Cenni, P.; Fagarazzi, G. [ENEA, Centro Ricerche Ezio Clementel, Bologna (Italy). Dipt. Ambiente; Sarchielli, M.; Zanobini, F. [Bologna Univ., Bologna (Italy). Dipt. di Psicologia
1999-07-01
The aim of this research on 143 workers of the ENEA area in Bologna, has been to survey the degree of well-being perceived and expressed by these workers with respect to different factors of the work environment. This study follows some training/information seminars on environment, health and safety organized in ENEA by Occupational Medicine Group to comply with Leg. Decr. 626/94. In a multidisciplinary approach the health idea has been interpreted not as lack of illness but as pursuit and preservation of the well-being in the work environment. For this purpose, also the involvement and participation of the workers seem to be very useful for subjective reports about individual task, equipment, interfaces, workplace and work organization. In this research, we have adopted an ergonomic checklist based on guiding principles to be applied to the design of optimal working conditions with regard to human well-being, safety and health (see UNI ENV 26385, 1991). Data processing and analysis have requested occupational medicine, ergonomics and statistics competencies. [Italian] La ricerca condotta su un campione ENEA di 143 dipendenti dell'area bolognese ha inteso verificare il grado di benessere percepito ed espresso dai lavoratori in rapporto alle diverse variabili presenti nel contesto lavorativo. Tale indagine e' stata preceduta da specifici seminari di formazione/informazione su ambiente, salute e sicurezza, organizzati a cura della Medicina del Lavoro di Bologna presso le sedi ENEA, a seguito delle disposizioni contenute nel D.Lvo. 626/94. In un'ottica multidisciplinare, il concetto di salute e' stato interpretato non tanto come assenza di malattia quanto come ricerca e mantenimento del benessere lavorativo e, per raggiungere questo scopo, sembra essere molto utile anche il diretto coinvolgimento e la partecipazione dei lavoratori per valutazioni soggettive sulle mansioni assegnate, le attrezzature, le interfacce, la postazione di lavoro e l
Nucci, M. C.; Leach, P. G. L.
2007-01-01
Searching for a Lagrangian may seem either a trivial endeavour or an impossible task. In this paper we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H Goldstein, {\\it Classical Mechanics}, 2nd edition (Addison-Wesley, Reading, 1980)] and the damped harmonic ...
Nucci, M. C.; Leach, P. G. L.
2007-12-01
Searching for a Lagrangian may seem either a trivial endeavor or an impossible task. In this paper, we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H. Goldstein, Classical Mechanics, 2nd edition (Addison-Wesley, Reading, MA, 1980)], and the damped harmonic oscillator. This is the first paper in a series dedicated to this subject.
Lakshminarayanan, Vasudevan; Thyagarajan, K
2002-01-01
Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Many features oflight propagation can be analyzed in terms ofrays,ofcourse, subtle effects near foci, caustics or turning points would need an analysis based on the wave natureoflight. Allofgeometric optics can be derived from Fermat's principle which is an extremum principle. The counterpart in classical mechanics is of course Hamilton's principle. There is a very close analogy between mechanics ofparticles and optics oflight rays. Much insight (and useful results) can be obtained by analyzing these analogies. Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, 1956), classical mechanics is only a geometrical optics approximation to a wave theory! In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of ray propagation through various media. Given the ...
Lagrangian Quantum Homology for Lagrangian cobordism
Singer, Berit
2015-01-01
We extend the definition of Lagrangian quantum homology to monotone Lagrangian cobordism and establish its general algebraic properties. In particular we develop a relative version of Lagrangian quantum homology associated to a cobordism relative to a part of its boundary and study relations of this invariant to the ambient quantum homology.
Application expérimentale du bilan de puissance réactive à la mesure de l'anche de saxophone
Boutillon, Xavier; Gibiat, V.
1994-01-01
La notion de bilan de puissance réactive permet de lier le fonctionnement d'une anche modélisée par un ressort à celui du résonateur qu'elle excite. Un instrument à anche simple ne joue pas exactement sur les fréquences des pics d'impédance. Chaque partiel du tuyau absorbe donc (ou fournit) une puissance réactive. Leur somme algébrique est égale à celle fournie par le ressort qui représente l'anche. Sur le plan expérimental, nous avons mesuré le spectre de pression interne d'un saxophone et s...
Sepe, D.
2013-01-01
The obstruction to construct a Lagrangian bundle over a fixed integral affine manifold was constructed by Dazord and Delzant (J Differ Geom 26:223–251, 1987) and shown to be given by ‘twisted’ cup products in Sepe (Differ GeomAppl 29(6): 787–800, 2011). This paper uses the topology of universal Lagr
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Symmetries in Lagrangian Field Theory
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
Symplectic Applicability of Lagrangian Surfaces
Lorenzo Nicolodi
2009-06-01
Full Text Available We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equations. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.
