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

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.

Perfect fluid Lagrangian and its cosmological implications in theories of gravity with nonminimally coupled matter fields

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.

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

PubMed

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

2017-10-11

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

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.

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.

Extending geometrical optics: A Lagrangian theory for vector waves

NASA Astrophysics Data System (ADS)

Ruiz, D. E.

2016-10-01

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

Form of the manifestly covariant Lagrangian

NASA Astrophysics Data System (ADS)

Johns, Oliver Davis

1985-10-01

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

Lagrangian 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.

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

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories

NASA Astrophysics Data System (ADS)

Román-Roy, Narciso

2009-11-01

This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.

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

PubMed

Cheng, Ching-An; Huang, Han-Pang

2016-12-01

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

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

PubMed

Holm, Darryl D.

2002-06-01

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

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

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

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

1975-07-01

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

Extending geometrical optics: A Lagrangian theory for vector waves

DOE PAGES

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

2017-03-16

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

Extending geometrical optics: A Lagrangian theory for vector waves

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

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

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

Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches

NASA Astrophysics Data System (ADS)

Antonowicz, Marek; Szczyrba, Wiktor

1985-06-01

We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.

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.

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.

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.

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

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.

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

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.

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.

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.

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.

Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data

DTIC Science & Technology

2015-09-30

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

Extended Lagrangian Excited State Molecular Dynamics.

PubMed

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

2018-02-13

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

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.

Mean-Lagrangian formalism and covariance of fluid turbulence.

PubMed

Ariki, Taketo

2017-05-01

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

Extended Lagrangian Excited State Molecular Dynamics

DOE PAGES

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

2018-01-09

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

Extended Lagrangian Excited State Molecular Dynamics

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

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

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

Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation

NASA Astrophysics Data System (ADS)

Frønsdal, Christian

Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein-Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier-Stokes-Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the B-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.

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

PubMed

Samelson, R M

2013-01-01

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

Next generation extended Lagrangian first principles molecular dynamics

NASA Astrophysics Data System (ADS)

Niklasson, Anders M. N.

2017-08-01

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

Next generation extended Lagrangian first principles molecular dynamics.

PubMed

Niklasson, Anders M N

2017-08-07

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Generalized extended Lagrangian Born-Oppenheimer molecular dynamics

DOE PAGES

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

2014-10-29

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

Sakata-Taketani spin-0 theory with external field interactions - Lagrangian formalism and causal properties

NASA Technical Reports Server (NTRS)

Guertin, R. F.; Wilson, T. L.

1977-01-01

To illustrate that a relativistic field theory need not be manifestly covariant, Lorentz-invariant Lagrangian densities are constructed that yield the equation satisfied by an interacting (two-component) Sakata-Taketani spin-0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric second-rank tensor, and a symmetric second-rank tensor, with the results specialized to electromagnetic interactions. For either of the two second-rank couplings, the equation is found to describe noncausal wave propagation, a property that is apparent from the dependence of the coefficients of the space derivatives on the external field; in contrast, the noncausality of the corresponding manifestly covariant Duffin-Kemmer-Petiau spin-0 equation is not so obvious. The possibilities for generalizing the results to higher spin theories involving only the essential 2(2J + 1) components for a particle with a definite spin J and mass m are discussed in considerable detail.

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.

Deconstructing field-induced ketene isomerization through Lagrangian descriptors.

PubMed

Craven, Galen T; Hernandez, Rigoberto

2016-02-07

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

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.

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.

Differential geometry based solvation model II: Lagrangian formulation.

PubMed

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

2011-12-01

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

Differential geometry based solvation model II: Lagrangian formulation

PubMed Central

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

2010-01-01

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

Foundations for a theory of gravitation theories

NASA Technical Reports Server (NTRS)

Thorne, K. S.; Lee, D. L.; Lightman, A. P.

1972-01-01

A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold. The foundation consists of (1) a glossary of fundamental concepts; (2) a theorem that delineates the overlap between Lagrangian-based theories and metric theories; (3) a conjecture (due to Schiff) that the Weak Equivalence Principle implies the Einstein Equivalence Principle; and (4) a plausibility argument supporting this conjecture for the special case of relativistic, Lagrangian-based theories.

Spectral-clustering approach to Lagrangian vortex detection.

PubMed

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

2016-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Some Lagrangians for systems without a Lagrangian

NASA Astrophysics Data System (ADS)

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

2011-03-01

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

Lagrangian descriptors of driven chemical reaction manifolds.

PubMed

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

2017-08-01

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

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

PubMed

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

2015-08-01

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

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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

PubMed

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

2017-03-28

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

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

DOE PAGES

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

2017-03-28

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

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

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

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex

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

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

PubMed

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

2017-09-01

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

Toroidal regularization of the guiding center Lagrangian

DOE PAGES

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

2017-11-22

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

Toroidal regularization of the guiding center Lagrangian

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

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

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

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.

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

PubMed Central

Cotter, C. J.

2017-01-01

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

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

USGS Publications Warehouse

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

1986-01-01

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

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.

Reconstructing baryon oscillations: A Lagrangian theory perspective

NASA Astrophysics Data System (ADS)

Padmanabhan, Nikhil; White, Martin; Cohn, J. D.

2009-03-01

Recently Eisenstein and collaborators introduced a method to “reconstruct” the linear power spectrum from a nonlinearly evolved galaxy distribution in order to improve precision in measurements of baryon acoustic oscillations. We reformulate this method within the Lagrangian picture of structure formation, to better understand what such a method does, and what the resulting power spectra are. We show that reconstruction does not reproduce the linear density field, at second order. We however show that it does reduce the damping of the oscillations due to nonlinear structure formation, explaining the improvements seen in simulations. Our results suggest that the reconstructed power spectrum is potentially better modeled as the sum of three different power spectra, each dominating over different wavelength ranges and with different nonlinear damping terms. Finally, we also show that reconstruction reduces the mode-coupling term in the power spectrum, explaining why miscalibrations of the acoustic scale are reduced when one considers the reconstructed power spectrum.

The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems

NASA Astrophysics Data System (ADS)

Koon, Wang Sang; Marsden, Jerrold E.

1997-08-01

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

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.

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

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

NASA Astrophysics Data System (ADS)

Sandler, U.

2017-11-01

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

Extreme Lagrangian acceleration in confined turbulent flow.

PubMed

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

2008-05-09

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

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

PubMed

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

2014-02-01

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

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

PubMed

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

2015-07-14

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

Lagrangian averaging with geodesic mean

NASA Astrophysics Data System (ADS)

Oliver, Marcel

2017-11-01

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

Lagrangian averaging with geodesic mean.

PubMed

Oliver, Marcel

2017-11-01

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

A Theoretical Framework for Lagrangian Descriptors

NASA Astrophysics Data System (ADS)

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

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

Sigma decomposition: the CP-odd Lagrangian

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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.

Ordered rate constitutive theories for thermoviscoelastic solids with memory in Lagrangian description using Gibbs potential

NASA Astrophysics Data System (ADS)

Surana, K. S.; Reddy, J. N.; Nunez, Daniel

2015-11-01

This paper presents ordered rate constitutive theories of orders m and n, i.e., ( m, n) for finite deformation of homogeneous, isotropic, compressible and incompressible thermoviscoelastic solids with memory in Lagrangian description using entropy inequality in Gibbs potential Ψ as an alternate approach of deriving constitutive theories using entropy inequality in terms of Helmholtz free energy density Φ. Second Piola-Kirchhoff stress σ [0] and Green's strain tensor ɛ [0] are used as conjugate pair. We consider Ψ, heat vector q, entropy density η and rates of upto orders m and n of σ [0] and ɛ [0], i.e., σ [ i]; i = 0, 1, . . . , m and ɛ [ j]; j = 0, 1, . . . , n. We choose Ψ, ɛ [ n], q and η as dependent variables in the constitutive theories with ɛ [ j]; j = 0, 1, . . . , n - 1, σ [ i]; i = 0, 1, . . . , m, temperature gradient g and temperature θ as their argument tensors. Rationale for this choice is explained in the paper. Entropy inequality, decomposition of σ [0] into equilibrium and deviatoric stresses, the conditions resulting from entropy inequality and the theory of generators and invariants are used in the derivations of ordered rate constitutive theories of orders m and n in stress and strain tensors. Constitutive theories for the heat vector q (of up to orders m and n - 1) that are consistent (in terms of the argument tensors) with the constitutive theories for ɛ [ n] (of up to orders m and n) are also derived. Many simplified forms of the rate theories of orders ( m, n) are presented. Material coefficients are derived by considering Taylor series expansions of the coefficients in the linear combinations representing ɛ [ n] and q using the combined generators of the argument tensors about a known configuration {{\\underline{\\varOmega}}} in the combined invariants of the argument tensors and temperature. It is shown that the rate constitutive theories of order one ( m = 1, n = 1) when further simplified result in constitutive

On redundant variables in Lagrangian mechanics, with applications to perturbation theory and KS regularization. [Kustaanheimo-Stiefel two body problem

NASA Technical Reports Server (NTRS)

Broucke, R.; Lass, H.

