-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
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.
Collaborative Visual Seafloor Imaging using a Photographic AUV and a Lagrangian Imaging Float
NASA Astrophysics Data System (ADS)
Friedman, A.; Pizarro, O.; Roman, C.; Toohey, L.; Snyder, W.; Johnson-Roberson, M.; Iscar, E.; Williams, S. B.
2016-02-01
High resolution seafloor imaging from mobile autonomous platforms has become a valuable tool for habitat classification, stock assessment and seafloor exploration. This abstract addresses the concept of joint seafloor survey planning using both navigable and drifting platforms, and presents results from an experiment using a bottom surveying AUV and a drifting Lagrangian camera float. We consider two classes of vehicles; one which is able to self propel and execute structured surveys, and one which is Lagrangian and moves only with the currents. The navigable vehicle is the more capable and the more expensives asset of the two. The Lagrangian platforms is a low cost imaging tool that can actively control its altitude above the seafloor to obtain high quality images but can not otherwise control its trajectory over the bottom. When used together the vehicles offer several scenarios for joint operations. When used in an exploratory manner the Lagrangian float is an inexpensive way to collect images from an unknown area. Depending on the collected images, a follow on structured survey with the navigable AUV can collect additional information if the cost is acceptable given the need and prior data. When used simultaneously the drifting float can guide the AUV trajectory over an area. When both platforms are equipped with acoustic tracking and communications the AUV trajectory can be automatically redirected to follow the Lagrangian float using one of many patterns. This capability allows for surveys that are potentially more representative of the near bottom oceanographic conditions at the desired location. Results will be presented from a cruise to Scott Reef, Australia, where both platforms were used as part of a coral habitat monitoring project.
Dry intrusions: Lagrangian climatology and impact on the boundary layer
NASA Astrophysics Data System (ADS)
Raveh-Rubin, Shira; Wernli, Heini
2017-04-01
Dry air intrusions (DIs) are large-scale descending airstreams. A DI is typically referred to as a coherent airstream in the cold sector of an extratropical cyclone. Emerging evidence suggests that DIs are linked to severe surface wind gusts. However, there is yet no strict Lagrangian definition of DIs, and so their climatological frequency, dynamical characteristics as well as their seasonal and spatial distributions are unknown. Furthermore, the dynamical interaction between DIs and the planetary boundary layer is not fully understood. Here, we suggest a Lagrangian definition for DI air parcels, namely a minimum pressure increase along a trajectory of 400 hPa in 48 hours. Based on this criterion, the open questions are addressed by: (i) a novel global Lagrangian climatology for the ECMWF ERA-Interim reanalysis dataset for the years 1979-2014; (ii) a case study illustrating the interaction between DIs and the boundary layer. We find that DIs occur predominantly in winter. DIs coherently descend from the upper troposphere (their stratospheric origin is small), to the mid- and low levels, where they mix with their environment and diverge. Different physical characteristics typify DIs in the different regions and seasons. Finally, we demonstrate the different mechanisms by which DIs can destabilize the boundary layer and facilitate the formation of strong surface winds.
Hirakawa, Teruo; Suzuki, Teppei; Bowler, David R; Miyazaki, Tsuyoshi
2017-10-11
We discuss the development and implementation of a constant temperature (NVT) molecular dynamics scheme that combines the Nosé-Hoover chain thermostat with the extended Lagrangian Born-Oppenheimer molecular dynamics (BOMD) scheme, using a linear scaling density functional theory (DFT) approach. An integration scheme for this canonical-ensemble extended Lagrangian BOMD is developed and discussed in the context of the Liouville operator formulation. Linear scaling DFT canonical-ensemble extended Lagrangian BOMD simulations are tested on bulk silicon and silicon carbide systems to evaluate our integration scheme. The results show that the conserved quantity remains stable with no systematic drift even in the presence of the thermostat.
Hamiltonian vs Lagrangian Embedding of a Massive Spin-One Theory Involving Two-Form Field
NASA Astrophysics Data System (ADS)
Harikumar, E.; Sivakumar, M.
We consider the Hamiltonian and Lagrangian embedding of a first-order, massive spin-one, gauge noninvariant theory involving antisymmetric tensor field. We apply the BFV-BRST generalized canonical approach to convert the model to a first class system and construct nilpotent BFV-BRST charge and a unitarizing Hamiltonian. The canonical analysis of the Stückelberg formulation of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the Lagrangian embedded model. We show that to obtain manifestly covariant Stückelberg Lagrangian from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.
Lagrangian particle method for compressible fluid dynamics
DOE Office of Scientific and Technical Information (OSTI.GOV)
Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremalmore » points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.« less
Lagrangian particle method for compressible fluid dynamics
Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang
2018-02-09
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremalmore » points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.« less
Gravitational Lagrangians, Mach's Principle, and the Equivalence Principle in an Expanding Universe
NASA Astrophysics Data System (ADS)
Essén, Hanno
2014-08-01
Gravitational Lagrangians as derived by Fock for the Einstein-Infeld-Hoffmann approach, and by Kennedy assuming only a fourth rank tensor interaction, contain long range interactions. Here we investigate how these affect the local dynamics when integrated over an expanding universe out to the Hubble radius. Taking the cosmic expansion velocity into account in a heuristic manner it is found that these long range interactions imply Mach's principle, provided the universe has the critical density, and that mass is renormalized. Suitable higher order additions to the Lagrangians make the formalism consistent with the equivalence principle.
High Order Semi-Lagrangian Advection Scheme
NASA Astrophysics Data System (ADS)
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2014-11-01
In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
Soltanian, Mohamad Reza; Ritzi, Robert W; Dai, Zhenxue; Huang, Chao Cheng
2015-03-01
Physical and chemical heterogeneities have a large impact on reactive transport in porous media. Examples of heterogeneous attributes affecting reactive mass transport are the hydraulic conductivity (K), and the equilibrium sorption distribution coefficient (Kd). This paper uses the Deng et al. (2013) conceptual model for multimodal reactive mineral facies and a Lagrangian-based stochastic theory in order to analyze the reactive solute dispersion in three-dimensional anisotropic heterogeneous porous media with hierarchical organization of reactive minerals. An example based on real field data is used to illustrate the time evolution trends of reactive solute dispersion. The results show that the correlation between the hydraulic conductivity and the equilibrium sorption distribution coefficient does have a significant effect on reactive solute dispersion. The anisotropy ratio does not have a significant effect on reactive solute dispersion. Furthermore, through a sensitivity analysis we investigate the impact of changing the mean, variance, and integral scale of K and Kd on reactive solute dispersion. Copyright © 2014 Elsevier Ltd. All rights reserved.
Construction of Lagrangians and Hamiltonians from the Equation of Motion
ERIC Educational Resources Information Center
Yan, C. C.
1978-01-01
Demonstrates that infinitely many Lagrangians and Hamiltonians can be constructed from a given equation of motion. Points out the lack of an established criterion for making a proper selection. (Author/GA)
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.
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.
NASA Astrophysics Data System (ADS)
Sakhel, Asaad R.; Sakhel, Roger R.
2018-02-01
We examine the dynamics of a one-dimensional harmonically trapped Bose-Einstein condensate (BEC), induced by the addition of a dimple trap whose depth oscillates with time. For this purpose, the Lagrangian variational method (LVM) is applied to provide the required analytical equations. The goal is to provide an analytical explanation for the quasiperiodic oscillations of the BEC size at resonance, that is additional to the one given by Adhikari (J Phys B At Mol Opt Phys 36:1109, 2003). It is shown that LVM is able to reproduce instabilities in the dynamics along the same lines outlined by Lellouch et al. (Phys Rev X 7:021015, 2017). Moreover, it is found that at resonance the energy dynamics display ordered oscillations, whereas at off-resonance they tend to be chaotic. Further, by using the Poincare-Lindstedt method to solve the LVM equation of motion, the resulting solution is able to reproduce the quasiperiodic oscillations of the BEC.
Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models
NASA Technical Reports Server (NTRS)
Buchert, T.; Melott, A. L.; Weiss, A. G.
1993-01-01
We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the
Segmental Analysis of Cardiac Short-Axis Views Using Lagrangian Radial and Circumferential Strain.
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
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 3D tracking of fluorescent microscopic objects in motion
NASA Astrophysics Data System (ADS)
Darnige, T.; Figueroa-Morales, N.; Bohec, P.; Lindner, A.; Clément, E.
2017-05-01
We describe the development of a tracking device, mounted on an epi-fluorescent inverted microscope, suited to obtain time resolved 3D Lagrangian tracks of fluorescent passive or active micro-objects in microfluidic devices. The system is based on real-time image processing, determining the displacement of a x, y mechanical stage to keep the chosen object at a fixed position in the observation frame. The z displacement is based on the refocusing of the fluorescent object determining the displacement of a piezo mover keeping the moving object in focus. Track coordinates of the object with respect to the microfluidic device as well as images of the object are obtained at a frequency of several tenths of Hertz. This device is particularly well adapted to obtain trajectories of motile micro-organisms in microfluidic devices with or without flow.
Lagrangian 3D tracking of fluorescent microscopic objects in motion.
Darnige, T; Figueroa-Morales, N; Bohec, P; Lindner, A; Clément, E
2017-05-01
We describe the development of a tracking device, mounted on an epi-fluorescent inverted microscope, suited to obtain time resolved 3D Lagrangian tracks of fluorescent passive or active micro-objects in microfluidic devices. The system is based on real-time image processing, determining the displacement of a x, y mechanical stage to keep the chosen object at a fixed position in the observation frame. The z displacement is based on the refocusing of the fluorescent object determining the displacement of a piezo mover keeping the moving object in focus. Track coordinates of the object with respect to the microfluidic device as well as images of the object are obtained at a frequency of several tenths of Hertz. This device is particularly well adapted to obtain trajectories of motile micro-organisms in microfluidic devices with or without flow.
NASA Astrophysics Data System (ADS)
Avelino, P. P.; Azevedo, R. P. L.
2018-03-01
In this paper we show that the on-shell Lagrangian of a perfect fluid depends on microscopic properties of the fluid, giving specific examples of perfect fluids with different on-shell Lagrangians but with the same energy-momentum tensor. We demonstrate that if the fluid is constituted by localized concentrations of energy with fixed rest mass and structure (solitons) then the average on-shell Lagrangian of a perfect fluid is given by Lm=T , where T is the trace of the energy-momentum tensor. We show that our results have profound implications for theories of gravity where the matter Lagrangian appears explicitly in the equations of motion of the gravitational and matter fields, potentially leading to observable deviations from a nearly perfect cosmic microwave background black body spectrum: n -type spectral distortions, affecting the normalization of the spectral energy density. Finally, we put stringent constraints on f (R ,Lm) theories of gravity using the COBE-FIRAS measurement of the spectral radiance of the cosmic microwave background.
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.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Baskan, O.; Clercx, H. J. H; Speetjens, M. F. M.
Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progressionmore » by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.« less
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.
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.