Renormalization and effective lagrangians
Polchinski, Joseph
1984-01-01
There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional λø 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed.
Gravity, Time, and Lagrangians
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…
Gravity, Time, and Lagrangians
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…
2010-09-30
the vertical interpolation adjustment given by Equation 8 (SL OMT ), NOGAPS SL/SI with non-interpolation in the vertical (SL NIV), and the non semi...interpolation scheme (SL OMT ), the non-interpolating scheme in the vertical (SL NIV) and the non semi-Lagrangian NOGAPS (EULER). Figures 4 and...2009 comparing the control NOGAPS SL/SI with the adjusted vertical interpolation scheme (SL OMT ), the non-interpolating scheme in the vertical (SL NIV
Generalized Superfield Lagrangian Quantization
Lavrov, P M; Moshin, P Y
2002-01-01
We consider an extension of the gauge-fixing procedure in the framework of the Lagrangian superfield BRST and BRST-antiBRST quantization schemes for arbitrary gauge theories, taking into account the possible ambiguity in the choice of the superfield antibracket. We show that this ambiguity is fixed by the algebraic properties of the antibracket and the form of the BRST and antiBRST transformations, realized in terms of superspace translations. The Ward identities related to the generalized gauge-fixing procedure are obtained.
Lagrangian vector field and Lagrangian formulation of partial differential equations
M.Chen
2005-01-01
Full Text Available In this paper we consider the Lagrangian formulation of a system of second order quasilinear partial differential equations. Specifically we construct a Lagrangian vector field such that the flows of the vector field satisfy the original system of partial differential equations.
Topological Classification of Lagrangian Fibrations
Sepe, D
2009-01-01
We define topological invariants of regular Lagrangian fibrations using the integral affine structure on the base space and we show that these coincide with the classes known in the literature. We also classify all symplectic types of Lagrangian fibrations with base $\\rpr$ and fixed monodromy representation, generalising a construction due to Bates.
Lagrangian-Only Quantum Theory
Wharton, K B
2013-01-01
Despite the importance of the path integral, there have been relatively few attempts to look to the Lagrangian for a more realistic framework that might underlie quantum theory. While such realism is not available for the standard path integral or quantum field theory, a promising alternative is to only consider field histories for which the Lagrangian density is always zero. With this change, it appears possible to replace amplitudes with equally-weighted probabilities. This paper demonstrates a proof-of-principle for this approach, using a toy Lagrangian that corresponds to an arbitrary spin state. In this restricted framework one can derive both the Born rule and its limits of applicability. The fact that the Lagrangian obeys future boundary constraints also results in the first continuous, spacetime-based, hidden-variable description of a Bell-inequality-violating system.
Lagrangian Modeling of the Atmosphere
Schultz, Colin
2013-08-01
Like watching a balloon borne by the breeze, a Lagrangian model tracks a parcel of air as it flows through the atmosphere. Whether running forward or backward in time, Lagrangian models offer a powerful tool for tracking and understanding the fates, or origins, of atmospheric flows. In the AGU monograph Lagrangian Modeling of the Atmosphere, editors John Lin, Dominik Brunner, Christoph Gerbig, Andreas Stohl, Ashok Luhar, and Peter Webley explore the nuances of the modeling technique. In this interview Eos talks to Lin about the growing importance of Lagrangian modeling as the world settles on climate change mitigation strategies, the societal value of operational modeling, and how recent advances are making it possible to run these complex calculations at home.
The Lagrangian in Quantum Mechanics
Dirac, P. A. M.
Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue, as a result of which the whole of the classical Hamiltonian theory, which is just a structure built up on this notion, could be taken over in all its details into quantum mechanics. Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. In the first place the Lagrangian method allows one to collect together all the equations of motion and express them as the stationary property of a certain action function. (This action function is just the time-integral of the Lagrangian.) There is no corresponding action principle in terms of the coordinates and momenta of the Hamiltonian theory. Secondly the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially non-relativistic in form, since it marks out a particular time variable as the canonical conjugate of the Hamiltonian function. For these reasons it would seem desirable to take up the question of what corresponds in the quantum theory to the Lagrangian method of the classical theory. A little consideration shows, however, that one cannot expect to be able to take over the classical Lagrangian equations in any very direct way. These equations involve partial derivatives of the Lagrangian with respect to the coordinates and velocities and no meaning can be given to such derivatives in quantum mechanics. The only differentiation process that can be carried out with respect to the dynamical variables of
Lagrangian description of nonlinear chromatography
LIANG Heng; LIU Xiaolong
2004-01-01
Under the framework of non-equilibrium thermodynamic separation theory (NTST), Local Lagrangian approach (LLA) was proposed to deal with the essential issues of the convection and diffusion (shock waves) phenomena in nonlinear chromatography with recursion equations based on the three basic theorems, Lagrangian description, continuity axiom and local equilibrium assumption (LEA). This approach remarkably distinguished from the system of contemporary chromatographic theories (Eulerian description-partial differential equations), and can felicitously match modern cybernetics.