1975-01-01

It is shown that it is possible to make a change of variables in a Lagrangian in such a way that the number of variables is increased. The Euler-Lagrange equations in the redundant variables are obtained in the standard way (without the use of Lagrange multipliers). These equations are not independent but they are all valid and consistent. In some cases they are simpler than if the minimum number of variables are used. The redundant variables are supposed to be related to each other by several constraints (not necessarily holonomic), but these constraints are not used in the derivation of the equations of motion. The method is illustrated with the well known Kustaanheimo-Stiefel regularization. Some interesting applications to perturbation theory are also described.

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.

Microscopic Lagrangian description of warm plasmas. I - Linear wave propagation. II - Nonlinear wave interactions

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.

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

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

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

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

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

DOE PAGES

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

2015-06-26

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

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

USGS Publications Warehouse

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

2014-01-01

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

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.)

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

Lagrangian postprocessing of computational hemodynamics.

PubMed

Shadden, Shawn C; Arzani, Amirhossein

2015-01-01

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

Lagrangian postprocessing of computational hemodynamics

PubMed Central

Shadden, Shawn C.; Arzani, Amirhossein

2014-01-01

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

Hamiltonian analysis for linearly acceleration-dependent Lagrangians

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

Cruz, Miguel, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Gómez-Cortés, Rosario, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Rojas, Efraín, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx

2016-06-15

We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies togethermore » with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant field theories.« less

Forecasting Future Sea Ice Conditions: A Lagrangian Approach

DTIC Science & Technology

2015-09-30

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

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.

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.

Uncovering the Geometry of Barrierless Reactions Using Lagrangian Descriptors.

PubMed

Junginger, Andrej; Hernandez, Rigoberto

2016-03-03

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

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.

Coherent Lagrangian swirls among submesoscale motions.

PubMed

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

2018-03-05

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

Alternative kinetic energy metrics for Lagrangian systems

NASA Astrophysics Data System (ADS)

Sarlet, W.; Prince, G.

2010-11-01

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

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.

On the Lagrangian description of unsteady boundary-layer separation. I - General theory

NASA Technical Reports Server (NTRS)

Van Dommelen, Leon L.; Cowley, Stephen J.

1990-01-01

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

An extended Lagrangian method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1992-01-01

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

Extended vector-tensor theories

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

Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp

Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Procamore » theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.« less

Target Lagrangian kinematic simulation for particle-laden flows.

PubMed

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

2016-09-01

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

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

PubMed

Krause, Katharina; Klopper, Wim

2016-01-28

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

Communication: A simplified coupled-cluster Lagrangian for polarizable embedding

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

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

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

A Chiang-type lagrangian in CP^2

NASA Astrophysics Data System (ADS)

Cannas da Silva, Ana

2018-03-01

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

Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

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

Langlois, David; Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr

2016-02-01

Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering ''degenerate'' Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degeneratemore » cases. We also identify new families of scalar-tensor theories with the property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.« 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.

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.

Computing eddy-driven effective diffusivity using Lagrangian particles

DOE PAGES

Wolfram, Phillip J.; Ringler, Todd D.

2017-08-14

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

Computing eddy-driven effective diffusivity using Lagrangian particles

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

Wolfram, Phillip J.; Ringler, Todd D.

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

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

NASA Astrophysics Data System (ADS)

Verma, Aman; Mahesh, Krishnan

2012-08-01

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

Loop amplitudes in an extended gravity theory

NASA Astrophysics Data System (ADS)

Dunbar, David C.; Godwin, John H.; Jehu, Guy R.; Perkins, Warren B.

2018-05-01

We extend the S-matrix of gravity by the addition of the minimal three-point amplitude or equivalently adding R3 terms to the Lagrangian. We demonstrate how Unitarity can be used to simply examine the renormalisability of this theory and determine the R4 counter-terms that arise at one-loop. We find that the combination of R4 terms that arise in the extended theory is complementary to the R4 counter-term associated with supersymmetric Lagrangians.

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.

Improving fast generation of halo catalogues with higher order Lagrangian perturbation theory

NASA Astrophysics Data System (ADS)

Munari, Emiliano; Monaco, Pierluigi; Sefusatti, Emiliano; Castorina, Emanuele; Mohammad, Faizan G.; Anselmi, Stefano; Borgani, Stefano

2017-03-01

We present the latest version of PINOCCHIO, a code that generates catalogues of dark matter haloes in an approximate but fast way with respect to an N-body simulation. This code version implements a new on-the-fly production of halo catalogue on the past light cone with continuous time sampling, and the computation of particle and halo displacements are extended up to third-order Lagrangian perturbation theory (LPT), in contrast with previous versions that used Zel'dovich approximation. We run PINOCCHIO on the same initial configuration of a reference N-body simulation, so that the comparison extends to the object-by-object level. We consider haloes at redshifts 0 and 1, using different LPT orders either for halo construction or to compute halo final positions. We compare the clustering properties of PINOCCHIO haloes with those from the simulation by computing the power spectrum and two-point correlation function in real and redshift space (monopole and quadrupole), the bispectrum and the phase difference of halo distributions. We find that 2LPT and 3LPT give noticeable improvement. 3LPT provides the best agreement with N-body when it is used to displace haloes, while 2LPT gives better results for constructing haloes. At the highest orders, linear bias is typically recovered at a few per cent level. In Fourier space and using 3LPT for halo displacements, the halo power spectrum is recovered to within 10 per cent up to kmax ∼ 0.5 h Mpc-1. The results presented in this paper have interesting implications for the generation of large ensemble of mock surveys for the scientific exploitation of data from big surveys.

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

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

Dvoeglazov, V.V.

1993-12-01

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

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

NASA Technical Reports Server (NTRS)

Vandommelen, Leon L.; Cowley, Stephen J.

1989-01-01

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Cosmological bouncing solutions in extended teleparallel gravity theories

NASA Astrophysics Data System (ADS)

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

2018-05-01

In the context of extended teleparallel gravity theories with a 3 +1 -dimensional Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological bouncing scenarios in a four-dimensional Friedmann-Lemaître-Robertson-Walker geometry. We study which types of gravitational Lagrangians are capable of reconstructing bouncing solutions provided by analytical expressions for symmetric, oscillatory, superbounce, matter bounce, and singular bounce. Some of the Lagrangians discovered are analytical at the origin, having both Minkowski and Schwarzschild vacuum solutions. All these results open up the possibility for such theories to be competitive candidates of extended theories of gravity in cosmological scales.

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.

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

PubMed

Anderson, James S M; Ayers, Paul W

2018-06-30

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

Lagrangian speckle model and tissue-motion estimation--theory.

PubMed

Maurice, R L; Bertrand, M

1999-07-01

It is known that when a tissue is subjected to movements such as rotation, shearing, scaling, etc., changes in speckle patterns that result act as a noise source, often responsible for most of the displacement-estimate variance. From a modeling point of view, these changes can be thought of as resulting from two mechanisms: one is the motion of the speckles and the other, the alterations of their morphology. In this paper, we propose a new tissue-motion estimator to counteract these speckle decorrelation effects. The estimator is based on a Lagrangian description of the speckle motion. This description allows us to follow local characteristics of the speckle field as if they were a material property. This method leads to an analytical description of the decorrelation in a way which enables the derivation of an appropriate inverse filter for speckle restoration. The filter is appropriate for linear geometrical transformation of the scattering function (LT), i.e., a constant-strain region of interest (ROI). As the LT itself is a parameter of the filter, a tissue-motion estimator can be formulated as a nonlinear minimization problem, seeking the best match between the pre-tissue-motion image and a restored-speckle post-motion image. The method is tested, using simulated radio-frequency (RF) images of tissue undergoing axial shear.

