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Journal articles on the topic 'Lagrangian study'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

ROMÁN-ROY, NARCISO, MODESTO SALGADO, and SILVIA VILARIÑO. "SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY." Reviews in Mathematical Physics 19, no. 10 (November 2007): 1117–47. http://dx.doi.org/10.1142/s0129055x07003188.

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This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.

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2

PAVLOTSKY, I. P., and M. STRIANESE. "SOME PECULIAR PROPERTIES OF THE DARWIN’S LAGRANGIAN." International Journal of Modern Physics B 09, no. 23 (October 20, 1995): 3069–83. http://dx.doi.org/10.1142/s0217979295001166.

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In the post-Galilean approximation the Lagrangians are singular on a submanifold of the phase space. It is a local singularity, which differs from the ones considered by Dirac. The dynamical properties are essentially peculiar on the studied singular surfaces. In the preceding publications,1,2,3 two models of singular relativistic Lagrangians and the rectilinear motion of two electrons, determined by Darwin’s Lagrangian, were examined. In the present paper we study the peculiar dynamical properties of the two-dimensional Darwin’s Lagrangian. In particular, it is shown that the minimal distance between two electrons (the so called “radius of electron”) appears in the two-dimensional motion as well as in one-dimensional case. Some new peculiar properties are discovered.

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3

Obaidullah, U., and Sameerah Jamal. "pp-wave potential functions: A complete study using Noether symmetries." International Journal of Geometric Methods in Modern Physics 18, no. 07 (March 18, 2021): 2150108. http://dx.doi.org/10.1142/s0219887821501085.

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In this paper, we examine the functional forms of the potentials [Formula: see text] that emerge from the Lagrangian of the pp-wave spacetime. To facilitate this investigation, Noether symmetries are employed as well as their linear combinations and subalgebras. We exploit the geometric fact that Noether point symmetries of geodesic Lagrangians are generated from the Homothetic algebra of spacetimes. Thus, we provide a complete analysis of the potentials of this spacetime, which are split into 14 isometry categories.

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4

BUHOVSKY, LEV. "THE MASLOV CLASS OF LAGRANGIAN TORI AND QUANTUM PRODUCTS IN FLOER COHOMOLOGY." Journal of Topology and Analysis 02, no. 01 (March 2010): 57–75. http://dx.doi.org/10.1142/s1793525310000240.

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We use Floer cohomology to prove the monotone version of a conjecture of Audin: the minimal Maslov number of a monotone Lagrangian torus in ℝ2n is 2. Our approach is based on the study of the quantum cup product on Floer cohomology and in particular the behavior of Oh's spectral sequence with respect to this product. As further applications, we prove existence of holomorphic disks with boundaries on Lagrangians as well as new results on Lagrangian intersections.

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Hirica, Iulia, Constantin Udriste, Gabriel Pripoae, and Ionel Tevy. "Least Squares Approximation of Flatness on Riemannian Manifolds." Mathematics 8, no. 10 (October 13, 2020): 1757. http://dx.doi.org/10.3390/math8101757.

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The purpose of this paper is fourfold: (i) to introduce and study the Euler–Lagrange prolongations of flatness PDEs solutions (best approximation of flatness) via associated least squares Lagrangian densities and integral functionals on Riemannian manifolds; (ii) to analyze some decomposable multivariate dynamics represented by Euler–Lagrange PDEs of least squares Lagrangians generated by flatness PDEs and Riemannian metrics; (iii) to give examples of explicit flat extremals and non-flat approximations; (iv) to find some relations between geometric least squares Lagrangian densities.

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Singh, Bhupendra, Ranjit Kumar, and Loukrakpam Kennedy Meitei. "A Study of Non-Canonical Lagrangian." Natural Science 08, no. 05 (2016): 211–15. http://dx.doi.org/10.4236/ns.2016.85024.

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7

Naz, R., I. Naeem, and F. M. Mahomed. "First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators." Mathematical Problems in Engineering 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/831647.

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We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators for such equations. The difference arises in the gauge terms due to Lagrangians being different for respective approaches. This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian. We have illustrated it here for nonlinear Duffing oscillators.

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8

Mason, Evan, Francois Colas, and Josep L. Pelegrí. "A Lagrangian study tracing water parcel origins in the Canary Upwelling System." Scientia Marina 76, S1 (August 31, 2012): 79–94. http://dx.doi.org/10.3989/scimar.03608.18d.

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BALACHANDRAN, A. P., G. BIMONTE, and P. TEOTONIO-SOBRINHO. "EDGE STATES IN 4D AND THEIR 3D GROUPS AND FIELDS." Modern Physics Letters A 08, no. 14 (May 10, 1993): 1305–13. http://dx.doi.org/10.1142/s0217732393001033.