Fingerprints of heavy scales in electroweak effective Lagrangians
NASA Astrophysics Data System (ADS)
Pich, Antonio; Rosell, Ignasi; Santos, Joaquín; Sanz-Cillero, Juan José
2017-04-01
The couplings of the electroweak effective theory contain information on the heavy-mass scales which are no-longer present in the low-energy Lagrangian. We build a general effective Lagrangian, implementing the electroweak chiral symmetry breaking SU(2) L ⊗ SU(2) R → SU(2) L+ R , which couples the known particle fields to heavier states with bosonic quantum numbers J P = 0± and 1±. We consider colour-singlet heavy fields that are in singlet or triplet representations of the electroweak group. Integrating out these heavy scales, we analyze the pattern of low-energy couplings among the light fields which are generated by the massive states. We adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs, without making any assumption about its possible doublet structure. Special attention is given to the different possible descriptions of massive spin-1 fields and the differences arising from naive implementations of these formalisms, showing their full equivalence once a proper short-distance behaviour is required.
Wang, Fang; Wang, Lin; Chen, Yuming
2017-08-31
In order to investigate the time-dependent cross-correlations of fine particulate (PM2.5) series among neighboring cities in Northern China, in this paper, we propose a new cross-correlation coefficient, the time-lagged q-L dependent height crosscorrelation coefficient (denoted by p q (τ, L)), which incorporates the time-lag factor and the fluctuation amplitude information into the analogous height cross-correlation analysis coefficient. Numerical tests are performed to illustrate that the newly proposed coefficient ρ q (τ, L) can be used to detect cross-correlations between two series with time lags and to identify different range of fluctuations at which two series possess cross-correlations. Applying the new coefficient to analyze the time-dependent cross-correlations of PM2.5 series between Beijing and the three neighboring cities of Tianjin, Zhangjiakou, and Baoding, we find that time lags between the PM2.5 series with larger fluctuations are longer than those between PM2.5 series withsmaller fluctuations. Our analysis also shows that cross-correlations between the PM2.5 series of two neighboring cities are significant and the time lags between two PM2.5 series of neighboring cities are significantly non-zero. These findings providenew scientific support on the view that air pollution in neighboring cities can affect one another not simultaneously but with a time lag.
Mean Lagrangian drift in continental shelf waves
NASA Astrophysics Data System (ADS)
Drivdal, M.; Weber, J. E. H.
2012-04-01
The time- and depth-averaged mean drift induced by barotropic continental shelf waves (CSW's) is studied theoretically for idealized shelf topography by calculating the mean volume fluxes to second order in wave amplitude. The waves suffer weak spatial damping due to bottom friction, which leads to radiation stress forcing of the mean fluxes. In terms of the total wave energy density E¯ over the shelf region, the radiation stress tensor component S¯11 for CSW's is found to be different from that of shallow water surface waves in a non-rotating ocean. For CSW's, the ratio ¯S11/¯E depends strongly on the wave number. The mean Lagrangian flow forced by the radiation stress can be subdivided into a Stokes drift and a mean Eulerian drift current. The magnitude of the latter depends on the ratio between the radiation stress and the bottom stress acting on the mean flow. When the effect of bottom friction acts equally strong on the waves and the mean current, calculations for short CSW's show that the Stokes drift and the friction-dependent wave-induced mean Eulerian current varies approximately in anti-phase over the shelf, and that the latter is numerically the largest. For long CSW's they are approximately in phase. In both cases the mean Lagrangian current, which is responsible for the net particle drift, has its largest numerical value at the coast on the shallow part of the shelf. Enhancing the effect of bottom friction on the Eulerian mean flow, results in a general current speed reduction, as well as a change in spatial structure for long waves. Applying realistic physical parameters for the continental shelf west of Norway, calculations yield along-shelf mean drift velocities for short CSW's that may be important for the transport of biological material, neutral tracers, and underwater plumes of dissolved oil from deep water drilling accidents.
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.
NASA Technical Reports Server (NTRS)
Kim, H.; Crawford, F. W.
1977-01-01
It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the Lagrangian method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion scheme described by Galloway and Kim (1971), and Lagrangians to third order in perturbation are considered. Attention is given to the averaged-Lagrangian density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.
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
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.
On the Perturbative Equivalence Between the Hamiltonian and Lagrangian Quantizations
NASA Astrophysics Data System (ADS)
Batalin, I. A.; Tyutin, I. V.
The Hamiltonian (BFV) and Lagrangian (BV) quantization schemes are proved to be perturbatively equivalent to each other. It is shown in particular that the quantum master equation being treated perturbatively possesses a local formal solution.
Vanderborght, Jan; Vereecken, Harry
2002-01-01
The local scale dispersion tensor, Dd, is a controlling parameter for the dilution of concentrations in a solute plume that is displaced by groundwater flow in a heterogeneous aquifer. In this paper, we estimate the local scale dispersion from time series or breakthrough curves, BTCs, of Br concentrations that were measured at several points in a fluvial aquifer during a natural gradient tracer test at Krauthausen. Locally measured BTCs were characterized by equivalent convection dispersion parameters: equivalent velocity, v(eq)(x) and expected equivalent dispersivity, [lambda(eq)(x)]. A Lagrangian framework was used to approximately predict these equivalent parameters in terms of the spatial covariance of log(e) transformed conductivity and the local scale dispersion coefficient. The approximate Lagrangian theory illustrates that [lambda(eq)(x)] increases with increasing travel distance and is much larger than the local scale dispersivity, lambda(d). A sensitivity analysis indicates that [lambda(eq)(x)] is predominantly determined by the transverse component of the local scale dispersion and by the correlation scale of the hydraulic conductivity in the transverse to flow direction whereas it is relatively insensitive to the longitudinal component of the local scale dispersion. By comparing predicted [lambda(eq)(x)] for a range of Dd values with [lambda(eq)(x)] obtained from locally measured BTCs, the transverse component of Dd, DdT, was estimated. The estimated transverse local scale dispersivity, lambda(dT) = DdT/U1 (U1 = mean advection velocity) is in the order of 10(1)-10(2) mm, which is relatively large but realistic for the fluvial gravel sediments at Krauthausen.
Lagrangian statistics of mesoscale turbulence in a natural environment: The Agulhas return current.
Carbone, Francesco; Gencarelli, Christian N; Hedgecock, Ian M
2016-12-01
The properties of mesoscale geophysical turbulence in an oceanic environment have been investigated through the Lagrangian statistics of sea surface temperature measured by a drifting buoy within the Agulhas return current, where strong temperature mixing produces locally sharp temperature gradients. By disentangling the large-scale forcing which affects the small-scale statistics, we found that the statistical properties of intermittency are identical to those obtained from the multifractal prediction in the Lagrangian frame for the velocity trajectory. The results suggest a possible universality of turbulence scaling.
NASA Astrophysics Data System (ADS)
Meneveau, Charles; Johnson, Perry; Hamilton, Stephen; Burns, Randal
2016-11-01
An intrinsic property of turbulent flows is the exponential deformation of fluid elements along Lagrangian paths. The production of enstrophy by vorticity stretching follows from a similar mechanism in the Lagrangian view, though the alignment statistics differ and viscosity prevents unbounded growth. In this paper, the stretching properties of fluid elements and vorticity along Lagrangian paths are studied in a channel flow at Reτ = 1000 and compared with prior, known results from isotropic turbulence. To track Lagrangian paths in a public database containing Direct Numerical Simulation (DNS) results, the task-parallel approach previously employed in the isotropic database is extended to the case of flow in a bounded domain. It is shown that above 100 viscous units from the wall, stretching statistics are equal to their isotropic values, in support of the local isotropy hypothesis. Normalized by dissipation rate, the stretching in the buffer layer and below is less efficient due to less favorable alignment statistics. The Cramér function characterizing cumulative Lagrangian stretching statistics shows that overall the channel flow has about half of the stretching per unit dissipation compared with isotropic turbulence. Supported by a National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1232825, and by National Science Foundation Grants CBET-1507469, ACI-1261715, OCI-1244820 and by JHU IDIES.
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.
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.
A new correlation coefficient for bivariate time-series data
NASA Astrophysics Data System (ADS)
Erdem, Orhan; Ceyhan, Elvan; Varli, Yusuf
2014-11-01
The correlation in time series has received considerable attention in the literature. Its use has attained an important role in the social sciences and finance. For example, pair trading in finance is concerned with the correlation between stock prices, returns, etc. In general, Pearson’s correlation coefficient is employed in these areas although it has many underlying assumptions which restrict its use. Here, we introduce a new correlation coefficient which takes into account the lag difference of data points. We investigate the properties of this new correlation coefficient. We demonstrate that it is more appropriate for showing the direction of the covariation of the two variables over time. We also compare the performance of the new correlation coefficient with Pearson’s correlation coefficient and Detrended Cross-Correlation Analysis (DCCA) via simulated examples.
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.
Space-time correlations of fluctuating velocities in turbulent shear flows
NASA Astrophysics Data System (ADS)
Zhao, Xin; He, Guo-Wei
2009-04-01
Space-time correlations or Eulerian two-point two-time correlations of fluctuating velocities are analytically and numerically investigated in turbulent shear flows. An elliptic model for the space-time correlations in the inertial range is developed from the similarity assumptions on the isocorrelation contours: they share a uniform preference direction and a constant aspect ratio. The similarity assumptions are justified using the Kolmogorov similarity hypotheses and verified using the direct numerical simulation (DNS) of turbulent channel flows. The model relates the space-time correlations to the space correlations via the convection and sweeping characteristic velocities. The analytical expressions for the convection and sweeping velocities are derived from the Navier-Stokes equations for homogeneous turbulent shear flows, where the convection velocity is represented by the mean velocity and the sweeping velocity is the sum of the random sweeping velocity and the shear-induced velocity. This suggests that unlike Taylor’s model where the convection velocity is dominating and Kraichnan and Tennekes’ model where the random sweeping velocity is dominating, the decorrelation time scales of the space-time correlations in turbulent shear flows are determined by the convection velocity, the random sweeping velocity, and the shear-induced velocity. This model predicts a universal form of the space-time correlations with the two characteristic velocities. The DNS of turbulent channel flows supports the prediction: the correlation functions exhibit a fair good collapse, when plotted against the normalized space and time separations defined by the elliptic model.
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.
Bounded fractional diffusion in geological media: Definition and Lagrangian approximation
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.
Complex-valued time-series correlation increases sensitivity in FMRI analysis.