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.

A new theory of gravity

NASA Technical Reports Server (NTRS)

Ni, W.

1972-01-01

A new relativistic theory of gravity is presented. This theory agrees with all experiments to date. It is a metric theory, it is Lagrangian-based, and it possesses a preferred frame with conformally-flat space slices. With an appropriate choice of certain adjustable functions and parameters, this theory possesses precisely the same post-Newtonian limit as general relativity.

Lagrangian ocean analysis: Fundamentals and practices

DOE PAGES

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

2017-11-24

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

Lagrangian ocean analysis: Fundamentals and practices

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Lagrangian ocean analysis: Fundamentals and practices

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

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

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

Beyond Lovelock gravity: Higher derivative metric theories

NASA Astrophysics Data System (ADS)

Crisostomi, M.; Noui, K.; Charmousis, C.; Langlois, D.

2018-02-01

We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than 2 degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-tensor theories." Although they all raise the same concern as Chern-Simons gravity, they can nevertheless make sense as low energy effective field theories or, by restricting them to the unitary gauge (where the scalar field is uniform), as Lorentz breaking theories with a parity violating sector.

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.

Product Distribution Theory for Control of Multi-Agent Systems

NASA Technical Reports Server (NTRS)

Lee, Chia Fan; Wolpert, David H.

2004-01-01

Product Distribution (PD) theory is a new framework for controlling Multi-Agent Systems (MAS's). First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint stare of the agents. Accordingly we can consider a team game in which the shared utility is a performance measure of the behavior of the MAS. For such a scenario the game is at equilibrium - the Lagrangian is optimized - when the joint distribution of the agents optimizes the system's expected performance. One common way to find that equilibrium is to have each agent run a reinforcement learning algorithm. Here we investigate the alternative of exploiting PD theory to run gradient descent on the Lagrangian. We present computer experiments validating some of the predictions of PD theory for how best to do that gradient descent. We also demonstrate how PD theory can improve performance even when we are not allowed to rerun the MAS from different initial conditions, a requirement implicit in some previous work.

Two-dimensional Lagrangian simulation of suspended sediment

USGS Publications Warehouse

Schoellhamer, David H.

1988-01-01

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

A new theory of gravity.

NASA Technical Reports Server (NTRS)

Ni, W.-T.

1973-01-01

A new relativistic theory of gravity is presented. This theory agrees with all experiments to date. It is a metric theory; it is Lagrangian-based; and it possesses a preferred frame with conformally flat space slices. With an appropriate choice of certain adjustable functions and parameters and of the cosmological model, this theory possesses precisely the same post-Newtonian limit as general relativity.

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.

A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation.

PubMed

Kristensen, Kasper; Eriksen, Janus J; Matthews, Devin A; Olsen, Jeppe; Jørgensen, Poul

2016-02-14

We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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.

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.

Chaotic Lagrangian models for turbulent relative dispersion.

PubMed

Lacorata, Guglielmo; Vulpiani, Angelo

2017-04-01

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

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.

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.

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

NASA Technical Reports Server (NTRS)

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

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-08-01

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

Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations

NASA Astrophysics Data System (ADS)

Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

2012-06-01

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics.

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.

A few words about resonances in the electroweak effective Lagrangian

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

Rosell, Ignasi; Pich, Antonio; Santos, Joaquín

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

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.

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.

Euler-Lagrangian computation for estuarine hydrodynamics

USGS Publications Warehouse

Cheng, Ralph T.

1983-01-01

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

Instability of black strings in the third-order Lovelock theory

NASA Astrophysics Data System (ADS)

Giacomini, Alex; Henríquez-Báez, Carla; Lagos, Marcela; Oliva, Julio; Vera, Aldo

2016-05-01

We show that homogeneous black strings of third-order Lovelock theory are unstable under s-wave perturbations. This analysis is done in dimension D =9 , which is the lowest dimension that allows the existence of homogeneous black strings in a theory that contains only the third-order Lovelock term in the Lagrangian. As is the case in general relativity, the instability is produced by long wavelength perturbations and it stands for the perturbative counterpart of a thermal instability. We also provide a comparative analysis of the instabilities of black strings at a fixed radius in general relativity, Gauss-Bonnet, and third-order Lovelock theories. We show that the minimum critical wavelength that triggers the instability grows with the power of the curvature defined in the Lagrangian. The maximum exponential growth during the time of the perturbation is the largest in general relativity and it decreases with the number of curvatures involved in the Lagrangian.

An Extended Lagrangian Method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1995-01-01

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

An extended Lagrangian method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1993-01-01

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

Soft collinear effective theory for gravity

NASA Astrophysics Data System (ADS)

Okui, Takemichi; Yunesi, Arash

2018-03-01

We present how to construct a soft collinear effective theory (SCET) for gravity at the leading and next-to-leading powers from the ground up. The soft graviton theorem and decoupling of collinear gravitons at the leading power are manifest from the outset in the effective symmetries of the theory. At the next-to-leading power, certain simple structures of amplitudes, which are completely obscure in Feynman diagrams of the full theory, are also revealed, which greatly simplifies calculations. The effective Lagrangian is highly constrained by effectively multiple copies of diffeomorphism invariance that are inevitably present in gravity SCET due to mode separation, an essential ingredient of any SCET. Further explorations of effective theories of gravity with mode separation may shed light on Lagrangian-level understandings of some of the surprising properties of gravitational scattering amplitudes. A gravity SCET with an appropriate inclusion of Glauber modes may serve as a powerful tool for studying gravitational scattering in the Regge limit.

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.

Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics.

PubMed

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

2015-04-21

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

Adaptive reconnection-based arbitrary Lagrangian Eulerian method

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

Bo, Wurigen; Shashkov, Mikhail

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

Adaptive reconnection-based arbitrary Lagrangian Eulerian method

DOE PAGES

Bo, Wurigen; Shashkov, Mikhail

2015-07-21

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

The canonical Lagrangian approach to three-space general relativity

NASA Astrophysics Data System (ADS)

Shyam, Vasudev; Venkatesh, Madhavan

2013-07-01

We study the action for the three-space formalism of general relativity, better known as the Barbour-Foster-Ó Murchadha action, which is a square-root Baierlein-Sharp-Wheeler action. In particular, we explore the (pre)symplectic structure by pulling it back via a Legendre map to the tangent bundle of the configuration space of this action. With it we attain the canonical Lagrangian vector field which generates the gauge transformations (3-diffeomorphisms) and the true physical evolution of the system. This vector field encapsulates all the dynamics of the system. We also discuss briefly the observables and perennials for this theory. We then present a symplectic reduction of the constrained phase space.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

USGS Publications Warehouse

Cheng, Ralph T.; Casulli, Vincenzo

1982-01-01

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

Covariant conserved currents for scalar-tensor Horndeski theory

NASA Astrophysics Data System (ADS)

Schmidt, J.; Bičák, J.

2018-04-01

The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for perturbations of spacetimes in standard general relativity, we extend these methods to the general Horndeski theory and find the covariant conserved currents for all four Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar fields. As a specific illustration, we derive a superpotential that leads to the covariantly conserved current in the Branse-Dicke theory.

Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics

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

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

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

Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics

DOE PAGES

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

2015-04-21

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

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.

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

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.

Lagrangian descriptors in dissipative systems.

PubMed

Junginger, Andrej; Hernandez, Rigoberto

2016-11-09

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

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.

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.

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.

MatchingTools: A Python library for symbolic effective field theory calculations

NASA Astrophysics Data System (ADS)

Criado, Juan C.

2018-06-01

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

Lagrangian methods in nonlinear plasma wave interaction

NASA Technical Reports Server (NTRS)

Crawford, F. W.

1980-01-01

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

A Primer to Relativistic MOND Theory

NASA Astrophysics Data System (ADS)

Bekenstein, J. D.; Sanders, R. H.

We first review the nonrelativistic Lagrangian theory as a framework for the MOND equation. Obstructions to a relativistic version of it are discussed leading up to TeVeS, a relativistic tensor-vector-scalar field theory which displays both MOND and Newtonian limits. The whys for its particular structure are discussed and its achievements so far are summarized.

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…

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

Acoustic streaming: an arbitrary Lagrangian-Eulerian perspective.