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It is known that the Lagrangian for the edge states of a Chern-Simons theory describes a coadjoint orbit of a Kac-Moody (KM) group with its associated Kirillov symplectic form and group representation. It can also be obtained from a chiral sector of a non-chiral field theory. We study the edge states of the Abelian BF system in four dimensions (4D) and show the following results in almost exact analogy: 1) The Lagrangian for these states is associated with a certain 2D generalization of the KM group. It describes a coadjoint orbit of this group as a Kirillov symplectic manifold and also the corresponding group representation. 2) It can be obtained from with a "self-dual" or "anti-self-dual" sector of a Lagrangian describing a massless scalar and a Maxwell field (the phrase "self-dual" here being used essentially in its sense in monopole theory). There are similar results for the non-Abelian BF system as well. These shared features of edge states in 3D and 4D suggest that the edge Lagrangians for BF systems are certain natural generalizations of field theory Lagrangians related to KM groups.

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Li, Jiayu, and Yongbing Zhang. "Lagrangian F-stability of closed Lagrangian self-shrinkers." Journal für die reine und angewandte Mathematik (Crelles Journal) 2017, no. 733 (December 1, 2017): 1–23. http://dx.doi.org/10.1515/crelle-2015-0002.

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AbstractIn this paper we study the Lagrangian F-stability of closed Lagrangian self-shrinkers in complex Euclidean space. We show that any closed Lagrangian self-shrinker with first Betti number greater than one is Lagrangian F-unstable. For a closed Lagrangian self-shrinker with first Betti number equal to one, we show that Lagrangian F-stability is equivalent to Hamiltonian F-stability. We also characterize Hamiltonian F-stability of a closed Lagrangian self-shrinker by its spectral property of a drift Laplacian.

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11

Torri, Giuseppe, and Zhiming Kuang. "A Lagrangian Study of Precipitation-Driven Downdrafts*." Journal of the Atmospheric Sciences 73, no. 2 (February 1, 2016): 839–54. http://dx.doi.org/10.1175/jas-d-15-0222.1.

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Abstract Precipitation-driven downdrafts are an important component of deep convective systems. They stabilize the atmosphere by injecting relatively cold and dry air into the boundary layer. They have also been invoked as responsible for balancing surface latent and sensible heat fluxes in the heat and moisture budget of tropical boundary layers. This study is focused on precipitation-driven downdrafts and basic aspects of their dynamics in a case of radiative–convective equilibrium. Using Lagrangian particle tracking, it is shown that such downdrafts have very low initial heights, with most parcels originating within 1.5 km from the surface. The tracking is also used to compute the contribution of downdrafts to the flux of moist static energy at the top of the boundary layer, and it is found that this is on the same order of magnitude as the contribution due to convective updrafts, but much smaller than that due to turbulent mixing across the boundary layer top in the environment. Furthermore, considering the mechanisms driving the downdrafts, it is shown that the work done by rain evaporation is less than half that done by condensate loading.

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12

Huang, X. X., and X. Q. Yang. "Further Study on Augmented Lagrangian Duality Theory." Journal of Global Optimization 31, no. 2 (February 2005): 193–210. http://dx.doi.org/10.1007/s10898-004-5695-7.

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13

Jamal, Sameerah. "A study of the approximate singular Lagrangian-conditional Noether symmetries and first integrals." International Journal of Geometric Methods in Modern Physics 16, no. 03 (March 2019): 1950033. http://dx.doi.org/10.1142/s0219887819500336.

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The investigation of approximate symmetries of reparametrization invariant Lagrangians of [Formula: see text] degrees of freedom and quadratic velocities is presented. We show that extra conditions emerge which give rise to approximate and conditional Noether symmetries of such constrained actions. The Noether symmetries are the simultaneous conformal Killing vectors of both the kinetic metric and the potential. In order to recover these conditional symmetry generators which would otherwise be lost in gauge fixing the lapse function entering the perturbative Lagrangian, one must consider the lapse among the degrees of freedom. We establish a geometric framework in full generality to determine the admitted Noether symmetries. Additionally, we obtain the corresponding first integrals (modulo a constraint equation). For completeness, we present a pedagogical application of our method.

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Matsumoto, Masao. "Restriction on types of coherent states due to gauge symmetry." International Journal of Modern Physics B 28, no. 14 (April 25, 2014): 1450082. http://dx.doi.org/10.1142/s0217979214500829.