Kociuba, Mary C; Rowe, Daniel B
2016-07-01
To develop a linear matrix representation of correlation between complex-valued (CV) time-series in the temporal Fourier frequency domain, and demonstrate its increased sensitivity over correlation between magnitude-only (MO) time-series in functional MRI (fMRI) analysis. The standard in fMRI is to discard the phase before the statistical analysis of the data, despite evidence of task related change in the phase time-series. With a real-valued isomorphism representation of Fourier reconstruction, correlation is computed in the temporal frequency domain with CV time-series data, rather than with the standard of MO data. A MATLAB simulation compares the Fisher-z transform of MO and CV correlations for varying degrees of task related magnitude and phase amplitude change in the time-series. The increased sensitivity of the complex-valued Fourier representation of correlation is also demonstrated with experimental human data. Since the correlation description in the temporal frequency domain is represented as a summation of second order temporal frequencies, the correlation is easily divided into experimentally relevant frequency bands for each voxel's temporal frequency spectrum. The MO and CV correlations for the experimental human data are analyzed for four voxels of interest (VOIs) to show the framework with high and low contrast-to-noise ratios in the motor cortex and the supplementary motor cortex. The simulation demonstrates the increased strength of CV correlations over MO correlations for low magnitude contrast-to-noise time-series. In the experimental human data, the MO correlation maps are noisier than the CV maps, and it is more difficult to distinguish the motor cortex in the MO correlation maps after spatial processing. Including both magnitude and phase in the spatial correlation computations more accurately defines the correlated left and right motor cortices. Sensitivity in correlation analysis is important to preserve the signal of interest in f
Lagrangian submanifolds with constant angle functions of the nearly Kähler S3 ×S3
NASA Astrophysics Data System (ADS)
Bektaş, Burcu; Moruz, Marilena; Van der Veken, Joeri; Vrancken, Luc
2018-04-01
We study Lagrangian submanifolds of the nearly Kähler S3 ×S3 with respect to their so called angle functions. We show that if all angle functions are constant, then the submanifold is either totally geodesic or has constant sectional curvature and there is a classification theorem that follows from Dioos et al. (2018). Moreover, we show that if precisely one angle function is constant, then it must be equal to 0 , π/3 or 2π/3. Using then two remarkable constructions together with the classification of Lagrangian submanifolds of which the first component has nowhere maximal rank from, Bektaş et al. (2018), we obtain a classification of such Lagrangian submanifolds.
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
Efficient quantum algorithm for computing n-time correlation functions.
Pedernales, J S; Di Candia, R; Egusquiza, I L; Casanova, J; Solano, E
2014-07-11
We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.
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.
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
Benefits of Time Correlation Measurements for Passive Screening
NASA Astrophysics Data System (ADS)
Murer, David; Blackie, Douglas; Peerani, Paolo
2014-02-01
The “FLASH Portals Project” is a collaboration between Arktis Radiation Detectors Ltd (CH), the Atomic Weapons Establishment (UK), and the Joint Research Centre (European Commission), supported by the Technical Support Working Group (TSWG). The program's goal was to develop and demonstrate a technology to detect shielded special nuclear materials (SNM) more efficiently and less ambiguously by exploiting time correlation. This study presents experimental results of a two-sided portal monitor equipped with in total 16 4He fast neutron detectors as well as four polyvinyltoluene (PVT) plastic scintillators. All detectors have been synchronized to nanosecond precision, thereby allowing the resolution of time correlations from timescales of tens of microseconds (such as (n, γ) reactions) down to prompt fission correlations directly. Our results demonstrate that such correlations can be detected in a typical radiation portal monitor (RPM) geometry and within operationally acceptable time scales, and that exploiting these signatures significantly improves the performance of the RPM compared to neutron counting. Furthermore, the results show that some time structure remains even in the presence of heavy shielding, thus significantly improving the sensitivity of the detection system to shielded SNM.
Remarks on the "Non-canonicity Puzzle": Lagrangian Symmetries of the Einstein-Hilbert Action
NASA Astrophysics Data System (ADS)
Kiriushcheva, N.; Komorowski, P. G.; Kuzmin, S. V.
2012-07-01
Given the non-canonical relationship between variables used in the Hamiltonian formulations of the Einstein-Hilbert action (due to Pirani, Schild, Skinner (PSS) and Dirac) and the Arnowitt-Deser-Misner (ADM) action, and the consequent difference in the gauge transformations generated by the first-class constraints of these two formulations, the assumption that the Lagrangians from which they were derived are equivalent leads to an apparent contradiction that has been called "the non-canonicity puzzle". In this work we shall investigate the group properties of two symmetries derived for the Einstein-Hilbert action: diffeomorphism, which follows from the PSS and Dirac formulations, and the one that arises from the ADM formulation. We demonstrate that unlike the diffeomorphism transformations, the ADM transformations (as well as others, which can be constructed for the Einstein-Hilbert Lagrangian using Noether's identities) do not form a group. This makes diffeomorphism transformations unique (the term "canonical" symmetry might be suggested). If the two Lagrangians are to be called equivalent, canonical symmetry must be preserved. The interplay between general covariance and the canonicity of the variables used is discussed.
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.
Floating shock fitting via Lagrangian adaptive meshes
NASA Technical Reports Server (NTRS)
Vanrosendale, John
1995-01-01
In recent work we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.
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.
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.
Lagrangian based methods for coherent structure detection
DOE Office of Scientific and Technical Information (OSTI.GOV)
Allshouse, Michael R., E-mail: mallshouse@chaos.utexas.edu; Peacock, Thomas, E-mail: tomp@mit.edu
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other twomore » approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.« less
Lagrangian based methods for coherent structure detection
NASA Astrophysics Data System (ADS)
Allshouse, Michael R.; Peacock, Thomas
2015-09-01
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.
On the use of Lagrangian variables in descriptions of unsteady boundary-layer separation
NASA Technical Reports Server (NTRS)
Cowley, Stephen J.; Vandommelen, Leon L.; Lam, Shui T.
1990-01-01
The Lagrangian description of unsteady boundary layer separation is reviewed from both analytical and numerical perspectives. It is explained in simple terms how particle distortion gives rise to unsteady separation, and why a theory centered on Lagrangian coordinates provides the clearest description of this phenomenon. Some of the more recent results for unsteady three dimensional compressible separation are included. The different forms of separation that can arise from symmetries are emphasized. A possible description of separation is also included when the detaching vorticity layer exits the classical boundary layer region, but still remains much closer to the surface than a typical body-lengthscale.
Pearson correlation estimation for irregularly sampled time series
NASA Astrophysics Data System (ADS)
Rehfeld, K.; Marwan, N.; Heitzig, J.; Kurths, J.
2012-04-01
Many applications in the geosciences call for the joint and objective analysis of irregular time series. For automated processing, robust measures of linear and nonlinear association are needed. Up to now, the standard approach would have been to reconstruct the time series on a regular grid, using linear or spline interpolation. Interpolation, however, comes with systematic side-effects, as it increases the auto-correlation in the time series. We have searched for the best method to estimate Pearson correlation for irregular time series, i.e. the one with the lowest estimation bias and variance. We adapted a kernel-based approach, using Gaussian weights. Pearson correlation is calculated, in principle, as a mean over products of previously centralized observations. In the regularly sampled case, observations in both time series were observed at the same time and thus the allocation of measurement values into pairs of products is straightforward. In the irregularly sampled case, however, measurements were not necessarily observed at the same time. Now, the key idea of the kernel-based method is to calculate weighted means of products, with the weight depending on the time separation between the observations. If the lagged correlation function is desired, the weights depend on the absolute difference between observation time separation and the estimation lag. To assess the applicability of the approach we used extensive simulations to determine the extent of interpolation side-effects with increasing irregularity of time series. We compared different approaches, based on (linear) interpolation, the Lomb-Scargle Fourier Transform, the sinc kernel and the Gaussian kernel. We investigated the role of kernel bandwidth and signal-to-noise ratio in the simulations. We found that the Gaussian kernel approach offers significant advantages and low Root-Mean Square Errors for regular, slightly irregular and very irregular time series. We therefore conclude that it is a good
Atmospheric correlation time measurements using coherent CO2 lidar
NASA Technical Reports Server (NTRS)
Ancellet, G. M.; Menzies, R. T.
1986-01-01
A pulsed TEA-CO2 lidar with coherent detection was used to measure the correlation time of backscatter from an ensemble of atmospheric aerosol particles which are illuminated by the pulsed radiation. The correlation time of the backscatter return signal is important in studies of atmospheric turbulence and its effects on optical propagation and backscatter. If the temporal coherence of the pulse is large enough, then the temporal coherence of the return signal is dominated by the turbulence and shear for a variety of interesting atmospheric conditions. Various techniques for correlation time measurement are discussed and evaluated.
AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...
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.
Dirac and Pauli form factors of nucleons using nonlocal chiral effective Lagrangian
NASA Astrophysics Data System (ADS)
He, Fangcheng; Wang, Ping
2017-11-01
Dirac and Pauli form factors are investigated in the relativistic chiral effective Lagrangian. The octet and decuplet intermediate states are included in the one-loop calculation. The 4-dimensional regulator is introduced to deal with the divergence. Different from the non-relativistic case, this 4-dimensional regulator is generated from the nonlocal Lagrangian with the gauge link, which guarantees local gauge invariance. As a result, additional diagrams appear which ensure electric charge 1 and 0 for proton and neutron respectively. The obtained Dirac and Pauli form factors of the nucleons are all reasonable up to relatively large Q 2. Supported by National Natural Science Foundation of China (11475186) and Sino-German CRC 110 (NSFC 11621131001)
Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.
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.
NASA Astrophysics Data System (ADS)
Zehe, Erwin; Jackisch, Conrad; Rodriguez, Nicolas; Klaus, Julian
2017-04-01
Only a minute amount of global fresh water is stored in the unsaturated zone. Yet this tiny compartment controls soil microbial activity and associated trace gas emissions, transport and transformations of contaminants, plant productivity, runoff generation and groundwater recharge. To date, the processes controlling renewal and age of different fractions of the soil water stock are far from being understood. Current theories and process concepts were largely inferred either from over-simplified laboratory experiments, or non-exhaustive point observations and tracer data in the field. Tracer data provide key but yet integrated information about the distribution of travel times of the tracer molecules to a certain depth or on their travel depth distribution within a given time. We hence are able to observe the "effect" of soil structure i.e. partitioning of infiltrating water between fast preferential and slow flow paths and imperfect subsequent mixing between these flow paths in the subsurface and the related plant water uptake. However, we are not able to study the "cause" - because technologies for in-situ observations of flow, flow path topology and exchange processes at relevant interfaces have up to now not been at hand. In the present study we will make use of a Lagrangian model for subsurface water dynamics to explore how subsurface heterogeneity and mixing among different storage fractions affects residence time distribution in the unsaturated zone in a forward approach. Soil water is represented by particles of constant mass, which travel according to the Itô form of the Fokker Planck equation. The model concept builds on established soil physics by estimating the drift velocity and the diffusion term based on the soil water characteristics. The model has been shown to simulate capillary driven soil moisture dynamics in good accordance with a) the Richards equation and b) observed soil moisture data in different soil. The particle model may furthermore
von Kármán–Howarth and Corrsin equations closure based on Lagrangian description of the fluid motion
DOE Office of Scientific and Technical Information (OSTI.GOV)
Divitiis, Nicola de, E-mail: n.dedivitiis@gmail.com
A new approach to obtain the closure formulas for the von Kármán–Howarth and Corrsin equations is presented, which is based on the Lagrangian representation of the fluid motion, and on the Liouville theorem associated to the kinematics of a pair of fluid particles. This kinematics is characterized by the finite scale separation vector which is assumed to be statistically independent from the velocity field. Such assumption is justified by the hypothesis of fully developed turbulence and by the property that this vector varies much more rapidly than the velocity field. This formulation leads to the closure formulas of von Kármán–Howarthmore » and Corrsin equations in terms of longitudinal velocity and temperature correlations following a demonstration completely different with respect to the previous works. Some of the properties and the limitations of the closed equations are discussed. In particular, we show that the times of evolution of the developed kinetic energy and temperature spectra are finite quantities which depend on the initial conditions.« less
Lagrangian approach to understanding the origin of the gill-kinematics switch in mayfly nymphs.