PubMed

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

2017-08-25

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

Generalized Lee-Wick formulation from higher derivative field theories

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

Cho, Inyong; Kwon, O-Kab; Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Sungkyunkwan University, Suwon 440-746

2010-07-15

We study a higher derivative (HD) field theory with an arbitrary order of derivative for a real scalar field. The degree of freedom for the HD field can be converted to multiple fields with canonical kinetic terms up to the overall sign. The Lagrangian describing the dynamics of the multiple fields is known as the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to the original HD Lagrangian up to the quantum level. Until now, the AF Lagrangian has been studiedmore » only for N=2 and 3 cases, where N is the number of poles of the two-point function of the HD scalar field. We construct the AF Lagrangian for arbitrary N. By the linear combinations of AF fields, we also obtain the corresponding LW form. We find the explicit mapping matrices among the HD fields, the AF fields, and the LW fields. As an exercise of our construction, we calculate the relations among parameters and mapping matrices for N=2, 3, and 4 cases.« less

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.

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

PubMed

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

2016-07-01

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

Lagrangian solution of supersonic real gas flows

NASA Technical Reports Server (NTRS)

Loh, Ching-Yuen; Liou, Meng-Sing

1993-01-01

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

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

PubMed

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

2015-07-01

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

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)

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

PubMed

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

2011-03-01

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

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

DTIC Science & Technology

2015-09-30

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

Effective description of higher-order scalar-tensor theories

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

Langlois, David; Mancarella, Michele; Vernizzi, Filippo

Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initialmore » Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called 'beyond Horndeski' theories. We also discuss Lorentz-breaking models inspired by Horava gravity.« less

Momentum conserving defects in affine Toda field theories

NASA Astrophysics Data System (ADS)

Bristow, Rebecca; Bowcock, Peter

2017-05-01

Type II integrable defects with more than one degree of freedom at the defect are investigated. A condition on the form of the Lagrangian for such defects is found which ensures the existence of a conserved momentum in the presence of the defect. In addition it is shown that for any Lagrangian satisfying this condition, the defect equations of motion, when taken to hold everywhere, can be extended to give a Bäcklund transformation between the bulk theories on either side of the defect. This strongly suggests that such systems are integrable. Momentum conserving defects and Bäcklund transformations for affine Toda field theories based on the A n , B n , C n and D n series of Lie algebras are found. The defect associated with the D 4 affine Toda field theory is examined in more detail. In particular classical time delays for solitons passing through the defect are calculated.

Asymptotically flat black holes in Horndeski theory and beyond

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

Babichev, E.; Charmousis, C.; Lehébel, A., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr

We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for a pure quartic Lagrangian, the metric of which ismore » Schwarzschild. We show that under two requirements on the theory in question, any vacuum GR solution is also solution to the quartic theory. As an example, we show that a Kerr black hole with a non-trivial scalar field is an exact solution to these theories.« less

A contemporary look at Hermann Hankel's 1861 pioneering work on Lagrangian fluid dynamics

NASA Astrophysics Data System (ADS)

Frisch, Uriel; Grimberg, Gérard; Villone, Barbara

2017-12-01

The present paper is a companion to the paper by Villone and Rampf (2017), titled "Hermann Hankel's On the general theory of motion of fluids, an essay including an English translation of the complete Preisschrift from 1861" together with connected documents [Eur. Phys. J. H 42, 557-609 (2017)]. Here we give a critical assessment of Hankel's work, which covers many important aspects of fluid dynamics considered from a Lagrangian-coordinates point of view: variational formulation in the spirit of Hamilton for elastic (barotropic) fluids, transport (we would now say Lie transport) of vorticity, the Lagrangian significance of Clebsch variables, etc. Hankel's work is also put in the perspective of previous and future work. Hence, the action spans about two centuries: from Lagrange's 1760-1761 Turin paper on variational approaches to mechanics and fluid mechanics problems to Arnold's 1966 founding paper on the geometrical/variational formulation of incompressible flow. The 22-year-old Hankel - who was to die 12 years later — emerges as a highly innovative master of mathematical fluid dynamics, fully deserving Riemann's assessment that his Preisschrift contains "all manner of good things."

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.

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

NASA Technical Reports Server (NTRS)

Lee, C. H.

1978-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Vakonomic Constraints in Higher-Order Classical Field Theory

NASA Astrophysics Data System (ADS)

Campos, Cédric M.

2010-07-01

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. The result is that we obtain a unique and global intrinsic description of the dynamics. The case of vakonomic constraints is also studied within this formalism.

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.

Gravity, Time, and Lagrangians

ERIC Educational Resources Information Center

Huggins, Elisha

2010-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Staggered chiral random matrix theory

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

Osborn, James C.

2011-02-01

We present a random matrix theory for the staggered lattice QCD Dirac operator. The staggered random matrix theory is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.

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

A Cohomological Perspective on Algebraic Quantum Field Theory

NASA Astrophysics Data System (ADS)

Hawkins, Eli

2018-05-01

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

Finite density two color chiral perturbation theory revisited

NASA Astrophysics Data System (ADS)

Adhikari, Prabal; Beleznay, Soma B.; Mannarelli, Massimo

2018-06-01

We revisit two-color, two-flavor chiral perturbation theory at finite isospin and baryon density. We investigate the phase diagram obtained varying the isospin and the baryon chemical potentials, focusing on the phase transition occurring when the two chemical potentials are equal and exceed the pion mass (which is degenerate with the diquark mass). In this case, there is a change in the order parameter of the theory that does not lend itself to the standard picture of first order transitions. We explore this phase transition both within a Ginzburg-Landau framework valid in a limited parameter space and then by inspecting the full chiral Lagrangian in all the accessible parameter space. Across the phase transition between the two broken phases the order parameter becomes an SU(2) doublet, with the ground state fixing the expectation value of the sum of the magnitude squared of the pion and the diquark fields. Furthermore, we find that the Lagrangian at equal chemical potentials is invariant under global SU(2) transformations and construct the effective Lagrangian of the three Goldstone degrees of freedom by integrating out the radial fluctuations.

Users manual for a one-dimensional Lagrangian transport model

USGS Publications Warehouse

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

1986-01-01

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

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.

Electron correlation in the interacting quantum atoms partition via coupled-cluster lagrangian densities.

PubMed

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.

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

NASA Technical Reports Server (NTRS)

Squires, Kyle D.; Eaton, John K.

1991-01-01

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

Spontaneous CP breaking in QCD and the axion potential: an effective Lagrangian approach

NASA Astrophysics Data System (ADS)

Di Vecchia, Paolo; Rossi, Giancarlo; Veneziano, Gabriele; Yankielowicz, Shimon

2017-12-01

Using the well-known low-energy effective Lagrangian of QCD — valid for small (non-vanishing) quark masses and a large number of colors — we study in detail the regions of parameter space where CP is spontaneously broken/unbroken for a vacuum angle θ = π. In the CP broken region there are first order phase transitions as one crosses θ = π, while on the (hyper)surface separating the two regions, there are second order phase transitions signalled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the CP spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised if the QCD parameters fall in the above mentioned CP broken region, in spite of the fact that the axion solves the strong- CP problem. These last results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.

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

PubMed

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

2013-01-01

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

Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations

PubMed Central

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

2013-01-01

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

Programmers manual for a one-dimensional Lagrangian transport model

USGS Publications Warehouse

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

1986-01-01

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

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.

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.

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.

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.

Unification Principle and a Geometric Field Theory

NASA Astrophysics Data System (ADS)

Wanas, Mamdouh I.; Osman, Samah N.; El-Kholy, Reham I.

2015-08-01

In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.

A Hamilton-Jacobi theory for implicit differential systems

NASA Astrophysics Data System (ADS)

Esen, Oǧul; de León, Manuel; Sardón, Cristina

2018-02-01

In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of TT*Q generated by Morse families. The implicit character implies the nonexistence of a Hamiltonian function describing the dynamics. This fact is here amended by a generating family of Morse functions which plays the role of a Hamiltonian. A Hamilton-Jacobi equation is obtained with the aid of this generating family of functions. To conclude, we apply our results to singular Lagrangians by employing the construction of special symplectic structures.

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

PubMed

Tian, Siyu; Huang, Xiaoxia; Li, Hongga

2017-03-15

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

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).