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From the viewpoint of the SU(2) coherent states (CS) and their path integrals (PI) labeled by a full set of Euler angles (ϕ, θ, ψ) which we developed in the previous paper, we study the relations between gauge symmetries of Lagrangians and allowed quantum states; We investigate permissible types of fiducial vectors (FV) in the full quantum dynamics in terms of SU(2) CS for typical Lagrangians. We propose a general framework for a Lagrangian having a certain gauge symmetry with respect to one of the Euler angles ψ. We find that for the case FV are so restricted that they belong to the eigenstates of Ŝ3 or to the orbits of them under the action of the SU(2); And the strength of a fictitious monopole, which appears in the Lagrangian, is a multiple of ½. In this case Dirac strings are permitted. Our formulations and results deepen those of the preceding work by Stone that has piloted us; We illustrate the relation between the two methods. The reasoning here does not work for a Lagrangian without the gauge symmetry. This suggests a new possibility about monopole charge quantization. Besides analogies to field theory and entanglements in quantum information (QI) are briefly mentioned.

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15

Morel, X., M. A. Lucas, and F. Dos Santos. "A Lagrangian study of the Brazil-Malvinas confluence: Lagrangian coherent structures and several lyapunov exponents." Journal of Operational Oceanography 7, no. 2 (August 2014): 13–23. http://dx.doi.org/10.1080/1755876x.2014.11020155.

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16

Padberg-Gehle, Kathrin, and Christiane Schneide. "Network-based study of Lagrangian transport and mixing." Nonlinear Processes in Geophysics 24, no. 4 (October 20, 2017): 661–71. http://dx.doi.org/10.5194/npg-24-661-2017.

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Abstract. 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.

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17

Paparella, F., A. Babiano, C. Basdevant, A. Provenzale, and P. Tanga. "A Lagrangian study of the Antarctic polar vortex." Journal of Geophysical Research: Atmospheres 102, no. D6 (March 1, 1997): 6765–73. http://dx.doi.org/10.1029/96jd03377.

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18

Prants, Sergey V. "A Lagrangian study of eddies in the ocean." Regular and Chaotic Dynamics 21, no. 3 (May 2016): 335–50. http://dx.doi.org/10.1134/s1560354716030060.

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19

Yamazaki, Hidekatsu, and Loren R. Haury. "A new Lagrangian model to study animal aggregation." Ecological Modelling 69, no. 1-2 (September 1993): 99–111. http://dx.doi.org/10.1016/0304-3800(93)90051-s.

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20

Blair, David E. "On Lagrangian Catenoids." Canadian Mathematical Bulletin 50, no. 3 (September 1, 2007): 321–33. http://dx.doi.org/10.4153/cmb-2007-031-4.

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AbstractRecently I. Castro and F.Urbano introduced the Lagrangian catenoid. Topologically, it is ℝ × Sn–1 and its induced metric is conformally flat, but not cylindrical. Their result is that if a Lagrangian minimal submanifold in ℂn is foliated by round (n – 1)-spheres, it is congruent to a Lagrangian catenoid. Here we study the question of conformally flat, minimal, Lagrangian submanifolds in ℂn. The general problem is formidable, but we first show that such a submanifold resembles a Lagrangian catenoid in that its Schouten tensor has an eigenvalue of multiplicity one. Then, restricting to the case of at most two eigenvalues, we show that the submanifold is either flat and totally geodesic or is homothetic to (a piece of) the Lagrangian catenoid.

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21

Wan, Xiao Hang, Jian Gang Wang, Zhao Wei Dong, and Shi Jun Zhang. "Study on the Economical Distribution of Load Based on the Lagrangian Multipliers." Advanced Materials Research 712-715 (June 2013): 2600–2603. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.2600.

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The main objective of this study is to investigate the economical distribution of generator load based on the Lagrangian Multipliers. The reasonable economical distribution of generator load based on the lagrangian multipliers model is established in this paper, which uses the appropriate mathematics optimized algorithms whose computation precision is higher and convergence characteristics is good too. This algorithm improves the efficiency of computation, which is very significant in engineering

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22

YANG, YUE, and D. I. PULLIN. "Geometric study of Lagrangian and Eulerian structures in turbulent channel flow." Journal of Fluid Mechanics 674 (March 2, 2011): 67–92. http://dx.doi.org/10.1017/s0022112010006427.