Chabreyrie, R; Balaras, E; Abdelaziz, K; Kiger, K
2014-12-01
The mayfly nymph breathes under water through an oscillating array of plate-shaped tracheal gills. As the nymph grows, the kinematics of these gills change abruptly from rowing to flapping. The classical fluid dynamics approach to consider the mayfly nymph as a pumping device fails in giving clear reasons for this switch. In order to shed some light on this switch between the two distinct kinematics, we analyze the problem under a Lagrangian viewpoint. We consider that a good Lagrangian transport that effectively distributes and stirs water and dissolved oxygen between and around the gills is the main goal of the gill motion. Using this Lagrangian approach, we are able to provide possible reasons behind the observed switch from rowing to flapping. More precisely, we conduct a series of in silico mayfly nymph experiments, where body shape, as well as gill shapes, structures, and kinematics are matched to those from in vivo. In this paper, we show both qualitatively and quantitatively how the change of kinematics enables better attraction, confinement, and stirring of water charged of dissolved oxygen inside the gills area. We reveal the attracting barriers to transport, i.e., attracting Lagrangian coherent structures, that form the transport skeleton between and around the gills. In addition, we quantify how well the fluid particles are stirred inside the gills area, which by extension leads us to conclude that it will increase the proneness of molecules of dissolved oxygen to be close enough to the gills for extraction.
The VLBA correlator: Real-time in the distributed era
NASA Technical Reports Server (NTRS)
Wells, D. C.
1992-01-01
The correlator is the signal processing engine of the Very Long Baseline Array (VLBA). Radio signals are recorded on special wideband (128 Mb/s) digital recorders at the 10 telescopes, with sampling times controlled by hydrogen maser clocks. The magnetic tapes are shipped to the Array Operations Center in Socorro, New Mexico, where they are played back simultaneously into the correlator. Real-time software and firmware controls the playback drives to achieve synchronization, compute models of the wavefront delay, control the numerous modules of the correlator, and record FITS files of the fringe visibilities at the back-end of the correlator. In addition to the more than 3000 custom VLSI chips which handle the massive data flow of the signal processing, the correlator contains a total of more than 100 programmable computers, 8-, 16- and 32-bit CPUs. Code is downloaded into front-end CPU's dependent on operating mode. Low-level code is assembly language, high-level code is C running under a RT OS. We use VxWorks on Motorola MVME147 CPU's. Code development is on a complex of SPARC workstations connected to the RT CPU's by Ethernet. The overall management of the correlation process is dependent on a database management system. We use Ingres running on a Sparcstation-2. We transfer logging information from the database of the VLBA Monitor and Control System to our database using Ingres/NET. Job scripts are computed and are transferred to the real-time computers using NFS, and correlation job execution logs and status flow back by the route. Operator status and control displays use windows on workstations, interfaced to the real-time processes by network protocols. The extensive network protocol support provided by VxWorks is invaluable. The VLBA Correlator's dependence on network protocols is an example of the radical transformation of the real-time world over the past five years. Real-time is becoming more like conventional computing. Paradoxically, 'conventional
Shear wave arrival time estimates correlate with local speckle pattern.
Mcaleavey, Stephen A; Osapoetra, Laurentius O; Langdon, Jonathan
2015-12-01
We present simulation and phantom studies demonstrating a strong correlation between errors in shear wave arrival time estimates and the lateral position of the local speckle pattern in targets with fully developed speckle. We hypothesize that the observed arrival time variations are largely due to the underlying speckle pattern, and call the effect speckle bias. Arrival time estimation is a key step in quantitative shear wave elastography, performed by tracking tissue motion via cross-correlation of RF ultrasound echoes or similar methods. Variations in scatterer strength and interference of echoes from scatterers within the tracking beam result in an echo that does not necessarily describe the average motion within the beam, but one favoring areas of constructive interference and strong scattering. A swept-receive image, formed by fixing the transmit beam and sweeping the receive aperture over the region of interest, is used to estimate the local speckle pattern. Metrics for the lateral position of the speckle are found to correlate strongly (r > 0.7) with the estimated shear wave arrival times both in simulations and in phantoms. Lateral weighting of the swept-receive pattern improved the correlation between arrival time estimates and speckle position. The simulations indicate that high RF echo correlation does not equate to an accurate shear wave arrival time estimate-a high correlation coefficient indicates that motion is being tracked with high precision, but the location tracked is uncertain within the tracking beam width. The presence of a strong on-axis speckle is seen to imply high RF correlation and low bias. The converse does not appear to be true-highly correlated RF echoes can still produce biased arrival time estimates. The shear wave arrival time bias is relatively stable with variations in shear wave amplitude and sign (-20 μm to 20 μm simulated) compared with the variation with different speckle realizations obtained along a given tracking
Comment on ``Canonical formalism for Lagrangians with nonlocality of finite extent''
NASA Astrophysics Data System (ADS)
Llosa, Josep
2003-01-01
The paper by Woodward [Phys. Rev. A 62, 052105 (2000)] claimed to have proved that Lagrangian theories with a nonlocality of finite extent are necessarily unstable. In this Comment we propose that this conclusion is false.
NASA Astrophysics Data System (ADS)
Hernandez, Fabrice; Le Traon, Pierre-Yves; Morrow, Rosemary
1995-12-01
The SEMAPHORE mesoscale air/sea experiment was conducted in the Azores-Madeira region from July to November 1993. TOPEX/POSEIDON (T/P) and ERS 1 were flying simultaneously at that time. The main purposes of this paper are to evaluate the estimation of the oceanic mesoscale circulation from the two different sets of altimetric data (T/P and ERS 1) and to compare the results with in situ measurements provided by the SEMAPHORE hydrographic surveys and surface drifters (three expendable bathytermograph conductivity-temperature-depth surveys in a 500-km2 box and a set of 47 Lagrangian surface drifters drogued at 150 m). Comparisons are carried out through the maps obtained by objective analysis from the four data sets. The mapping accuracy of T/P, ERS 1, T/P and ERS 1 combined, and in situ data is investigated, as well as the sensitivity of the mapping to the correlation functions used. There is a good qualitative agreement between altimetric maps and corresponding drifter and hydrographic maps for the three hydrographic surveys. Correlations are about 0.8, and the regression fit is about 0.6-0.7; the lower values are due to the smooth climatology used to reference the altimetric maps. The correlation for time differences is better, with regression lines not significantly different from 1, especially when ERS 1 and T/P are combined. T/P mapping is almost as good as ERS 1 mapping, which was rather unexpected since the ERS 1 space-time sampling is better suited for the mesoscale. This may reflect the fact that the signal mapped by the hydrography and drifters does not contain the high frequency/wavenumber components. T/P and ERS 1 combined provide better results, although the improvement is not as large as expected, probably for the same reason.
Contractions of AdS brane algebra and superGalileon Lagrangians
DOE Office of Scientific and Technical Information (OSTI.GOV)
Kamimura, Kiyoshi; Onda, Seiji
2013-06-15
We examine AdS Galileon Lagrangians using the method of nonlinear realization. By contractions (1) flat curvature limit, (2) non-relativistic brane algebra limit, and (3) (1) + (2) limits we obtain DBI, Newton-Hoock, and Galilean Galileons, respectively. We make clear how these Lagrangians appear as invariant 4-forms and/or pseudo-invariant Wess-Zumino (WZ) terms using Maurer-Cartan (MC) equations on the coset G/SO(3, 1). We show the equations of motion are written in terms of the MC forms only and explain why the inverse Higgs condition is obtained as the equation of motion for all cases. The supersymmetric extension is also examined using amore » supercoset SU(2, 2 Double-Vertical-Line 1)/(SO(3, 1) Multiplication-Sign U(1)) and five WZ forms are constructed. They are reduced to the corresponding five Galileon WZ forms in the bosonic limit and are candidates for supersymmetric Galileon action.« less
NASA Astrophysics Data System (ADS)
Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M. N.; Head-Gordon, Teresa; Skylaris, Chris-Kriton
2017-03-01
Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.
Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M N; Head-Gordon, Teresa; Skylaris, Chris-Kriton
2017-03-28
Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes-in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.
Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; ...
2017-03-28
Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less
DOE Office of Scientific and Technical Information (OSTI.GOV)
Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex
Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less
DOE Office of Scientific and Technical Information (OSTI.GOV)
Yoon, Heesun; Cho, Jungyeon; Kim, Jongsoo, E-mail: hsyoon@cnu.ac.kr, E-mail: jcho@cnu.ac.kr, E-mail: jskim@kasi.re.kr
Turbulent motions naturally produce density and magnetic-field fluctuations. Correlation between the two fluctuations is important for interpretation of observations, such as observations of the rotation measure (RM). In this paper, we study the effect of driving schemes on the density-magnetic-field correlation. In particular, we numerically investigate how the correlation time of driving affects the correlation between density and magnetic field. We perform compressible magnetohydrodynamic turbulence simulations at different sonic Mach numbers ( M {sub s} ), using two different driving schemes—a finite-correlated driving and a delta-correlated driving. In the former, the forcing vectors change continuously with a correlation time comparablemore » to the large-eddy turnover time. In the latter, the direction (and amplitude) of driving changes in a very short timescale. The finite-correlated driving results in strong anti-correlation between two fields when the sonic and the Alfvénic Mach numbers are similar to unity (i.e., when M {sub s} ∼ 1 and M {sub A} ∼ 1, respectively). However, the anti-correlation becomes weaker and approaches zero for higher values of M {sub s} or M {sub A}. The delta-correlated driving produces virtually no correlation between two fields when M {sub s} ∼ 1 and M {sub A} ∼ 1, and produces more and more positive correlations as M {sub s} or M {sub A} increases. We conjecture that two competing effects, tendency for achieving balance between the gas and the magnetic pressure and simultaneous compression of fluid and magnetic field, determine the correlation behavior. We also investigate how different driving schemes affect the Probability Density Function of three-dimensional density, dispersion measure, and RM.« less
Effects of Eddy Viscosity on Time Correlations in Large Eddy Simulation
NASA Technical Reports Server (NTRS)
He, Guowei; Rubinstein, R.; Wang, Lian-Ping; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
Subgrid-scale (SGS) models for large. eddy simulation (LES) have generally been evaluated by their ability to predict single-time statistics of turbulent flows such as kinetic energy and Reynolds stresses. Recent application- of large eddy simulation to the evaluation of sound sources in turbulent flows, a problem in which time, correlations determine the frequency distribution of acoustic radiation, suggest that subgrid models should also be evaluated by their ability to predict time correlations in turbulent flows. This paper compares the two-point, two-time Eulerian velocity correlation evaluated from direct numerical simulation (DNS) with that evaluated from LES, using a spectral eddy viscosity, for isotropic homogeneous turbulence. It is found that the LES fields are too coherent, in the sense that their time correlations decay more slowly than the corresponding time. correlations in the DNS fields. This observation is confirmed by theoretical estimates of time correlations using the Taylor expansion technique. Tile reason for the slower decay is that the eddy viscosity does not include the random backscatter, which decorrelates fluid motion at large scales. An effective eddy viscosity associated with time correlations is formulated, to which the eddy viscosity associated with energy transfer is a leading order approximation.