Hamiltonian analysis of higher derivative scalar-tensor theories

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

Langlois, David; Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: karim.noui@lmpt.univ-tours.fr

2016-07-01

We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of themore » dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.« less

Variational Lagrangian data assimilation in open channel networks

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

Lagrangian 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.

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.

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.

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.

Nonquadratic gauge fixing and ghosts for gauge theories on the hypersphere

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

Brandt, F. T.; McKeon, D. G. C.; Department of Mathematics and Computer Science, Algoma University, Sault St. Marie, Ontario P6A 2G4

2011-10-15

It has been suggested that using a gauge fixing Lagrangian that is not quadratic in a gauge fixing condition is most appropriate for gauge theories formulated on a hypersphere. We reexamine the appropriate ghost action that is to be associated with gauge fixing, applying a technique that has been used for ensuring that the propagator for a massless spin-two field is transverse and traceless. It is shown that this nonquadratic gauge fixing Lagrangian leads to two pair of complex Fermionic ghosts and two Bosonic real ghosts.

Orbital Maneuvers for Spacecrafts Travelling to/from the Lagrangian Points

NASA Astrophysics Data System (ADS)

Bertachini, A.

Points and the Moon, Journal of Guidance and Control, Vol. 2, Prado, A.F.B.A., (1969) Travelling Between the Lagrangian Points and the Earth, Acta Astronautica, Vol. 39, No. 7, pp. Press, W. H.; B. P. Flannery; S. A. Teukolsky and W. T. Vetterling (1989), Numerical Recipes, Cambridge University Szebehely, V., (1967), Theory of Orbits, Academic Press, New York.

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)

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

Macroscopic Lagrangian description of warm plasmas. II Nonlinear wave interactions

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1983-01-01

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

A non-conventional discontinuous Lagrangian for viscous flow

PubMed Central

Marner, F.

2017-01-01

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

A non-conventional discontinuous Lagrangian for viscous flow.

PubMed

Scholle, M; Marner, F

2017-02-01

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

Higher derivative theories for interacting massless gravitons in Minkowski spacetime

NASA Astrophysics Data System (ADS)

Bai, Dong; Xing, Yu-Hang

2018-07-01

We study a novel class of higher derivative theories for interacting massless gravitons in Minkowski spacetime. These theories were first discussed by Wald decades ago, and are characterized by scattering amplitudes essentially different from general relativity and many of its modifications. We discuss various aspects of these higher derivative theories, including the Lagrangian construction, violation of asymptotic causality, scattering amplitudes, non-renormalization, and possible implications in emergent gravitons from condensed matter systems.

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).

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

DOE PAGES

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

2017-12-11

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

A Godunov-like point-centered essentially Lagrangian hydrodynamic approach

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

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

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

A Godunov-like point-centered essentially Lagrangian hydrodynamic approach

DOE PAGES

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

2014-10-28

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

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

PubMed

Glavatskiy, K S

2015-05-28

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

Some novel features in 2D non-Abelian theory: BRST approach

NASA Astrophysics Data System (ADS)

Srinivas, N.; Kumar, S.; Kureel, B. K.; Malik, R. P.

2017-08-01

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss some novel features of a two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci-Ferrari (CF-)type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned.

Lagrangian chaos in three- dimensional steady buoyancy-driven flows

NASA Astrophysics Data System (ADS)

Contreras, Sebastian; Speetjens, Michel; Clercx, Herman

2016-11-01

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

Getting Things Sorted With Lagrangian Coherent Structures

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

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

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.

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

NASA Astrophysics Data System (ADS)

Maniatis, Georgios

2017-04-01

Fluvial sediment transport is controlled by hydraulics, sediment properties and arrangement, and flow history across a range of time scales. One reference frame descriptions (Eulerian or Lagrangian) yield useful results but restrict the theoretical understanding of the process as differences between the two phases (liquid and solid) are not explicitly accounted. Recently, affordable Inertial Measurement Units (IMUs) that can be embedded in coarse (100 mm diameter scale) natural or artificial particles became available. These sensors are subjected to technical limitations when deployed for natural sediment transport. However, they give us the ability to measure for the first time the inertial dynamics (acceleration and angular velocity) of moving sediment grains under fluvial transport. Theoretically, the assumption of an ideal (IMU), rigidly attached at the centre of the mass of a sediment particle can simplify greatly the derivation of a general Eulerian-Lagrangian (E-L) model. This approach accounts for inertial characteristics of particles in a Lagrangian (particle fixed) frame, and for the hydrodynamics in an independent Eulerian frame. Simplified versions of the E-L model have been evaluated in laboratory experiments using real-IMUs [Maniatis et. al 2015]. Here, experimental results are presented relevant to the evaluation of the complete E-L model. Artificial particles were deployed in a series of laboratory and field experiments. The particles are equipped with an IMU capable of recording acceleration at ± 400 g and angular velocities at ± 1200 rads/sec ranges. The sampling frequency ranges from 50 to 200 Hz for the total IMU measurement. Two sets of laboratory experiments were conducted in a 0.9m wide laboratory flume. The first is a set of entrainment threshold experiments using two artificial particles: a spherical of D=90mm (A) and an ellipsoid with axes of 100, 70 and 30 mm (B). For the second set of experiments, a spherical artificial enclosure of D

Effects of Helicity on Lagrangian and Eulerian Time Correlations in Turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Zhou, Ye

1998-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2011-08-01

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

Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics

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

Glavatskiy, K. S.

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

Lagrangian space consistency relation for large scale structure

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

Horn, Bart; Hui, Lam; Xiao, Xiao

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

Lagrangian space consistency relation for large scale structure

DOE PAGES

Horn, Bart; Hui, Lam; Xiao, Xiao

2015-09-29

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

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

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

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

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

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

PubMed

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

2017-10-01

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

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

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

2015-07-29

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

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)

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.

Cosmological perturbation theory in 1+1 dimensions

NASA Astrophysics Data System (ADS)

McQuinn, Matthew; White, Martin

2016-01-01

Many recent studies have highlighted certain failures of the standard Eulerian-space cosmological perturbation theory (SPT). Its problems include (1) not capturing large-scale bulk flows [leading to an Script O( 1) error in the 1-loop SPT prediction for the baryon acoustic peak in the correlation function], (2) assuming that the Universe behaves as a pressureless, inviscid fluid, and (3) treating fluctuations on scales that are non-perturbative as if they were. Recent studies have highlighted the successes of perturbation theory in Lagrangian space or theories that solve equations for the effective dynamics of smoothed fields. Both approaches mitigate some or all of the aforementioned issues with SPT. We discuss these physical developments by specializing to the simplified 1D case of gravitationally interacting sheets, which allows us to substantially reduces the analytic overhead and still (as we show) maintain many of the same behaviors as in 3D. In 1D, linear-order Lagrangian perturbation theory ("the Zeldovich approximation") is exact up to shell crossing, and we prove that nth-order Eulerian perturbation theory converges to the Zeldovich approximation as narrow ∞. In no 1D cosmology that we consider (including a CDM-like case and power-law models) do these theories describe accurately the matter power spectrum on any mildly nonlinear scale. We find that theories based on effective equations are much more successful at describing the dynamics. Finally, we discuss many topics that have recently appeared in the perturbation theory literature such as beat coupling, the shift and smearing of the baryon acoustic oscillation feature, and the advantages of Fourier versus configuration space. Our simplified 1D case serves as an intuitive review of these perturbation theory results.

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

PubMed

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

2014-08-01

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

Hamilton-Jacobi theory in multisymplectic classical field theories

NASA Astrophysics Data System (ADS)

de León, Manuel; Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso; Vilariño, Silvia

2017-09-01

The geometric framework for the Hamilton-Jacobi theory developed in the studies of Cariñena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Cariñena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de León et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.

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

NASA Astrophysics Data System (ADS)

Cornille, Brian; White, Dan

2017-10-01

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

Lagrangian transport properties of pulmonary interfacial flows

PubMed Central

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

2012-01-01

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

No black holes: A gravitational gauge theory possibility

NASA Astrophysics Data System (ADS)

Chang, David B.; Johnson, Harold H.

1980-06-01

The most general lowest order lagrangian that can be formed from gauge-derived vierbein invariants is constrained by the hypothesis that the speed of light as measured by conventional rods and clocks of atomic constitution is independent of direction in a gravitational field. It is shown that the standard weak field observational tests of general relativity serve to eliminate all possible combinations of parameters in this constrained lagrangian except two. One parameter choice gives the isotropic Schwarzchild black hole metric of the general theory of relativity. The other allowable choice leads to an exponential metric of the class proposed by Yilmaz, corresponding in strong fields to large red shifts without black hole formation. Permanent address: Trinity College; Deerfield, Illinois.