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We report the detailed multi-scale and multi-directional geometric study of both evolving Lagrangian and instantaneous Eulerian structures in turbulent channel flow at low and moderate Reynolds numbers. The Lagrangian structures (material surfaces) are obtained by tracking the Lagrangian scalar field, and Eulerian structures are extracted from the swirling strength field at a time instant. The multi-scale and multi-directional geometric analysis, based on the mirror-extended curvelet transform, is developed to quantify the geometry, including the averaged inclination and sweep angles, of both structures at up to eight scales ranging from the half-height δ of the channel to several viscous length scales δν. Here, the inclination angle is on the plane of the streamwise and wall-normal directions, and the sweep angle is on the plane of streamwise and spanwise directions. The results show that coherent quasi-streamwise structures in the near-wall region are composed of inclined objects with averaged inclination angle 35°–45°, averaged sweep angle 30°–40° and characteristic scale 20δν, and ‘curved legs’ with averaged inclination angle 20°–30°, averaged sweep angle 15°–30° and length scale 5δν–10δν. The temporal evolution of Lagrangian structures shows increasing inclination and sweep angles with time, which may correspond to the lifting process of near-wall quasi-streamwise vortices. The large-scale structures that appear to be composed of a number of individual small-scale objects are detected using cross-correlations between Eulerian structures with large and small scales. These packets are located at the near-wall region with the typical height 0.25δ and may extend over 10δ in the streamwise direction in moderate-Reynolds-number, long channel flows. In addition, the effects of the Reynolds number and comparisons between Lagrangian and Eulerian structures are discussed.

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23

Zhang, Yong, Yuemin Zhao, Zhonglin Gao, Chenlong Duan, Ji Xu, Liqiang Lu, Junwu Wang, and Wei Ge. "Experimental and Eulerian-Lagrangian-Lagrangian study of binary gas-solid flow containing particles of significantly different sizes." Renewable Energy 136 (June 2019): 193–201. http://dx.doi.org/10.1016/j.renene.2018.12.121.

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24

Semazzi, Fredrick H. M., Donald W. Webb, and George Pouliot. "A Study of Trajectory Uncentering in Semi-Lagrangian Models." Journal of the Meteorological Society of Japan. Ser. II 74, no. 5 (1996): 695–707. http://dx.doi.org/10.2151/jmsj1965.74.5_695.

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25

Dutrieux, Pierre, Christophe E. Menkes, Jerome Vialard, Pierre Flament, and Bruno Blanke. "Lagrangian Study of Tropical Instability Vortices in the Atlantic." Journal of Physical Oceanography 38, no. 2 (February 1, 2008): 400–417. http://dx.doi.org/10.1175/2007jpo3763.1.

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Abstract Tropical instability waves and tropical instability vortices (TIVs) exert major controls on ocean dynamics, thermodynamics, and biology on intraseasonal to seasonal time scales. To understand the fundamental mechanisms at play, a Lagrangian analysis of the 3D circulation of westward-propagating TIVs was performed in a high-resolution Atlantic Ocean simulation. The model reproduces the main temperature and velocity features of the tropical Atlantic mean state and the TIVs. Lagrangian diagnostics were used to track the water masses transported in vortices and exchanged with surrounding waters. The 3D circulation within vortices is consistent with previous observations and dominated by anticyclonic rotation with downwelling and upwelling near the leading and trailing edges of the vortex, respectively. This convergent flow creates sharp gradients at the TIV southwestern edge, where vertical mixing is most efficient. While TIVs remain highly dynamically coherent throughout their lifetime, significant exchanges occur with their surroundings, with 50% of their water being renewed over one rotation cycle. A detailed investigation of the eddies’ sources and sinks reveals that they mostly transport southern water zonally, while northern waters are mostly passing through or fluxed southward in their lee. A notable source of entrained water is the Equatorial Undercurrent.

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de la Barre, C. M., W. M. Kaula, and F. Varadi. "A Study of Orbits near Saturn's Triangular Lagrangian Points." Icarus 121, no. 1 (May 1996): 88–113. http://dx.doi.org/10.1006/icar.1996.0073.

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27

Jönsson, Bror F., Kristofer Döös, Kai Myrberg, and Peter A. Lundberg. "A Lagrangian-trajectory study of a gradually mixed estuary." Continental Shelf Research 31, no. 17 (November 2011): 1811–17. http://dx.doi.org/10.1016/j.csr.2011.07.007.

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28

Couzinet, Anthony, Benoit Bédat, and Olivier Simonin. "Numerical Study and Lagrangian Modelling of Turbulent Heat Transport." Flow, Turbulence and Combustion 80, no. 1 (July 3, 2007): 37–46. http://dx.doi.org/10.1007/s10494-007-9081-7.