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.
Lagrangian Statistics of Slightly Buoyant Droplets in Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Gopalan, Balaji; Malkiel, Edwin; Katz, Joseph
2006-11-01
This project examines the dynamics of slightly buoyant diesel droplets in isotropic turbulence using high speed in-line digital Holographic PIV. A cloud of droplets with specific gravity of 0.85 is injected into the central portion of an isotropic turbulence facility. The droplet trajectories are measured in a 50x50x50 mm̂3 sample volume using high speed in-line digital holography. An automated program has been developed to obtain accurate time history of droplet velocities. Data analysis determines the PDF of velocity and acceleration in three dimensions. The time histories enable us to calculate the three dimensional Lagrangian velocity autocorrelation function, and from them the diffusion coefficients. Due to buoyancy the vertical diffusion time scale exceeds the horizontal one by about 65% .The diffusion coefficients vary between 2.8 cm̂2/sec in the horizontal direction to 5.5 cm̂2/sec in the vertical direction. For droplets with size varying from 2 to 11 Kolmogorov scales there are no clear trends with size. The variations of diffusion rates for different turbulent intensities and the effect of finite window size are presently examined. For shorter time scales, when the diffusion need not be Fickian the three dimensional trajectories can be used to calculate the generalized dispersion tensor and measure the time elapsed for diffusion to become Fickian.
LAGRANGIAN MODELING OF A SUSPENDED-SEDIMENT PULSE.
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.
Gupta, Puneet; Bhowmick, Brojeshwar; Pal, Arpan
2017-07-01
Camera-equipped devices are ubiquitous and proliferating in the day-to-day life. Accurate heart rate (HR) estimation from the face videos acquired from the low cost cameras in a non-contact manner, can be used in many real-world scenarios and hence, require rigorous exploration. This paper has presented an accurate and near real-time HR estimation system using these face videos. It is based on the phenomenon that the color and motion variations in the face video are closely related to the heart beat. The variations also contain the noise due to facial expressions, respiration, eye blinking and environmental factors which are handled by the proposed system. Neither Eulerian nor Lagrangian temporal signals can provide accurate HR in all the cases. The cases where Eulerian temporal signals perform spuriously are determined using a novel poorness measure and then both the Eulerian and Lagrangian temporal signals are employed for better HR estimation. Such a fusion is referred as serial fusion. Experimental results reveal that the error introduced in the proposed algorithm is 1.8±3.6 which is significantly lower than the existing well known systems.
Heuristic approach to Satellite Range Scheduling with Bounds using Lagrangian Relaxation.
DOE Office of Scientific and Technical Information (OSTI.GOV)
Brown, Nathanael J. K.; Arguello, Bryan; Nozick, Linda Karen
This paper focuses on scheduling antennas to track satellites using a heuristic method. In order to validate the performance of the heuristic, bounds are developed using Lagrangian relaxation. The performance of the algorithm is established using several illustrative problems.
A Lagrangian perspective of the hydrological cycle in the Congo River basin
NASA Astrophysics Data System (ADS)
Sorí, Rogert; Nieto, Raquel; Vicente-Serrano, Sergio M.; Drumond, Anita; Gimeno, Luis
2017-08-01
The Lagrangian model FLEXPART is used to identify the moisture sources of the Congo River basin (CRB) and investigate their role in the hydrological cycle. This model allows us to track atmospheric parcels while calculating changes in the specific humidity through the budget of evaporation minus precipitation. This method permits the annual-scale identification of five continental and four oceanic principal regions that provide moisture to the CRB from both hemispheres over the course of the year. The most important is the CRB, which provides more than 50 % of the total atmospheric moisture contribution to precipitation over itself. Additionally, both the land that extends to the east of the CRB and the eastern equatorial South Atlantic Ocean are very important sources, while the Red Sea source is merely important in the (E - P) budget over the CRB despite its high evaporation rate. The moisture-sink patterns over the CRB in air masses that were tracked forward in time from all the sources follow the latitudinal rainfall migration and are mostly highly correlated with the pattern of the precipitation rate, ensuring a link between them. In wet (dry) years, the contribution of moisture to precipitation from the CRB over itself increases (decreases). Despite the enhanced evaporative conditions over the basin during dry years, the vertically integrated moisture flux (VIMF) divergence inhibits precipitation and suggests the transport of moisture from the CRB to remote regions.
Time series, correlation matrices and random matrix models
DOE Office of Scientific and Technical Information (OSTI.GOV)
Vinayak; Seligman, Thomas H.
2014-01-08
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series.more » By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc. The common theme of the lectures is thus the importance of random matrix theory in a wide range of fields in and around physics.« less
Dynamic correlations at different time-scales with empirical mode decomposition
NASA Astrophysics Data System (ADS)
Nava, Noemi; Di Matteo, T.; Aste, Tomaso
2018-07-01
We introduce a simple approach which combines Empirical Mode Decomposition (EMD) and Pearson's cross-correlations over rolling windows to quantify dynamic dependency at different time scales. The EMD is a tool to separate time series into implicit components which oscillate at different time-scales. We apply this decomposition to intraday time series of the following three financial indices: the S&P 500 (USA), the IPC (Mexico) and the VIX (volatility index USA), obtaining time-varying multidimensional cross-correlations at different time-scales. The correlations computed over a rolling window are compared across the three indices, across the components at different time-scales and across different time lags. We uncover a rich heterogeneity of interactions, which depends on the time-scale and has important lead-lag relations that could have practical use for portfolio management, risk estimation and investment decisions.
Shear Wave Arrival Time Estimates Correlate with Local Speckle Pattern
McAleavey, Stephen A.; Osapoetra, Laurentius O.; Langdon, Jonathan
2016-01-01
We present simulation and phantom studies demonstrating a strong correlation between errors in shear wave arrival time estimates and the lateral position of the local speckle pattern in targets with fully developed speckle. We hypothesize that the observed arrival time variations are largely due to the underlying speckle pattern, and call the effect speckle bias. Arrival time estimation is a key step in quantitative shear wave elastography, performed by tracking tissue motion via cross correlation of RF ultrasound echoes or similar methods. Variations in scatterer strength and interference of echoes from scatterers within the tracking beam result in an echo that does not necessarily describe the average motion within the beam, but one favoring areas of constructive interference and strong scattering. A swept-receive image, formed by fixing the transmit beam and sweeping the receive aperture over the region of interest, is used to estimate the local speckle pattern. Metrics for the lateral position of the speckle are found to correlate strongly (r>0.7) with the estimated shear wave arrival times both in simulations and in phantoms. Lateral weighting of the swept-receive pattern improved the correlation between arrival time estimates and speckle position. The simulations indicate that high RF echo correlation does not equate to an accurate shear wave arrival time estimate – a high correlation coefficient indicates that motion is being tracked with high precision, but the location tracked is uncertain within the tracking beam width. The presence of a strong on-axis speckle is seen to imply high RF correlation and low bias. The converse does not appear to be true – highly correlated RF echoes can still produce biased arrival time estimates. The shear wave arrival time bias is relatively stable with variations in shear wave amplitude and sign (−20 μm to 20 μm simulated) compared to the variation with different speckle realizations obtained along a given tracking
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
NASA Astrophysics Data System (ADS)
Wong, Jaime G.; Rosi, Giuseppe A.; Rouhi, Amirreza; Rival, David E.
2017-10-01
Particle tracking velocimetry (PTV) produces high-quality temporal information that is often neglected when computing spatial gradients. A method is presented here to utilize this temporal information in order to improve the estimation of spatial gradients for spatially unstructured Lagrangian data sets. Starting with an initial guess, this method penalizes any gradient estimate where the substantial derivative of vorticity along a pathline is not equal to the local vortex stretching/tilting. Furthermore, given an initial guess, this method can proceed on an individual pathline without any further reference to neighbouring pathlines. The equivalence of the substantial derivative and vortex stretching/tilting is based on the vorticity transport equation, where viscous diffusion is neglected. By minimizing the residual of the vorticity-transport equation, the proposed method is first tested to reduce error and noise on a synthetic Taylor-Green vortex field dissipating in time. Furthermore, when the proposed method is applied to high-density experimental data collected with `Shake-the-Box' PTV, noise within the spatial gradients is significantly reduced. In the particular test case investigated here of an accelerating circular plate captured during a single run, the method acts to delineate the shear layer and vortex core, as well as resolve the Kelvin-Helmholtz instabilities, which were previously unidentifiable without the use of ensemble averaging. The proposed method shows promise for improving PTV measurements that require robust spatial gradients while retaining the unstructured Lagrangian perspective.
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.
Chiral Lagrangian with Heavy Quark-Diquark Symmetry
DOE Office of Scientific and Technical Information (OSTI.GOV)
Jie Hu; Thomas Mehen
2005-11-29
We construct a chiral Lagrangian for doubly heavy baryons and heavy mesons that is invariant under heavy quark-diquark symmetry at leading order and includes the leading O(1/m{sub Q}) symmetry violating operators. The theory is used to predict the electromagnetic decay width of the J=3/2 member of the ground state doubly heavy baryon doublet. Numerical estimates are provided for doubly charm baryons. We also calculate chiral corrections to doubly heavy baryon masses and strong decay widths of low lying excited doubly heavy baryons.
Double-time correlation functions of two quantum operations in open systems
NASA Astrophysics Data System (ADS)
Ban, Masashi
2017-10-01
A double-time correlation function of arbitrary two quantum operations is studied for a nonstationary open quantum system which is in contact with a thermal reservoir. It includes a usual correlation function, a linear response function, and a weak value of an observable. Time evolution of the correlation function can be derived by means of the time-convolution and time-convolutionless projection operator techniques. For this purpose, a quasidensity operator accompanied by a fictitious field is introduced, which makes it possible to derive explicit formulas for calculating a double-time correlation function in the second-order approximation with respect to a system-reservoir interaction. The derived formula explicitly shows that the quantum regression theorem for calculating the double-time correlation function cannot be used if a thermal reservoir has a finite correlation time. Furthermore, the formula is applied for a pure dephasing process and a linear dissipative process. The quantum regression theorem and the the Leggett-Garg inequality are investigated for an open two-level system. The results are compared with those obtained by exact calculation to examine whether the formula is a good approximation.
Lagrangian analysis. Modern tool of the dynamics of solids
NASA Astrophysics Data System (ADS)
Cagnoux, J.; Chartagnac, P.; Hereil, P.; Perez, M.; Seaman, L.