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

NASA Technical Reports Server (NTRS)

Felici, Helene M.; Drela, Mark

1993-01-01

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

Lagrangian statistics in weakly forced two-dimensional turbulence.

PubMed

Rivera, Michael K; Ecke, Robert E

2016-01-01

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

Lagrangian statistics in weakly forced two-dimensional turbulence

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

Rivera, Michael K.; Ecke, Robert E.

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

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 statistics in weakly forced two-dimensional turbulence

DOE PAGES

Rivera, Michael K.; Ecke, Robert E.

2016-01-14

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

Lagrangian condensation microphysics with Twomey CCN activation

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Lagrangian formulation and symmetrical description of liquid dynamics.

PubMed

Trachenko, K

2017-12-01

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

Lagrangian space consistency relation for large scale structure

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

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

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

Lagrangian formulation and symmetrical description of liquid dynamics

NASA Astrophysics Data System (ADS)

Trachenko, K.

2017-12-01

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

Towards Lagrangian formulations of mixed-symmetry higher spin fields on AdS-space within BFV-BRST formalism

NASA Astrophysics Data System (ADS)

Reshetnyak, A. A.

2010-11-01

The spectrum of superstring theory on the AdS 5 × S 5 Ramond-Ramond background in tensionless limit contains integer and half-integer higher-spin fields subject at most to two-rows Young tableaux Y( s 1, s 2). We review the details of a gauge-invariant Lagrangian description of such massive and massless higher-spin fields in anti-de-Sitter spaces with arbitrary dimensions. The procedure is based on the construction of Verma modules, its oscillator realizations and of a BFV-BRST operator for non-linear algebras encoding unitary irreducible representations of AdS group.

GVVPT2 energy gradient using a Lagrangian formulation.

PubMed

Theis, Daniel; Khait, Yuriy G; Hoffmann, Mark R

2011-07-28

A Lagrangian based approach was used to obtain analytic formulas for GVVPT2 energy nuclear gradients. The formalism can use either complete or incomplete model (or reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. An efficient means of evaluating the gradient equations is described. Demonstrative calculations were performed and compared with finite difference calculations on several molecules and show that the GVVPT2 gradients are accurate. Of particular interest, the suggested formalism can straightforwardly use state-averaged MCSCF descriptions of the reference space in which the states have arbitrary weights. This capability is demonstrated by some calculations on the ground and first excited singlet states of LiH, including calculations near an avoided crossing. The accuracy and usefulness of the GVVPT2 method and its gradient are highlighted by comparing the geometry of the near-C(2v) minimum on the conical intersection seam between the 1 (1)A(1) and 2 (1)A(1) surfaces of O(3) with values that were calculated at the multireference configuration interaction, including single and double excitations (MRCISD), level of theory. © 2011 American Institute of Physics

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

NASA Technical Reports Server (NTRS)

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

Two-dimensional N = 2 Super-Yang-Mills Theory

NASA Astrophysics Data System (ADS)

August, Daniel; Wellegehausen, Björn; Wipf, Andreas

2018-03-01

Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the N = 1 Super-Yang-Mills (SYM) theory with gauge group SU(2) dimensionally reduced to two-dimensional N = 2 SYM theory. In our lattice formulation we break supersymmetry and chiral symmetry explicitly while preserving R symmetry. By fine tuning the bar-mass of the fermions in the Lagrangian we construct a supersymmetric continuum theory. To this aim we carefully investigate mass spectra and Ward identities, which both show a clear signal of supersymmetry restoration in the continuum limit.

Planetary Defense From Space: Part 1-Keplerian Theory

NASA Astrophysics Data System (ADS)

Maccone, Claudio

A system of two space bases housing missiles is proposed to achieve the Planetary Defense of the Earth against dangerous asteroids and comets. We show that the layout of the Earth-Moon system with the five relevant Lagrangian (or libration) points in space leads naturally to only one, unmistakable location of these two space bases within the sphere of influence of the Earth. These locations are at the two Lagrangian points L1 (in between the Earth and the Moon) and L3 (in the direction opposite to the Moon from the Earth). We show that placing bases of missiles at L1 and L3 would cause those missiles to deflect the trajectory of asteroids by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that the confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement. An additional remark is that the theory developed in this paper is just a beginning of a larger set of future research work. In fact, while in this paper we only develop the Keplerian analytical theory of the Optimal Planetary Defense achievable from the Earth-Moon Lagrangian points L1 and L3, much more sophisticated analytical refinements would be needed to: Take into account many perturbation forces of all kinds acting on both the asteroids and missiles shot from L1 and L3; add more (non-optimal) trajectories of missiles shot from either the Lagrangian points L4 and L5 of the Earth-Moon system or from the surface of the Moon itself; encompass the full range of missiles currently available to the US (and possibly other countries) so as to really see "which asteroids could be diverted by which missiles", even in the very simplified scheme outlined here. Outlined for the first time in February 2002, our Confocal Planetary Defense concept is a Keplerian Theory that proved simple enough to catch the attention of scholars, representatives of the US Military and popular writers. These developments could

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

Effective Theories for QCD-like at TeV Scale

NASA Astrophysics Data System (ADS)

Lu, Jie; Bijnens, Johan

2016-04-01

We study the Effective Field Theory of three QCD-like theories, which can be classified by having quarks in a complex, real or pseudo-real representations of the gauge group. The Lagrangians are written in a very similar way so that the calculations can be done using techniques from Chiral Perturbation Theory (ChPT). We calculated the vacuum-expectation-value, the mass and the decay constant of pseudo-Goldstone Bosons up to next-to-next-to leading order (NNLO) [J. Bijnens and J. Lu, JHEP 0911 (2009) 116 [arxiv:arXiv:0910.5424 [hep-ph

Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices.

PubMed

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

2015-08-01

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

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

PubMed

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

2013-04-01

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

Mass and angular momentum of black holes in low-energy heterotic string theory

NASA Astrophysics Data System (ADS)

Peng, Jun-Jin

2016-04-01

We investigate conserved charges in the low-energy effective field theory describing heterotic string theory. Starting with a general Lagrangian that consists of a metric, a scalar field, a vector gauge field, together with a two-form potential, we derive off-shell Noether potentials of the Lagrangian and generalize the Abbott-Deser-Tekin (ADT) formalism to the off-shell level by establishing one-to-one correspondence between the ADT potential and the off-shell Noether potential. It is proved that the off-shell generalized ADT formalism is conformally invariant. Then, we apply the formulation to compute mass and angular momentum of the four-dimensional Kerr-Sen black hole and the five-dimensional rotating charged black string in the string frame without a necessity to transform the metrics into the Einstein frame.

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.

Radiative double copy for Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Chester, David

2018-04-01

Recently, a double-copy formalism was used to calculate gravitational radiation from classical Yang-Mills radiation solutions. This work shows that the Yang-Mills theory coupled to a biadjoint scalar field admits a radiative double copy that agrees with solutions in the Einstein-Yang-Mills theory at the lowest finite order. Within this context, the trace-reversed metric h¯μ ν is a natural double copy of the gauge boson Aμ a . This work provides additional evidence that solutions in gauge and gravity theories are related, even though their respective Lagrangians and nonlinear equations of motion appear to be different.

The Lagrangian Ensemble metamodel for simulating plankton ecosystems

NASA Astrophysics Data System (ADS)

Woods, J. D.