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29

Farooqi, Muhammad Nufail, Daulet Izbassarov, Metin Muradoğlu, and Didem Unat. "Communication analysis and optimization of 3D front tracking method for multiphase flow simulations." International Journal of High Performance Computing Applications 33, no. 1 (March 15, 2017): 67–80. http://dx.doi.org/10.1177/1094342017694426.

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This paper presents a scalable parallelization of an Eulerian–Lagrangian method, namely the three-dimensional front tracking method, for simulating multiphase flows. Operating on Eulerian–Lagrangian grids makes the front tracking method challenging to parallelize and optimize because different types of communication (Lagrangian–Eulerian, Eulerian–Eulerian, and Lagrangian–Lagrangian) should be managed. In this work, we optimize the data movement in both the Eulerian and Lagrangian grids and propose two different strategies for handling the Lagrangian grid shared by multiple subdomains. Moreover, we model three different types of communication emerged as a result of parallelization and implement various latency-hiding optimizations to reduce the communication overhead. Good scalability of the parallelization strategies is demonstrated on two supercomputers. A strong scaling study using 256 cores simulating 1728 interfaces or bubbles achieves 32.5x speedup. We also conduct weak scaling study on 4096 cores simulating 27,648 bubbles on a 1024×1024×2048 Eulerian grid resolution.

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Mardani, Neda, Kabir Suara, Helen Fairweather, Richard Brown, Adrian McCallum, and Roy C. Sidle. "Improving the Accuracy of Hydrodynamic Model Predictions Using Lagrangian Calibration." Water 12, no. 2 (February 20, 2020): 575. http://dx.doi.org/10.3390/w12020575.

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While significant studies have been conducted in Intermittently Closed and Open Lakes and Lagoons (ICOLLs), very few have employed Lagrangian drifters. With recent attention on the use of GPS-tracked Lagrangian drifters to study the hydrodynamics of estuaries, there is a need to assess the potential for calibrating models using Lagrangian drifter data. Here, we calibrated and validated a hydrodynamic model in Currimundi Lake, Australia using both Eulerian and Lagrangian velocity field measurements in an open entrance condition. The results showed that there was a higher level of correlation (R2 = 0.94) between model output and observed velocity data for the Eulerian calibration compared to that of Lagrangian calibration (R2 = 0.56). This lack of correlation between model and Lagrangian data is a result of apparent difficulties in the use of Lagrangian data in Eulerian (fixed-mesh) hydrodynamic models. Furthermore, Eulerian and Lagrangian devices systematically observe different spatio-temporal scales in the flow with larger variability in the Lagrangian data. Despite these, the results show that Lagrangian calibration resulted in optimum Manning coefficients (n = 0.023) equivalent to those observed through Eulerian calibration. Therefore, Lagrangian data has the potential to be used in hydrodynamic model calibration in such aquatic systems.

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31

KAMANI, DAVOUD. "T-DUALITY AND NONCOMMUTATIVE DBI ACTION." Modern Physics Letters A 17, no. 04 (February 10, 2002): 237–43. http://dx.doi.org/10.1142/s021773230200645x.

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In this paper we study the noncommutative description of the DBI Lagrangian and its T-dual counterpart. We restrict the freedoms of the noncommutativity parameters of these Lagrangians. Therefore the noncommutativity parameter, the effective metric, the effective coupling constant of the string and the extra modulus [Formula: see text] of the effective T-dual theory, can be expressed in terms of the closed string variables g, B, gs and the noncommutativity parameter of the effective theory of open string.

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Na, Seon Hong. "Study on Pullout Behavior of Embedded Suction Anchors in Sand using ALE (Arbitrary Lagrangian Eulerian) Technique." Journal of the Korean Society of Civil Engineers 34, no. 1 (2014): 167. http://dx.doi.org/10.12652/ksce.2014.34.1.0167.

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33

Hoffmann, F. "The Effect of Spurious Cloud Edge Supersaturations in Lagrangian Cloud Models: An Analytical and Numerical Study." Monthly Weather Review 144, no. 1 (December 22, 2015): 107–18. http://dx.doi.org/10.1175/mwr-d-15-0234.1.

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Abstract This study analyzes the production and the effect of spurious cloud edge supersaturations in Lagrangian cloud models (LCMs), which simulate droplets and aerosols explicitly as Lagrangian particles. By applying an idealized one-dimensional setup, it is shown that the production of spurious cloud edge supersaturations in LCMs and Eulerian cloud models is identical. In LCMs, however, the effect of spurious supersaturations on the number of activated/deactivated particles is decreased due to (i) a physically more appropriate representation of the activation process, and (ii) the LCM’s ability to represent the distribution of liquid water on the subgrid scale. Additionally, an analytic solution for the production of spurious supersaturations in both Lagrangian and Eulerian cloud models is derived, enabling the identification of the upper limit of spurious supersaturations and the conditions under which they occur.