Explosive metal-working, material synthesis under shock loading, terminal ballistics, and explosive rock-blasting, are some of the civil and military fields of activity that call for a wider knowledge about the behavior of materials subjected to strong dynamic pressures. It is in these fields that Lagrangian analysis methods, the subject of this work, prove to be a useful investigative tool for the physicist. Lagrangian analysis was developed around 1970 by Fowles and Williams. The idea is based on the integration of the conservation equations of mechanics using stress or particle velocity records obtained by means of transducers placed in the path of a stress wave. In this way, all the kinematical and mechanical quantities contained in the conservation equations are obtained. In the first chapter the authors introduce the mathematical tools used to analyze plane and spherical one-dimensional motions. For plane motion, they describe the mathematical analysis methods pertinent to the three regimes of wave propagation encountered : the non-attenuating unsteady wave, the simple wave, and the attenuating unsteady wave. In each of these regimes, cases are treated for which either stress or particle velocity records are initially available. The authors insist that one or the other groups of data (stress and particle velocity) are sufficient to integrate the conservation equations in the case of the plane motion when both groups of data are necessary in the case of the spherical motion. However, in spite of this additional difficulty, Lagrangian analysis of the spherical motion remains particularly interesting for the physicist because it allows access to the behavior of the material under deformation processes other than that imposed by plane one-dimensional motion. The methods expounded in the first chapter are based on Lagrangian measurement of particle velocity and stress in relation to time in a material compressed by a plane or spherical dilatational wave. The
GPU-accelerated computing for Lagrangian coherent structures of multi-body gravitational regimes
NASA Astrophysics Data System (ADS)
Lin, Mingpei; Xu, Ming; Fu, Xiaoyu
2017-04-01
Based on a well-established theoretical foundation, Lagrangian Coherent Structures (LCSs) have elicited widespread research on the intrinsic structures of dynamical systems in many fields, including the field of astrodynamics. Although the application of LCSs in dynamical problems seems straightforward theoretically, its associated computational cost is prohibitive. We propose a block decomposition algorithm developed on Compute Unified Device Architecture (CUDA) platform for the computation of the LCSs of multi-body gravitational regimes. In order to take advantage of GPU's outstanding computing properties, such as Shared Memory, Constant Memory, and Zero-Copy, the algorithm utilizes a block decomposition strategy to facilitate computation of finite-time Lyapunov exponent (FTLE) fields of arbitrary size and timespan. Simulation results demonstrate that this GPU-based algorithm can satisfy double-precision accuracy requirements and greatly decrease the time needed to calculate final results, increasing speed by approximately 13 times. Additionally, this algorithm can be generalized to various large-scale computing problems, such as particle filters, constellation design, and Monte-Carlo simulation.
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.
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.
Application of Lagrangian blending functions for grid generation around airplane geometries
NASA Technical Reports Server (NTRS)
Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.
1990-01-01
A simple procedure was developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation was employed for the grid distributions.
Time correlation between mononucleosis and initial symptoms of MS
Endriz, John; Ho, Peggy P.
2017-01-01
Objective: To determine the average age of MS onset vs the age at which Epstein-Barr infection has previously occurred and stratify this analysis by sex and the blood level of Epstein-Barr nuclear antigen 1 (EBNA1) antibody. Methods: Using infectious mononucleosis (IM) as a temporal marker in data from the Swedish epidemiologic investigation of MS, 259 adult IM/MS cases were identified and then augmented to account for “missing” childhood data so that the average age of MS onset could be determined for cases binned by age of IM (as stratified by sex and EBNA1 titer level). Results: Mean age of IM vs mean age of MS reveals a positive time correlation for all IM ages (from ∼5 to ∼30 years), with IM-to-MS delay decreasing with increased age. When bifurcated by sex or EBNA1 blood titer levels, males and high-titer subpopulations show even stronger positive time correlation, while females and low-titer populations show negative time correlation in early childhood (long IM/MS delay). The correlation becomes positive in females beyond puberty. Conclusions: IM/MS time correlation implies causality if IM is time random. Alternative confounding models seem implausible, in light of constraints imposed by time-invariant delay observed here. Childhood infection with Epstein-Barr virus (EBV) in females and/or those genetically prone to low EBNA1 blood titers will develop MS slowly. Males and/or high EBNA1-prone develop MS more rapidly following IM infection at all ages. For all, postpubescent EBV infection is critical for the initiation and rapid development of MS. PMID:28271078
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
Ku, S.; Hager, R.; Chang, C. S.; ...
2016-04-01
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. In conclusion, the numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
DOE Office of Scientific and Technical Information (OSTI.GOV)
Ku, S.; Hager, R.; Chang, C. S.
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. In conclusion, the numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
DOE Office of Scientific and Technical Information (OSTI.GOV)
Ku, S., E-mail: sku@pppl.gov; Hager, R.; Chang, C.S.
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less
Laboratory experiment on the 3D tide-induced Lagrangian residual current using the PIV technique
NASA Astrophysics Data System (ADS)
Chen, Yang; Jiang, Wensheng; Chen, Xu; Wang, Tao; Bian, Changwei
2017-12-01
The 3D structure of the tide-induced Lagrangian residual current was studied using the particle image velocimetry (PIV) technique in a long shallow narrow tank in the laboratory. At the mouth of the tank, a wave generator was used to make periodic wave which represents the tide movement, and at the head of the tank, a laterally sloping topography with the length of one fifth of the water tank was installed, above which the tide-induced Lagrangian residual current was studied. Under the weakly nonlinear condition in the present experiment setup, the results show that the Lagrangian residual velocity (LRV) field has a three-layer structure. The residual current flows inwards (towards the head) in the bottom layer and flows outwards in the middle layer, while in the surface layer, it flows inwards along the shallow side of the sloping topography and outwards along the deep side. The depth-averaged and breadth-averaged LRV are also analyzed based on the 3D LRV observations. Our results are in good agreement with the previous experiment studies, the analytical solutions with similar conditions and the observational results in real bays. Moreover, the volume flux comparison between the Lagrangian and Eulerian residual currents shows that the Eulerian residual velocity violates the mass conservation law while the LRV truly represents the inter-tidal water transport. This work enriches the laboratory studies of the LRV and offers valuable references for the LRV studies in real bays.
Ghost-Free Theory with Third-Order Time Derivatives
NASA Astrophysics Data System (ADS)
Motohashi, Hayato; Suyama, Teruaki; Yamaguchi, Masahide
2018-06-01
As the first step to extend our understanding of higher-derivative theories, within the framework of analytic mechanics of point particles, we construct a ghost-free theory involving third-order time derivatives in Lagrangian. While eliminating linear momentum terms in the Hamiltonian is necessary and sufficient to kill the ghosts associated with higher derivatives for Lagrangian with at most second-order derivatives, we find that this is necessary but not sufficient for the Lagrangian with higher than second-order derivatives. We clarify a set of ghost-free conditions under which we show that the Hamiltonian is bounded, and that equations of motion are reducible into a second-order system.
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.
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.
Application of Quasi-Lagrangian Diagnostics and FGGE Data in a Study of East-Coast Cyclogenesis.
1981-09-01
QUASI-LAGRANGIAN UDIAGNOSTICS AND FGGE DATA IN A STUDY OF EAST-COAST CYCLOGENESIS by Donald A. Roman September 1981 Thesis Advisor: Dr. Carlyle H. Wash...REPORT DOCUMENTATION PAGE DEVFOR COMPLETING FORM I.M9PR UM19 2. GOV? AccaS "@ "mO L.VIPICUTS CA? ALOG MUUNW S TyP =F NOo’BP io OE4. TITLC (nd Sisle . ye i...n.J000 Application of Quasi-Lagrangian Master’s Thesis Diagnostics and FGGE Data in a Study 0#4 September 1981 East-Coast Cyclogenesis C PlaPranIWG
NASA Astrophysics Data System (ADS)
Mei, Dongcheng; Xie, Chongwei; Zhang, Li
2003-11-01
We study the effects of correlations between additive and multiplicative noise on relaxation time in a bistable system driven by cross-correlated noise. Using the projection-operator method, we derived an analytic expression for the relaxation time Tc of the system, which is the function of additive (α) and multiplicative (D) noise intensities, correlation intensity λ of noise, and correlation time τ of noise. After introducing a noise intensity ratio and a dimensionless parameter R=D/α, and then performing numerical computations, we find the following: (i) For the case of R<1, the relaxation time Tc increases as R increases. (ii) For the cases of R⩾1, there is a one-peak structure on the Tc-R plot and the effects of cross-correlated noise on the relaxation time are very notable. (iii) For the case of R<1, Tc almost does not change with both λ and τ, and for the cases of R⩾1, Tc decreases as λ increases, however Tc increases as τ increases. λ and τ play opposite roles in Tc, i.e., λ enhances the fluctuation decay of dynamical variable and τ slows down the fluctuation decay of dynamical variable.
Applications of Lagrangian blending functions for grid generation around airplane geometries
NASA Technical Reports Server (NTRS)
Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.; Smith, Robert E.
1990-01-01
A simple procedure has been developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation has been employed for the grid distributions.
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.
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.
An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics
DOE Office of Scientific and Technical Information (OSTI.GOV)
Wu, Tong; Shashkov, Mikhail Jurievich; Morgan, Nathaniel Ray
Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas dynamics. The new method evolves conserved unknowns in the current configuration, which obviates the Jacobi matrix that maps the element in a reference coordinate system or the initial coordinate system to the current configuration. The density, momentum, and total energy (ρ, ρu, E) are approximated with conservative higher-order Taylor expansions over the element and are limited toward a piecewise constant field near discontinuities using a limiter. Two new limiting methods are presented for enforcing the bounds on the primitive variables of density, velocity, and specific internal energymore » (ρ, u, e). The nodal velocity, and the corresponding forces, are calculated by solving an approximate Riemann problem at the element nodes. An explicit second-order method is used to temporally advance the solution. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. 1D Cartesian coordinates test problem results are presented to demonstrate the accuracy and convergence order of the new DG method with the new limiters.« less
An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics
Wu, Tong; Shashkov, Mikhail Jurievich; Morgan, Nathaniel Ray; ...
2018-04-09
Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas dynamics. The new method evolves conserved unknowns in the current configuration, which obviates the Jacobi matrix that maps the element in a reference coordinate system or the initial coordinate system to the current configuration. The density, momentum, and total energy (ρ, ρu, E) are approximated with conservative higher-order Taylor expansions over the element and are limited toward a piecewise constant field near discontinuities using a limiter. Two new limiting methods are presented for enforcing the bounds on the primitive variables of density, velocity, and specific internal energymore » (ρ, u, e). The nodal velocity, and the corresponding forces, are calculated by solving an approximate Riemann problem at the element nodes. An explicit second-order method is used to temporally advance the solution. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. 1D Cartesian coordinates test problem results are presented to demonstrate the accuracy and convergence order of the new DG method with the new limiters.« less
Pulse transmission receiver with higher-order time derivative pulse correlator
Dress, Jr., William B.; Smith, Stephen F.
2003-09-16
Systems and methods for pulse-transmission low-power communication modes are disclosed. A pulse transmission receiver includes: a higher-order time derivative pulse correlator; a demodulation decoder coupled to the higher-order time derivative pulse correlator; a clock coupled to the demodulation decoder; and a pseudorandom polynomial generator coupled to both the higher-order time derivative pulse correlator and the clock. The systems and methods significantly reduce lower-frequency emissions from pulse transmission spread-spectrum communication modes, which reduces potentially harmful interference to existing radio frequency services and users and also simultaneously permit transmission of multiple data bits by utilizing specific pulse shapes.