2005-10-01

This paper presents a detailed account of the Lagrangian Ensemble (LE) metamodel for simulating plankton ecosystems. It uses agent-based modelling to describe the life histories of many thousands of individual plankters. The demography of each plankton population is computed from those life histories. So too is bio-optical and biochemical feedback to the environment. The resulting “virtual ecosystem” is a comprehensive simulation of the plankton ecosystem. It is based on phenotypic equations for individual micro-organisms. LE modelling differs significantly from population-based modelling. The latter uses prognostic equations to compute demography and biofeedback directly. LE modelling diagnoses them from the properties of individual micro-organisms, whose behaviour is computed from prognostic equations. That indirect approach permits the ecosystem to adjust gracefully to changes in exogenous forcing. The paper starts with theory: it defines the Lagrangian Ensemble metamodel and explains how LE code performs a number of computations “behind the curtain”. They include budgeting chemicals, and deriving biofeedback and demography from individuals. The next section describes the practice of LE modelling. It starts with designing a model that complies with the LE metamodel. Then it describes the scenario for exogenous properties that provide the computation with initial and boundary conditions. These procedures differ significantly from those used in population-based modelling. The next section shows how LE modelling is used in research, teaching and planning. The practice depends largely on hindcasting to overcome the limits to predictability of weather forecasting. The scientific method explains observable ecosystem phenomena in terms of finer-grained processes that cannot be observed, but which are controlled by the basic laws of physics, chemistry and biology. What-If? Prediction ( WIP), used for planning, extends hindcasting by adding events that describe

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.

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

PubMed

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

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

USGS Publications Warehouse

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

1984-01-01

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

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

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

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

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

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

NASA Astrophysics Data System (ADS)

Bodenschatz, Eberhard

2014-11-01

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

Second order upwind Lagrangian particle method for Euler equations

DOE PAGES

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

2016-06-01

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

Second order upwind Lagrangian particle method for Euler equations

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

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

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

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

K-decompositions and 3d gauge theories

DOE PAGES

Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.

2016-11-24

This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K, C)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli spacemore » $$\\mathcal{L}$$ K(M) of framed flat connections on the boundary ∂M that extend to M. Our goal is to understand an open part of $$\\mathcal{L}$$ K(M) as a Lagrangian subvariety in the symplectic moduli space X un K(∂M) of framed flat connections on the boundary — and more so, as a “K 2-Lagrangian,” meaning that the K 2-avatar of the symplectic form restricts to zero. We construct an open part of $$\\mathcal{L}$$ K(M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston’s gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL(K, C)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of $$\\mathcal{L}$$ K(M) is K 2-isotropic as long as ∂M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that $$\\mathcal{L}$$ K(M) is K 2-Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K 2-Lagrangian property to a combinatorial statement. Physically, we translate the K-decomposition of an ideal triangulation of M and its symplectic properties to produce an explicit construction of 3d N = 2 superconformal field theories T K [M] resulting (conjecturally) from the compactification of K M5-branes on M. This extends known constructions for K = 2. Just as for K = 2, the theories T K [M] are described as IR fixed points of abelian Chern-Simons-matter theories. Changes of triangulation (2-3 moves) lead to abelian mirror symmetries that are all generated by the elementary duality

K-decompositions and 3d gauge theories

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

Dimofte, Tudor; Gabella, Maxime; Goncharov, Alexander B.

This paper combines several new constructions in mathematics and physics. Mathematically, we study framed flat PGL(K, C)-connections on a large class of 3-manifolds M with boundary. We introduce a moduli spacemore » $$\\mathcal{L}$$ K(M) of framed flat connections on the boundary ∂M that extend to M. Our goal is to understand an open part of $$\\mathcal{L}$$ K(M) as a Lagrangian subvariety in the symplectic moduli space X un K(∂M) of framed flat connections on the boundary — and more so, as a “K 2-Lagrangian,” meaning that the K 2-avatar of the symplectic form restricts to zero. We construct an open part of $$\\mathcal{L}$$ K(M) from elementary data associated with the hypersimplicial K-decomposition of an ideal triangulation of M, in a way that generalizes (and combines) both Thurston’s gluing equations in 3d hyperbolic geometry and the cluster coordinates for framed flat PGL(K, C)-connections on surfaces. By using a canonical map from the complex of configurations of decorated flags to the Bloch complex, we prove that any generic component of $$\\mathcal{L}$$ K(M) is K 2-isotropic as long as ∂M satisfies certain topological constraints (theorem 4.2). In some cases this easily implies that $$\\mathcal{L}$$ K(M) is K 2-Lagrangian. For general M, we extend a classic result of Neumann and Zagier on symplectic properties of PGL(2) gluing equations to reduce the K 2-Lagrangian property to a combinatorial statement. Physically, we translate the K-decomposition of an ideal triangulation of M and its symplectic properties to produce an explicit construction of 3d N = 2 superconformal field theories T K [M] resulting (conjecturally) from the compactification of K M5-branes on M. This extends known constructions for K = 2. Just as for K = 2, the theories T K [M] are described as IR fixed points of abelian Chern-Simons-matter theories. Changes of triangulation (2-3 moves) lead to abelian mirror symmetries that are all generated by the elementary duality

Order Reduction, Projectability and Constraints of Second-Order Field Theories and Higher-Order Mechanics

NASA Astrophysics Data System (ADS)

Gaset, Jordi; Román-Roy, Narciso

2016-12-01

The projectability of Poincaré-Cartan forms in a third-order jet bundle J3π onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint algorithm for the associated Euler-Lagrange equations in J3π. The results are applied to study the Hilbert Lagrangian for the Einstein equations (in vacuum) from a multisymplectic point of view. Thus we show how these equations are a consequence of the application of the constraint algorithm to the geometric field equations, meanwhile the other constraints are related with the fact that this second-order theory is equivalent to a first-order theory. Furthermore, the case of higher-order mechanics is also studied as a particular situation.

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.

PubMed

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

2018-01-03

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

Multiphase Interface Tracking with Fast Semi-Lagrangian Contouring.

PubMed

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

2016-08-01

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

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.

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

PubMed

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

2015-06-09

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

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.

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

PubMed

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

2016-06-07

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

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.

On the vanishing couplings in ADE affine Toda field theories

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

Saitoh, Y.; Shimada, T.

In this paper, the authors show that certain vanishing couplins in the ADE affine Toda field theories remain vanishing even after higher-order corrections are included. This is a requisite property for the Lagrangian formulation of the theory. The authors develop a new perturbative formulation and treat affine Toda field theories as a massless theory with exponential interaction terms. The authors shown that the nonrenormalization comes from the Dynkin automorphism of the Lie algebra associated with these theories. A charge balance conditions plays an important role in our scheme. The all-order nonrenormalization of vanishing couplings in [bar A][sub n] affine Todamore » field theory is also proved in a standard massive scheme.« less

The probability density function (PDF) of Lagrangian Turbulence

NASA Astrophysics Data System (ADS)

Birnir, B.

2012-12-01

The statistical theory of Lagrangian turbulence is derived from the stochastic Navier-Stokes equation. Assuming that the noise in fully-developed turbulence is a generic noise determined by the general theorems in probability, the central limit theorem and the large deviation principle, we are able to formulate and solve the Kolmogorov-Hopf equation for the invariant measure of the stochastic Navier-Stokes equations. The intermittency corrections to the scaling exponents of the structure functions require a multiplicative (multipling the fluid velocity) noise in the stochastic Navier-Stokes equation. We let this multiplicative noise, in the equation, consists of a simple (Poisson) jump process and then show how the Feynmann-Kac formula produces the log-Poissonian processes, found by She and Leveque, Waymire and Dubrulle. These log-Poissonian processes give the intermittency corrections that agree with modern direct Navier-Stokes simulations (DNS) and experiments. The probability density function (PDF) plays a key role when direct Navier-Stokes simulations or experimental results are compared to theory. The statistical theory of turbulence is determined, including the scaling of the structure functions of turbulence, by the invariant measure of the Navier-Stokes equation and the PDFs for the various statistics (one-point, two-point, N-point) can be obtained by taking the trace of the corresponding invariant measures. Hopf derived in 1952 a functional equation for the characteristic function (Fourier transform) of the invariant measure. In distinction to the nonlinear Navier-Stokes equation, this is a linear functional differential equation. The PDFs obtained from the invariant measures for the velocity differences (two-point statistics) are shown to be the four parameter generalized hyperbolic distributions, found by Barndorff-Nilsen. These PDF have heavy tails and a convex peak at the origin. A suitable projection of the Kolmogorov-Hopf equations is the

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

An assessment of first-order stochastic dispersion theories in porous media

NASA Astrophysics Data System (ADS)

Chin, David A.