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Montesinos, Merced, Diego Gonzalez, Rodrigo Romero, and Mariano Celada. "Off-Shell Noether Currents and Potentials for First-Order General Relativity." Symmetry 13, no. 2 (February 20, 2021): 348. http://dx.doi.org/10.3390/sym13020348.

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We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

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35

Gui, Nan, Xingtuan Yang, Jie Yan, Jiyuan Tu, and Shengyao Jiang. "Numerical Study of Correlation of Fluid Particle Acceleration and Turbulence Intensity in Swirling Flow." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/179072.

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Numerical investigation of correlation between the fluid particle acceleration and the intensity of turbulence in swirling flows at a large Reynolds number is carried out via direct numerical simulation. A weak power-law form correlationur.m.sE~C(aL)φbetween the Lagrangian acceleration and the Eulerian turbulence intensity is derived. It is found that the increase of the swirl level leads to the increase of the exponentφand the trajectory-conditioned correlation coefficientρ(aL,uE)and results in a weak power-law augmentation of the acceleration intermittency. The trajectory-conditioned convection of turbulence fluctuation in the Eulerian viewpoint is generally linearly proportional to the fluctuation of Lagrangian accelerations, indicating a weak but clear relation between the Lagrangian intermittency and Eulerian intermittency effects. Moreover, except the case with vortex breakdown, the weak linear dependency is maintained when the swirl levels change, only with the coefficient of slope varied.

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36

van den Bremer, T. S., C. Whittaker, R. Calvert, A. Raby, and P. H. Taylor. "Experimental study of particle trajectories below deep-water surface gravity wave groups." Journal of Fluid Mechanics 879 (September 20, 2019): 168–86. http://dx.doi.org/10.1017/jfm.2019.584.

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Owing to the interplay between the forward Stokes drift and the backward wave-induced Eulerian return flow, Lagrangian particles underneath surface gravity wave groups can follow different trajectories depending on their initial depth below the surface. The motion of particles near the free surface is dominated by the waves and their Stokes drift, whereas particles at large depths follow horseshoe-shaped trajectories dominated by the Eulerian return flow. For unidirectional wave groups, a small net displacement in the direction of travel of the group results near the surface, and is accompanied by a net particle displacement in the opposite direction at depth. For deep-water waves, we study these trajectories experimentally by means of particle tracking velocimetry in a two-dimensional flume. In doing so, we provide visual illustration of Lagrangian trajectories under groups, including the contributions of both the Stokes drift and the Eulerian return flow to both the horizontal and the vertical Lagrangian displacements. We compare our experimental results to leading-order solutions of the irrotational water wave equations, finding good agreement.

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37

Oloeriu, Florin, Oana Mocian, Roxana Nedelcu, Dănuţ Grosu, and Constantin Ilie. "Ballistic Impact: A Comparative Case Study Using Lagrangian Method with Erosion Criterion and SPH." Advanced Materials Research 1036 (October 2014): 568–73. http://dx.doi.org/10.4028/www.scientific.net/amr.1036.568.

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The ballistic simulation attempted in this work is among the most difficult as both the projectile and the target experience significant deformations. Traditionally these simulations have been performed using a Lagrangian approach, i.e. a deformable mesh with large mesh deformations. There are three often used techniques when studying ballistic problems with the Lagrangian method: remeshing (generally not available for 3D hexahedra meshes), the 'pilot hole' technique and material erosion. Because these techniques imply element removal, in order to allow the calculation to continue, the Lagrangian method lacks a physical basis. Moreover, no general guidance exists for selecting one of the three techniques mentioned before. The Smoothed Particle Hydrodynamic method as implemented in the commercial code LS-DYNA has been used in this paper to solve the problem of the impact between different caliber projectiles and various types of metal targets. The results are compared to those produced by dynamic analysis using conventional finite element methods with material erosion as implemented in LS-DYNA.

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Prants, S. V., M. V. Budyansky, and M. Yu Uleysky. "Lagrangian study of surface transport in the Kuroshio Extension area based on simulation of propagation of Fukushima-derived radionuclides." Nonlinear Processes in Geophysics 21, no. 1 (February 24, 2014): 279–89. http://dx.doi.org/10.5194/npg-21-279-2014.