Correlates of sedentary time in children: a multilevel modelling approach.
Gomes, Thayse Natacha; dos Santos, Fernanda Karina; Santos, Daniel; Pereira, Sara; Chaves, Raquel; Katzmarzyk, Peter Todd; Maia, José
2014-08-30
Sedentary behaviour (SB) has been implicated as a potential risk factor for chronic disease. Since children spend most of their awake time in schools, this study aimed to identify individual- and school-level correlates of sedentary time using a multilevel approach, and to determine if these correlates have a similar effect in normal weight (NW) and overweight/obese (O/O) children. Sample comprised 686 Portuguese children aged 9-10 years from 23 schools that took part in the ISCOLE project. Actigraph GT3X + accelerometers were used 24 hours/day for 7 days to assess sedentary time (daily minutes <100 counts/min); BMI was computed and WHO cut-points were used to classify subjects as NW or O/O. Sex, BMI, number of siblings, family income, computer use on school days, and sleep time on school days were used as individual-level correlates. At the school level, school size (number of students), percentage of students involved in sports or physical activity (PA) clubs, school promotion of active transportation, and students' access to equipment outside school hours were used. All multilevel modelling analysis was done in SPSS, WINPEPI, and HLM. School-level correlates explain ≈ 6.0% of the total variance in sedentary time. Results (β ± SE) showed that boys (-30.85 ± 5.23), children with more siblings (-8.56 ± 2.71) and those who sleep more (-17.78 ± 3.06) were less sedentary, while children with higher family income were more sedentary (4.32 ± 1.68). At the school level, no variable was significantly correlated with sedentary time. Among weight groups, variables related to sedentary time in NW were sex, sleep time and family income, while in O/O sex, number of siblings and sleep time were significant correlates. No school-level predictors were significantly associated in either of the weight groups. Notwithstanding the relevance of the school environment in the reduction of children's sedentary time, individual and family characteristics played a more relevant
Equilibrium time correlation functions and the dynamics of fluctuations
DOE Office of Scientific and Technical Information (OSTI.GOV)
Luban, Marshall; Luscombe, James H.
1999-12-01
Equilibrium time correlation functions are of great importance because they probe the equilibrium dynamical response to external perturbations. We discuss the properties of time correlation functions for several systems that are simple enough to illustrate the calculational steps involved. The discussion underscores the need for avoiding language which misleadingly suggests that thermal equilibrium is associated with a quiescent or moribund state of the system. (c) 1999 American Association of Physics Teachers.
Determination of the Time-Space Magnetic Correlation Functions in the Solar Wind
NASA Astrophysics Data System (ADS)
Weygand, J. M.; Matthaeus, W. H.; Kivelson, M.; Dasso, S.
2013-12-01
Magnetic field data from many different intervals and 7 different solar wind spacecraft are employed to estimate the scale-dependent time decorrelation function in the interplanetary magnetic field in both the slow and fast solar wind. This estimation requires correlations varying with both space and time lags. The two point correlation function with no time lag is determined by correlating time series data from multiple spacecraft separated in space and for complete coverage of length scales relies on many intervals with different spacecraft spatial separations. In addition we employ single spacecraft time-lagged correlations, and two spacecraft time lagged correlations to access different spatial and temporal correlation data. Combining these data sets gives estimates of the scale-dependent time decorrelation function, which in principle tells us how rapidly time decorrelation occurs at a given wavelength. For static fields the scale-dependent time decorrelation function is trivially unity, but in turbulence the nonlinear cascade process induces time-decorrelation at a given length scale that occurs more rapidly with decreasing scale. The scale-dependent time decorrelation function is valuable input to theories as well as various applications such as scattering, transport, and study of predictability. It is also a fundamental element of formal turbulence theory. Our results are extension of the Eulerian correlation functions estimated in Matthaeus et al. [2010], Weygand et al [2012; 2013].
A hybrid Lagrangian Voronoi-SPH scheme
NASA Astrophysics Data System (ADS)
Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.
2018-07-01
A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.
A hybrid Lagrangian Voronoi-SPH scheme
NASA Astrophysics Data System (ADS)
Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.
2017-11-01
A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.
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.
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
Scalable Methods for Eulerian-Lagrangian Simulation Applied to Compressible Multiphase Flows
NASA Astrophysics Data System (ADS)
Zwick, David; Hackl, Jason; Balachandar, S.
2017-11-01
Multiphase flows can be found in countless areas of physics and engineering. Many of these flows can be classified as dispersed two-phase flows, meaning that there are solid particles dispersed in a continuous fluid phase. A common technique for simulating such flow is the Eulerian-Lagrangian method. While useful, this method can suffer from scaling issues on larger problem sizes that are typical of many realistic geometries. Here we present scalable techniques for Eulerian-Lagrangian simulations and apply it to the simulation of a particle bed subjected to expansion waves in a shock tube. The results show that the methods presented here are viable for simulation of larger problems on modern supercomputers. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1315138. This work was supported in part by the U.S. Department of Energy under Contract No. DE-NA0002378.
Source apportion of atmospheric particulate matter: a joint Eulerian/Lagrangian approach.
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.
Lamb, D C; Müller, B K; Bräuchle, C
2005-10-01
Fluorescence correlation spectroscopy (FCS) and fluorescence cross-correlation spectroscopy (FCCS) are methods that extract information about a sample from the influence of thermodynamic equilibrium fluctuations on the fluorescence intensity. This method allows dynamic information to be obtained from steady state equilibrium measurements and its popularity has dramatically increased in the last 10 years due to the development of high sensitivity detectors and its combination with confocal microscopy. Using time-correlated single-photon counting (TCSPC) detection and pulsed excitation, information over the duration of the excited state can be extracted and incorporated in the analysis. In this short review, we discuss new methodologies that have recently emerged which incorporated fluorescence lifetime information or TCSPC data in the FCS and FCCS analysis. Time-gated FCS discriminates between which photons are to be incorporated in the analysis dependent upon their arrival time after excitation. This allows for accurate FCS measurements in the presence of fluorescent background, determination of sample homogeneity, and the ability to distinguish between static and dynamic heterogeneities. A similar method, time-resolved FCS can be used to resolve the individual correlation functions from multiple fluorophores through the different fluorescence lifetimes. Pulsed interleaved excitation (PIE) encodes the excitation source into the TCSPC data. PIE can be used to perform dual-channel FCCS with a single detector and allows elimination of spectral cross-talk with dual-channel detection. For samples that undergo fluorescence resonance energy transfer (FRET), quantitative FCCS measurements can be performed in spite of the FRET and the static FRET efficiency can be determined.
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
Lagrangian dynamics of the mistral during the HyMeX SOP2
NASA Astrophysics Data System (ADS)
Drobinski, P.; Alonzo, B.; Basdevant, C.; Cocquerez, P.; Doerenbecher, A.; Fourrié, N.; Nuret, M.
2017-02-01
The mistral refers to a severe wind blowing over the Gulf of Lions after being channeled in the Rhone valley. It influences the western Mediterranean climate as it brings cold and dry continental air over the warm western Mediterranean, generating intense air-sea heat exchanges and sea surface cooling, inducing the formation of the western Mediterranean deep water that moves into the Atlantic Ocean. The mistral is frequently observed to extend as far as a few hundred kilometers from the coast, and its fine-scale dynamics over the sea is still only partially understood as finely resolved observations in time and space are lacking. The boundary layer pressurized balloons (BLPB) developed by the Centre National d'Etudes Spatiales and deployed during HyMeX SOP2 allowed the Lagrangian documentation of the mistral events that occurred between beginning of February to mid-March 2013. Analyzed in synergy with the AROME-WMED weather forecast model, all the terms of the Lagrangian formulation of the momentum conservation equation could be quantified showing three different regions: (1) an injection zone where the mistral flow is directed toward the center of the Genoa cyclone due to a strong zonal pressure gradient, enhanced friction, and entrainment in the mountain wake; (2) an ejection zone where the flow is deflected outward of the cyclone due to either the nonnegligible inertia pseudoforce or an inertial oscillation caused by a sudden friction decrease; and (3) a region of geostrophic deceleration due to the weakening of the pressure gradient.
Lagrangian dynamics of the mistral during the HyMeX SOP2
NASA Astrophysics Data System (ADS)
Drobinski, Philippe; Alonzo, Bastien; Basdevant, Claude; Cocquerez, Philippe; Fourrié, Nadia; Nuret, Mathieu
2017-04-01
The mistral refers to a severe wind blowing over the Gulf of Lions after being channeled in the Rhone valley. It influences the western Mediterranean climate as it brings cold and dry continental air over the warm western Mediterranean, generating intense air-sea heat exchanges and sea surface cooling, inducing the formation of the western Mediterranean deep water that moves into the Atlantic Ocean. The mistral is frequently observed to extend as far as a few hundred kilometers from the coast, and its fine-scale dynamics over the sea is still only partially understood as finely resolved observations in time and space are lacking. The boundary layer pressurized balloons (BLPB) developed by the Centre National d'Etudes Spatiales and deployed during HyMeX SOP2 allowed the Lagrangian documentation of the mistral events that occurred between beginning of February to mid-March 2013. Analyzed in synergy with the AROME-WMED weather forecast model, all the terms of the Lagrangian formulation of the momentum conservation equation could be quantified showing three different regions: (1) an injection zone where the mistral flow is directed toward the center of the Genoa cyclone due to a strong zonal pressure gradient, enhanced friction, and entrainment in the mountain wake; (2) an ejection zone where the flow is deflected outward of the cyclone due to either the nonnegligible inertia pseudoforce or an inertial oscillation caused by a sudden friction decrease; and (3) a region of geostrophic deceleration due to the weakening of the pressure gradient.
Modeling space-time correlations of velocity fluctuations in wind farms
NASA Astrophysics Data System (ADS)
Lukassen, Laura J.; Stevens, Richard J. A. M.; Meneveau, Charles; Wilczek, Michael
2018-07-01
An analytical model for the streamwise velocity space-time correlations in turbulent flows is derived and applied to the special case of velocity fluctuations in large wind farms. The model is based on the Kraichnan-Tennekes random sweeping hypothesis, capturing the decorrelation in time while including a mean wind velocity in the streamwise direction. In the resulting model, the streamwise velocity space-time correlation is expressed as a convolution of the pure space correlation with an analytical temporal decorrelation kernel. Hence, the spatio-temporal structure of velocity fluctuations in wind farms can be derived from the spatial correlations only. We then explore the applicability of the model to predict spatio-temporal correlations in turbulent flows in wind farms. Comparisons of the model with data from a large eddy simulation of flow in a large, spatially periodic wind farm are performed, where needed model parameters such as spatial and temporal integral scales and spatial correlations are determined from the large eddy simulation. Good agreement is obtained between the model and large eddy simulation data showing that spatial data may be used to model the full temporal structure of fluctuations in wind farms.