Presymplectic structures and intrinsic Lagrangians
Grigoriev, Maxim
2016-01-01
It is well-known that a Lagrangian induces a compatible presymplectic form on the equation manifold (stationary surface, understood as a submanifold of the respective jet-space). Given an equation manifold and a compatible presymplectic form therein, we define the first-order Lagrangian system which is formulated in terms of the intrinsic geometry of the equation manifold. It has a structure of a presymplectic AKSZ sigma model for which the equation manifold, equipped with the presymplectic form and the horizontal differential, serves as the target space. For a wide class of systems (but not all) we show that if the presymplectic structure originates from a given Lagrangian, the proposed first-order Lagrangian is equivalent to the initial one and hence the Lagrangian per se can be entirely encoded in terms of the intrinsic geometry of its stationary surface. If the compatible presymplectic structure is generic, the proposed Lagrangian is only a partial one in the sense that its stationary surface contains the...
About non standard Lagrangians in cosmology
Dimitrijevic, Dragoljub D.; Milosevic, Milan [Department of Physics, Faculty of Science and Mathematics, University of Nis, Visegradska 33, P.O. Box 224, 18000 Nis (Serbia)
2012-08-17
A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.
Lagrangian continuum dynamics in ALEGRA.
Wong, Michael K. W.; Love, Edward
2007-12-01
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.
A Student's Guide to Lagrangians and Hamiltonians
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Lagrangian multi-particle statistics
Lüthi, Beat; Berg, Jacob; Ott, Søren
2007-01-01
Combined measurements of the Lagrangian evolution of particle constellations and the coarse-grained velocity derivative tensor. partial derivative(u) over tilde (i) /partial derivative x(j) are presented. The data are obtained from three-dimensional particle tracking measurements in a quasi isotr...
Galilean invariance in Lagrangian mechanics
Mohallem, J. R.
2015-10-01
The troublesome topic of Galilean invariance in Lagrangian mechanics is discussed in two situations: (i) A particular case involving a rheonomic constraint in uniform motion and (ii) the general translation of an entire system and the constants of motion involved. A widespread impropriety in most textbooks is corrected, concerning a condition for the equality h = E to hold.
Data Assimilation With Regional Lagrangian Models
1999-09-30
Journal of Marine Systems . RESULTS We are able to fit the inviscid Lagrangian model with synthetic Lagrangian data for short periods of time (1-2 days...Mead and A.F. Bennett, 1999. Towards regional assimilation of data: The Lagrangian form of the reduced gravity model and its inverse, (submitted), Journal of Marine Systems .
Anchored Lagrangian submanifolds and their Floer theory
Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru
2009-01-01
We introduce the notion of (graded) anchored Lagrangian submanifolds and use it to study the filtration of Floer' s chain complex. We then obtain an anchored version of Lagrangian Floer homology and its (higher) product structures. They are somewhat different from the more standard non-anchored version. The anchored version discussed in this paper is more naturally related to the variational picture of Lagrangian Floer theory and so to the likes of spectral invariants. We also discuss rationality of Lagrangian submanifold and reduction of the coefficient ring of Lagrangian Floer cohomology of thereof.
Effective Lagrangian for Nonrelativistic Systems
Haruki Watanabe
2014-09-01
Full Text Available The effective Lagrangian for Nambu-Goldstone bosons (NGBs in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing 1 dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in 1+1 dimensions.
Complex Lagrangians and phantom cosmology
Andrianov, A A; Kamenshchik, A Yu
2006-01-01
Motivated by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with PT symmetry, we show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. The model is based on a classical complex Lagrangian of a scalar field. Specific symmetry properties analogous to PT in non-Hermitian quantum mechanics lead to purely real equation of motion.
Alessandra Gilardini
2012-07-01
Full Text Available La sensibilità emotiva può riferirsi a fenomeni contagiosi, automatici come nel caso di un bambino che inizia a piangere perché sente un altro fare lo stesso, o con una forte componente cognitiva, come la compassione e la simpatia. L'empatia implica questo tipo di sensibilità. Ma è solo una dote dell'uomo?