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Abstract. Lagrangian approach is applied to study near-surface large-scale transport in the Kuroshio Extension area using a simulation with synthetic particles advected by AVISO altimetric velocity field. A material line technique is proposed and applied to find out the origin of water masses in cold-core cyclonic rings pinched off from the jet in summer 2011. Tracking and Lagrangian maps provide the evidence of cross-jet transport. Fukushima-derived caesium isotopes are used as Lagrangian tracers to study transport and mixing in the area a few months after the 11 March 2011 tsunami that caused heavy damage of the Fukushima Nuclear Power Plant (FNPP). Tracking maps are computed to trace the origin of water parcels with measured levels of 134Cs and 137Cs concentrations collected during two research vessel (R/V) cruises in June and July 2011 in the large area of the northwest Pacific (Kaeriyama et al., 2013; Buesseler et al., 2012). It is shown that Lagrangian simulations are useful for finding the surface areas that are potentially dangerous due to the risk of radioactive contamination. The results of simulation are supported by tracks of the surface drifters that were deployed in the area.

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Jeong, Sang-Seom, Kwang-Woo Lee, and Jun-Young Ko. "A Study on the 3D Analysis of Debris Flow Based on Large Deformation Technique (Coupled Eulerian-Lagrangian)." Journal of the Korean Geotechnical Society 31, no. 12 (December 31, 2015): 45–57. http://dx.doi.org/10.7843/kgs.2015.31.12.45.

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40

Valluri, S. R., W. J. Mielniczuk, and D. R. Lamm. "Numerical study of the properties of the real part of the Heisenberg–Euler effective Lagrangian." Canadian Journal of Physics 72, no. 11-12 (November 1, 1994): 786–92. http://dx.doi.org/10.1139/p94-103.

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Convenient series representations for both the real and imaginary parts of the Heisenberg–Euler Lagrangian of quantum electrodynamics for constant electric, E, and magnetic, B, fields of arbitrary relative angle have been presented previously by Valluri et al. along with numerical results for the real and imaginary parts of the Lagrangian for its approximate valid range of [Formula: see text] and [Formula: see text], where Ecr ≈ 1.7 × 1016 V cm−1 and Bcr ≈ 4.4 × 1013 G. These series representations are applied to the calculation of the Hamiltonian energy, polarization, and magnetization densities for the chargeless vacuum, and numerical results and plots are presented for the specific cases of parallel and perpendicular E and B fields. The series representation of the Heisenberg–Euler Lagrangian is then applied to the energy momentum tensor, Tμν, to calculate the nonlinear corrections to the Maxwell terms of this tensor. Strong and weak field corrections are calculated and the latter are compared to Schwinger's weak field corrections for Tμν.

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41

Chen, Bang-Yen. "CLASSIFICATION OF LAGRANGIAN SURFACES OF CONSTANT CURVATURE IN THE COMPLEX EUCLIDEAN PLANE." Proceedings of the Edinburgh Mathematical Society 48, no. 2 (May 23, 2005): 337–64. http://dx.doi.org/10.1017/s0013091504000203.

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AbstractOne of the most fundamental problems in the study of Lagrangian submanifolds from a Riemannian geometric point of view is the classification of Lagrangian immersions of real-space forms into complex-space forms. In this article, we solve this problem for the most basic case; namely, we classify Lagrangian surfaces of constant curvature in the complex Euclidean plane $\mathbb{C}^2$. Our main result states that there exist 19 families of Lagrangian surfaces of constant curvature in $\mathbb{C}^2$. Twelve of the 19 families are obtained via Legendre curves. Conversely, Lagrangian surfaces of constant curvature in $\mathbb{C}^2$ can be obtained locally from the 19 families.

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42

Rühs, Siren, Victor Zhurbas, Inga M. Koszalka, Jonathan V. Durgadoo, and Arne Biastoch. "Eddy Diffusivity Estimates from Lagrangian Trajectories Simulated with Ocean Models and Surface Drifter Data—A Case Study for the Greater Agulhas System." Journal of Physical Oceanography 48, no. 1 (January 2018): 175–96. http://dx.doi.org/10.1175/jpo-d-17-0048.1.