1997-12-01

Random realizations of three-dimensional exponentially correlated hydraulic conductivity fields are used in a finite-difference numerical flow model to calculate the mean and covariance of the corresponding Lagrangian-velocity fields. The dispersivity of the porous medium is then determined from the Lagrangian-velocity statistics using the Taylor definition. This estimation procedure is exact, except for numerical errors, and the results are used to assess the accuracy of various first-order dispersion theories in both isotropic and anisotropic porous media. The results show that the Dagan theory is by far the most robust in both isotropic and anisotropic media, producing accurate values of the principal dispersivity components for σy as high as 1.0, In the case of anisotropic media where the flow is at an angle to the principal axis of hydraulic conductivity, it is shown that the dispersivity tensor is rotated away from the flow direction in the non-Fickian phase, but eventually coincides with the flow direction in the Fickian phase.

Duality for massive spin two theories in arbitrary dimensions

NASA Astrophysics Data System (ADS)

González, B.; Khoudeir, A.; Montemayor, R.; Urrutia, L. F.

2008-09-01

Using the parent Lagrangian approach we construct a dual formulation, in the sense originally proposed by Curtright and Freund, of a massive spin two Fierz-Pauli theory in arbitrary dimensions D. This is achieved in terms of a mixed symmetry tensor TA[B1B2...BD-2], without the need of auxiliary fields. The relation of this method with an alternative formulation based on a gauge symmetry principle proposed by Zinoviev is elucidated. We show that the latter formulation in four dimensions, with a given gauge fixing together with a definite sequence of auxiliary fields elimination via their equations of motion, leads to the parent Lagrangian already considered by West completed by a Fierz-Pauli mass term, which in turns yields the Curtright-Freund action. This motivates our generalization to arbitrary dimensions leading to the corresponding extension of the four dimensional result. We identify the transverse true degrees of freedom of the dual theory and verify that their number is in accordance with those of the massive Fierz-Pauli field.

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

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.

Lagrangian particle method for compressible fluid dynamics

DOE PAGES

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

Effective field theory dimensional regularization

NASA Astrophysics Data System (ADS)

Lehmann, Dirk; Prézeau, Gary

2002-01-01

A Lorentz-covariant regularization scheme for effective field theories with an arbitrary number of propagating heavy and light particles is given. This regularization scheme leaves the low-energy analytic structure of Greens functions intact and preserves all the symmetries of the underlying Lagrangian. The power divergences of regularized loop integrals are controlled by the low-energy kinematic variables. Simple diagrammatic rules are derived for the regularization of arbitrary one-loop graphs and the generalization to higher loops is discussed.

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.

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.

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)

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

NASA Astrophysics Data System (ADS)

Huhn, Florian; Haller, George

2014-05-01

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

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

NASA Astrophysics Data System (ADS)

Liu, Y.; Weisberg, R. H.

2017-12-01

The Lagrangian separation distance between the endpoints of simulated and observed drifter trajectories is often used to assess the performance of numerical particle trajectory models. However, the separation distance fails to indicate relative model performance in weak and strong current regions, such as a continental shelf and its adjacent deep ocean. A skill score is proposed based on the cumulative Lagrangian separation distances normalized by the associated cumulative trajectory lengths. The new metrics correctly indicates the relative performance of the Global HYCOM in simulating the strong currents of the Gulf of Mexico Loop Current and the weaker currents of the West Florida Shelf in the eastern Gulf of Mexico. In contrast, the Lagrangian separation distance alone gives a misleading result. Also, the observed drifter position series can be used to reinitialize the trajectory model and evaluate its performance along the observed trajectory, not just at the drifter end position. The proposed dimensionless skill score is particularly useful when the number of drifter trajectories is limited and neither a conventional Eulerian-based velocity nor a Lagrangian-based probability density function may be estimated.

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

PubMed

Ma, Chi; Wang, Xiao; Varghese, Tomy

2016-11-01

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

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

PubMed Central

Ma, Chi; Wang, Xiao; Varghese, Tomy

2016-01-01

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

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

USGS Publications Warehouse

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

1995-01-01

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

Unified theory of nonlinear electrodynamics and gravity

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

Torres-Gomez, Alexander; Krasnov, Kirill; Scarinci, Carlos

2011-01-15

We describe a class of unified theories of electromagnetism and gravity. The Lagrangian is of the BF type, with a potential for the B field, the gauge group is U(2) (complexified). Given a choice of the potential function the theory is a deformation of (complex) general relativity and electromagnetism, and describes just two propagating polarizations of the graviton and two of the photon. When gravity is switched off the theory becomes the usual nonlinear electrodynamics with a general structure function. The Einstein-Maxwell theory can be recovered by sending some of the parameters of the defining potential to zero, but formore » any generic choice of the potential the theory is indistinguishable from Einstein-Maxwell at low energies. A real theory is obtained by imposing suitable reality conditions. We also study the spherically-symmetric solution and show how the usual Reissner-Nordstrom solution is recovered.« less

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.

New two-metric theory of gravity with prior geometry

NASA Technical Reports Server (NTRS)

Lightman, A. P.; Lee, D. L.

1973-01-01

A Lagrangian-based metric theory of gravity is developed with three adjustable constants and two tensor fields, one of which is a nondynamic 'flat space metric' eta. With a suitable cosmological model and a particular choice of the constants, the 'post-Newtonian limit' of the theory agrees, in the current epoch, with that of general relativity theory (GRT); consequently the theory is consistent with current gravitation experiments. Because of the role of eta, the gravitational 'constant' G is time-dependent and gravitational waves travel null geodesics of eta rather than the physical metric g. Gravitational waves possess six degrees of freedom. The general exact static spherically-symmetric solution is a four-parameter family. Future experimental tests of the theory are discussed.

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

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

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2018-03-01

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

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

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

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

2001-10-22

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

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.

Heavy Quark Effective Theory

NASA Astrophysics Data System (ADS)

Manohar, A. V.

2003-02-01

These lecture notes present some of the basic ideas of heavy quark effective theory. The topics covered include the classification of states, the derivation of the HQET Lagrangian at tree level, hadron masses, meson form factors, Luke's theorem, reparameterization invariance and inclusive decays. Radiative corrections are discussed in some detail, including an explicit computation of a matching correction for HQET. Borel summability, renormalons, and their connection with the QCD perturbation series is covered, as well as the use of the upsilon expansion to improve the convergence of the perturbation series.

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

PubMed

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

2016-12-01

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

Analysis of Lagrangian stretching in turbulent channel flow using a database task-parallel particle tracking approach

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.

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.

On the motion of hairy black holes in Einstein-Maxwell-dilaton theories

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis

2018-01-01

Starting from the static, spherically symmetric black hole solutions in massless Einstein-Maxwell-dilaton (EMD) theories, we build a "skeleton" action, that is, we phenomenologically replace black holes by an appropriate effective point particle action, which is well suited to the formal treatment of the many-body problem in EMD theories. We find that, depending crucially on the value of their scalar cosmological environment, black holes can undergo steep "scalarization" transitions, inducing large deviations to the general relativistic two-body dynamics, as shown, for example, when computing the first post-Keplerian Lagrangian of EMD theories.

Phenomenology of the Higgs effective Lagrangian via F eynR ules

NASA Astrophysics Data System (ADS)

Alloul, Adam; Fuks, Benjamin; Sanz, Verónica

2014-04-01

The Higgs discovery and the lack of any other hint for new physics favor a description of non-standard Higgs physics in terms of an effective field theory. We present an implementation of a general Higgs effective Lagrangian containing operators up to dimension six in the framework of F eynR ules and provide details on the translation between the mass and interaction bases, in particular for three- and four-point interaction vertices involving Higgs and gauge bosons. We illustrate the strengths of this implementation by using the UFO interface of F eynR ules capable to generate model files that can be understood by the M adG raph 5 event generator and that have the specificity to contain all interaction vertices, without any restriction on the number of external legs or on the complexity of the Lorentz structures. We then investigate several new physics effects in total rates and differential distributions for different Higgs production modes, including gluon fusion, associated production with a gauge boson and di-Higgs production. We finally study contact interactions of gauge and Higgs bosons to fermions.

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

PubMed

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

2018-03-26

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

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

NASA Astrophysics Data System (ADS)

Besse, Nicolas; Frisch, Uriel

2017-04-01

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

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

DTIC Science & Technology

2012-12-03

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

Ultraviolet divergences in non-renormalizable supersymmetric theories

NASA Astrophysics Data System (ADS)

Smilga, A.

2017-03-01

We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang-Mills theory and of N = 8 4 D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higherdimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.

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

USGS Publications Warehouse

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

2016-01-01

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

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.

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

DOE PAGES

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

2015-03-11

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

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

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

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

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

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.