On the Space-Time Structure of Sheared Turbulence
NASA Astrophysics Data System (ADS)
de Maré, Martin; Mann, Jakob
2016-09-01
We develop a model that predicts all two-point correlations in high Reynolds number turbulent flow, in both space and time. This is accomplished by combining the design philosophies behind two existing models, the Mann spectral velocity tensor, in which isotropic turbulence is distorted according to rapid distortion theory, and Kristensen's longitudinal coherence model, in which eddies are simultaneously advected by larger eddies as well as decaying. The model is compared with data from both observations and large-eddy simulations and is found to predict spatial correlations comparable to the Mann spectral tensor and temporal coherence better than any known model. Within the developed framework, Lagrangian two-point correlations in space and time are also predicted, and the predictions are compared with measurements of isotropic turbulence. The required input to the models, which are formulated as spectral velocity tensors, can be estimated from measured spectra or be derived from the rate of dissipation of turbulent kinetic energy, the friction velocity and the mean shear of the flow. The developed models can, for example, be used in wind-turbine engineering, in applications such as lidar-assisted feed forward control and wind-turbine wake modelling.
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.
Correlated errors in geodetic time series: Implications for time-dependent deformation
Langbein, J.; Johnson, H.
1997-01-01
Analysis of frequent trilateration observations from the two-color electronic distance measuring networks in California demonstrate that the noise power spectra are dominated by white noise at higher frequencies and power law behavior at lower frequencies. In contrast, Earth scientists typically have assumed that only white noise is present in a geodetic time series, since a combination of infrequent measurements and low precision usually preclude identifying the time-correlated signature in such data. After removing a linear trend from the two-color data, it becomes evident that there are primarily two recognizable types of time-correlated noise present in the residuals. The first type is a seasonal variation in displacement which is probably a result of measuring to shallow surface monuments installed in clayey soil which responds to seasonally occurring rainfall; this noise is significant only for a small fraction of the sites analyzed. The second type of correlated noise becomes evident only after spectral analysis of line length changes and shows a functional relation at long periods between power and frequency of and where f is frequency and ?? ??? 2. With ?? = 2, this type of correlated noise is termed random-walk noise, and its source is mainly thought to be small random motions of geodetic monuments with respect to the Earth's crust, though other sources are possible. Because the line length changes in the two-color networks are measured at irregular intervals, power spectral techniques cannot reliably estimate the level of I//" noise. Rather, we also use here a maximum likelihood estimation technique which assumes that there are only two sources of noise in the residual time series (white noise and randomwalk noise) and estimates the amount of each. From this analysis we find that the random-walk noise level averages about 1.3 mm/Vyr and that our estimates of the white noise component confirm theoretical limitations of the measurement technique. In
Tao, Guohua; Miller, William H
2011-07-14
An efficient time-dependent importance sampling method is developed for the Monte Carlo calculation of time correlation functions via the initial value representation (IVR) of semiclassical (SC) theory. A prefactor-free time-dependent sampling function weights the importance of a trajectory based on the magnitude of its contribution to the time correlation function, and global trial moves are used to facilitate the efficient sampling the phase space of initial conditions. The method can be generally applied to sampling rare events efficiently while avoiding being trapped in a local region of the phase space. Results presented in the paper for two system-bath models demonstrate the efficiency of this new importance sampling method for full SC-IVR calculations.
Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics.
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.
Anderson, James S M; Ayers, Paul W
2018-06-30
Generalizing our recent work on relativistic generalizations of the quantum theory of atoms in molecules, we present the general setting under which the principle of stationary action for a region leads to open quantum subsystems. The approach presented here is general and works for any Hamiltonian, and when a reasonable Lagrangian is selected, it often leads to the integral of the Laplacian of the electron density on the region vanishing as a necessary condition for the zero-flux surface. Alternatively, with this method, one can design a Lagrangian that leads to a surface of interest (though this Lagrangian may not be, and indeed probably will not be, "reasonable"). For any reasonable Lagrangian for the electronic wave function and any two-component method (related by integration by parts to the Hamiltonian) considered, the Bader definition of an atom is recaptured. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.
Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems
NASA Astrophysics Data System (ADS)
Campoamor-Stursberg, Rutwig
2017-03-01
Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.
Lagrangians and Euler morphisms from connections on the frame bundle
NASA Astrophysics Data System (ADS)
Kurek, J.; Mikulski, W. M.
2011-07-01
We classify all natural operators transforming torsion free classical linear connections ∇ on m-dimensional manifolds M into r-th order Lagrangians λ(∇) and Euler morphisms E(∇) on the linear frame bundle P1M. We also briefly write how this classification result can be generalized on higher order frame bundles PkM instead of P1M.
Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems
DOE Office of Scientific and Technical Information (OSTI.GOV)
Campoamor-Stursberg, Rutwig, E-mail: rutwig@ucm.es
Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.
Local normalization: Uncovering correlations in non-stationary financial time series
NASA Astrophysics Data System (ADS)
Schäfer, Rudi; Guhr, Thomas
2010-09-01
The measurement of correlations between financial time series is of vital importance for risk management. In this paper we address an estimation error that stems from the non-stationarity of the time series. We put forward a method to rid the time series of local trends and variable volatility, while preserving cross-correlations. We test this method in a Monte Carlo simulation, and apply it to empirical data for the S&P 500 stocks.
Multiscale multifractal detrended cross-correlation analysis of financial time series
NASA Astrophysics Data System (ADS)
Shi, Wenbin; Shang, Pengjian; Wang, Jing; Lin, Aijing
2014-06-01
In this paper, we introduce a method called multiscale multifractal detrended cross-correlation analysis (MM-DCCA). The method allows us to extend the description of the cross-correlation properties between two time series. MM-DCCA may provide new ways of measuring the nonlinearity of two signals, and it helps to present much richer information than multifractal detrended cross-correlation analysis (MF-DCCA) by sweeping all the range of scale at which the multifractal structures of complex system are discussed. Moreover, to illustrate the advantages of this approach we make use of the MM-DCCA to analyze the cross-correlation properties between financial time series. We show that this new method can be adapted to investigate stock markets under investigation. It can provide a more faithful and more interpretable description of the dynamic mechanism between financial time series than traditional MF-DCCA. We also propose to reduce the scale ranges to analyze short time series, and some inherent properties which remain hidden when a wide range is used may exhibit perfectly in this way.
Temporal and spectral manipulations of correlated photons using a time lens
NASA Astrophysics Data System (ADS)
Mittal, Sunil; Orre, Venkata Vikram; Restelli, Alessandro; Salem, Reza; Goldschmidt, Elizabeth A.; Hafezi, Mohammad
2017-10-01
A common challenge in quantum information processing with photons is the limited ability to manipulate and measure correlated states. An example is the inability to measure picosecond-scale temporal correlations of a multiphoton state, given state-of-the-art detectors have a temporal resolution of about 100 ps. Here, we demonstrate temporal magnification of time-bin-entangled two-photon states using a time lens and measure their temporal correlation function, which is otherwise not accessible because of the limited temporal resolution of single-photon detectors. Furthermore, we show that the time lens maps temporal correlations of photons to frequency correlations and could be used to manipulate frequency-bin-entangled photons. This demonstration opens a new avenue to manipulate and analyze spectral and temporal wave functions of many-photon states.
Space-time correlations in urban sprawl.
Hernando, A; Hernando, R; Plastino, A
2014-02-06
Understanding demographic and migrational patterns constitutes a great challenge. Millions of individual decisions, motivated by economic, political, demographic, rational and/or emotional reasons underlie the high complexity of demographic dynamics. Significant advances in quantitatively understanding such complexity have been registered in recent years, as those involving the growth of cities but many fundamental issues still defy comprehension. We present here compelling empirical evidence of a high level of regularity regarding time and spatial correlations in urban sprawl, unravelling patterns about the inertia in the growth of cities and their interaction with each other. By using one of the world's most exhaustive extant demographic data basis--that of the Spanish Government's Institute INE, with records covering 111 years and (in 2011) 45 million people, distributed among more than 8000 population nuclei--we show that the inertia of city growth has a characteristic time of 15 years, and its interaction with the growth of other cities has a characteristic distance of 80 km. Distance is shown to be the main factor that entangles two cities (60% of total correlations). The power of our current social theories is thereby enhanced.
Distributed Control by Lagrangian Steepest Descent
NASA Technical Reports Server (NTRS)
Wolpert, David H.; Bieniawski, Stefan
2004-01-01
Often adaptive, distributed control can be viewed as an iterated game between independent players. The coupling between the players mixed strategies, arising as the system evolves from one instant to the next, is determined by the system designer. Information theory tells us that the most likely joint strategy of the players, given a value of the expectation of the overall control objective function, is the minimizer of a function o the joint strategy. So the goal of the system designer is to speed evolution of the joint strategy to that Lagrangian mhimbhgpoint,lowerthe expectated value of the control objective function, and repeat Here we elaborate the theory of algorithms that do this using local descent procedures, and that thereby achieve efficient, adaptive, distributed control.
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.
LSPRAY-V: A Lagrangian Spray Module
NASA Technical Reports Server (NTRS)
Raju, M. S.
2015-01-01
LSPRAY-V is a Lagrangian spray solver developed for application with unstructured grids and massively parallel computers. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray encountered over a wide range of operating conditions in modern aircraft engine development. It could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. 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. With the development of LSPRAY-V, we have advanced the state-of-the-art in spray computations in several important ways.
Lagrangian Vortices in Developing Tropical Cyclones
2015-06-25
45 −6 −4 −2 0 2 4 6 8 10 Hyperbolic trajectory Vortex core Shear sheath Lagrangian...5 10 15 20 25 30 35 40 45 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 × 10−9 (a) P13LP16E P17L 700 hPa 700 hPa 4590804102 100 80 60 40 20 0 0 5 10...15 20 25 30 35 40 45 −8 −6 −4 −2 0 2 4 6 8 10(b) Figure 4. The (a) OW (s−2) and (b) OWLag (radians) fields for the Atlantic development region at
Alternative transfer to the Earth-Moon Lagrangian points L4 and L5 using lunar gravity assist
NASA Astrophysics Data System (ADS)
Salazar, F. J. T.; Macau, E. E. N.; Winter, O. C.
2014-02-01
Lagrangian points L4 and L5 lie at 60° ahead of and behind the Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. As so, these Lagrangian points represent remarkable positions to host astronomical observatories or space stations. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies elliptic trajectories from an Earth circular parking orbit to reach the Moon's sphere of influence and apply a swing-by maneuver in order to re-direct the path of a spacecraft to a vicinity of the Lagrangian points L4 and L5. Once the geocentric transfer orbit and the initial impulsive thrust have been determined, the goal is to establish the angle at which the geocentric trajectory crosses the lunar sphere of influence in such a way that when the spacecraft leaves the Moon's gravitational field, its trajectory and velocity with respect to the Earth change in order to the spacecraft arrives at L4 and L5. In this work, the planar Circular Restricted Three Body Problem approximation is used and in order to avoid solving a two boundary problem, the patched-conic approximation is considered.
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
DOE Office of Scientific and Technical Information (OSTI.GOV)
Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich
Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of Lagrangian methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible Lagrangian methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less