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AbstractThe Lagrangian analysis of sets of particles advected with the flow fields of ocean models is used to study connectivity, that is, exchange pathways, time scales, and volume transports, between distinct oceanic regions. One important factor influencing the dispersion of fluid particles and, hence, connectivity is the Lagrangian eddy diffusivity, which quantifies the influence of turbulent processes on the rate of particle dispersal. Because of spatial and temporal discretization, turbulence is not fully resolved in modeled velocities, and the concept of eddy diffusivity is used to parameterize the impact of unresolved processes. However, the relations between observation- and model-based Lagrangian eddy diffusivity estimates, as well as eddy parameterizations, are not clear. This study presents an analysis of the spatially variable near-surface lateral eddy diffusivity estimates obtained from Lagrangian trajectories simulated with 5-day mean velocities from an eddy-resolving ocean model (INALT01) for the Agulhas system. INALT01 features diffusive regimes for dynamically different regions, some of which exhibit strong suppression of eddy mixing by mean flow, and it is consistent with the pattern and magnitude of drifter-based eddy diffusivity estimates. Using monthly mean velocities decreases the estimated diffusivities less than eddy kinetic energy, supporting the idea that large and persistent eddy features dominate eddy diffusivities. For a noneddying ocean model (ORCA05), Lagrangian eddy diffusivities are greatly reduced, particularly when the Gent and McWilliams parameterization of mesoscale eddies is employed.

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JOYCE, DOMINIC. "RULED SPECIAL LAGRANGIAN 3-FOLDS IN [Copf ]3." Proceedings of the London Mathematical Society 85, no. 1 (March 2002): 233–56. http://dx.doi.org/10.1112/s0024611502013485.

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This is the fifth in a series of papers constructing explicit examples of special Lagrangian submanifolds in ${\mathbb C}^m$. A submanifold of ${\mathbb C}^m$ is ruled if it is fibred by a family of real straight lines in ${\mathbb C}^m$. This paper studies ruled special Lagrangian 3-folds in ${\mathbb C}^3$, giving both general theory and families of examples. Our results are related to previous work of Harvey and Lawson, Borisenko, and Bryant. Special Lagrangian cones in ${\mathbb C}^3$ are automatically ruled, and each ruled special Lagrangian 3-fold is asymptotic to a unique special Lagrangian cone. We study the family of ruled special Lagrangian 3-folds N asymptotic to a fixed special Lagrangian cone N0. We find that this depends on solving a linear equation, so that the family of such N has the structure of a vector space. We also show that the intersection $\Sigma$ of N0 with the unit sphere ${\mathcal S}^5$ in ${\mathbb C}^3$ is a Riemann surface, and construct a ruled special Lagrangian 3-fold N asymptotic to N0 for each holomorphic vector field w on $\Sigma$. As corollaries of this we write down two large families of explicit special Lagrangian 3-folds in ${\mathbb C}^3$ depending on a holomorphic function on $\mathbb C$, which include many new examples of singularities of special Lagrangian 3-folds. We also show that each special Lagrangian T2-cone N0 can be extended to a 2-parameter family of ruled special Lagrangian 3-folds asymptotic to N0, and diffeomorphic to $T^2\times{\mathbb R}$.2000 Mathematical Subject Classification: 53C38, 53D12.

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44

Ding Guang-Tao. "A study on the Lagrangian image of the Birkhoffian representations." Acta Physica Sinica 59, no. 1 (2010): 15. http://dx.doi.org/10.7498/aps.59.15.

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45

Joseph, Binson, and P. S. Swathi. "Lagrangian particle transport in the Indian Ocean: A model study." Journal of Geophysical Research: Oceans 104, no. C3 (March 15, 1999): 5211–24. http://dx.doi.org/10.1029/1998jc900093.

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Dong, Yubing, and Yizhan Wang. "A study of pion structures in an effective Lagrangian approach." Journal of Physics G: Nuclear and Particle Physics 39, no. 2 (January 12, 2012): 025003. http://dx.doi.org/10.1088/0954-3899/39/2/025003.

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47

Rocha, Ana Maria A. C., and Edite M. G. P. Fernandes. "Numerical study of augmented Lagrangian algorithms for constrained global optimization." Optimization 60, no. 10-11 (October 2011): 1359–78. http://dx.doi.org/10.1080/02331934.2011.628671.

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48

Ma, Jingsen, Georges L. Chahine, and Chao-Tsung Hsiao. "An Eulerian-Lagrangian study of cloud dynamics near a wall." Journal of the Acoustical Society of America 139, no. 4 (April 2016): 2029. http://dx.doi.org/10.1121/1.4949987.

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49

Wang, Junmin, Lei Fu, Haibo Xu, and Yeechung Jin. "Numerical study on flow over stepped spillway using Lagrangian method." IOP Conference Series: Earth and Environmental Science 121 (February 2018): 052019. http://dx.doi.org/10.1088/1755-1315/121/5/052019.

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50

Guida, M., F. Marulo, M. Meo, A. Grimaldi, and G. Olivares. "SPH – Lagrangian study of bird impact on leading edge wing." Composite Structures 93, no. 3 (February 2011): 1060–71. http://dx.doi.org/10.1016/j.compstruct.2010.10.001.

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