Alternative expression for the electromagnetic Lagrangian
Saldanha, Pablo L
2015-01-01
We propose an alternative expression for the Lagrangian density that governs the interaction of a charged particle with external electromagnetic fields. The proposed Lagrangian is written in terms of the local superposition of the particle fields with the applied electromagnetic fields, not in terms of the particle charge and of the electromagnetic potentials as is usual. The total Lagrangian for a set of charged particles assumes a simple elegant form with the alternative formulation, giving an aesthetic support for it. The proposed Lagrangian is equivalent to the traditional one in their domain of validity and provides an interesting description of the Aharonov-Bohm effect.
Tamara van Kessel
2012-05-01
Full Text Available Si deve amare la mamma anche se povera’. La Società Dante Alighieri, l’emigrazione italiana e la protezione dell’italianità all’estero, 1870-1925L’attività della Società Dante Alighieri per la tutela degli emigrati italiani agli inizi del Novecento dimostra quanto erano intrecciati la costruzione dell’identità nazionale ed il desiderio di mantenere i legami con gli italiani all’estero. Benché nell’Italia unita ci fossero state diverse opinioni sul fenomeno dell’emigrazione di massa, il governo cominciò a vedere questi concittadini sparsi per il mondo non come segno di povertà, ma come un veicolo per comprovare all’estero le doti attribuite al proprio paese. In un simile spirito nazionalista, la Dante si occupò di fare dell’emigrato un degno rappresentate della cultura e società italiane. Un esempio di come cercarono di guidare l’emigrato è ‘Il Decalogo degli Emigranti’: un documento divulgato tramite il bollettino della Dante nel 1925. Si direbbe che le raccomandazioni di questo ‘Decalogo’si inseriscono armoniosamente nella propaganda fascista di quell’epoca. Un documento simile del 1913 fa vedere invece come già allora era invocata una forte lealtà alla nazione. Ciò che colpisce nelle due fonti è che l’italiano all’estero veniva incoraggiato a consumare prodotti esclusivamente italiani. Questo motivo economico era parte integrante di molta della politica culturale internazionale di quel periodo. Infine, la forma scelta – quella del decalogo – è emblematica per il modo in cui si dovette ricorrere ai modelli religiosi per consolidare l’identità italiana laica.
An example of special Lagrangian fibration
FU Jixiang
2005-01-01
On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4directions.
Electroweak Chiral Lagrangian for Neutral Higgs Boson
WANG Shun-Zhi; WANG Qing
2008-01-01
A neutral Higgs boson is added into the traditional electroweak chiral Lagrangian by writing down all possible high dimension operators. The matter part of the Lagrangian is investigated in detail. We find that if Higgs field dependence of Yukawa couplings can be factorized out, there will be no flavour changing neutral couplings; neutral Higgs can induce coupling between light and heavy neutrinos.
A functional LMO invariant for Lagrangian cobordisms
Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël
2008-01-01
Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le–Murakami–Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category...
Anomalous effective lagrangians and vector resonance models
Pallante, E.; Petronzio, R.
1993-01-01
Chiral lagrangians including vector resonances have been shown to saturate the finite part of some of the counterterms needed to regularize ordinary one-loop effective lagrangians of pseudoscalar interactions with external currents. The equivalence between different models has been discussed in the
A Lagrangian approach to classical thermodynamics
Stokes, A.
2017-02-01
The specification of microstates of interacting dynamical systems is different in Lagrangian and Hamiltonian approaches whenever the interaction Lagrangian depends on generalised velocities. In almost all cases of physical interest however, velocity-dependent interaction Lagrangians do not couple velocities belonging to different subsystems. For these cases we define reduced system and bath Lagrangian macrostates, which like the underlying microstates differ from their Hamiltonian counterparts. We then derive exact first and second laws of thermodynamics without any modification of the original system and bath quantities. This approach yields manifestly gauge-invariant definitions of work and free energy, and a gauge-invariant Jarzynski equality is derived. The formalism is applied in deriving the thermodynamic laws for a material system within the radiation reservoir. The Lagrangian partition of the total energy is manifestly gauge-invariant and is in accordance with Poynting's theorem.
On Attracting Lagrangian Coherent Structures
Karrasch, Daniel
2013-01-01
In this note, we show that in the autonomous, two-dimensional incompressible saddle flow, contrary to common intuition, also attracting Lagrangian Coherent Structures (LCSs) can show up as ridges of the forward finite-time Lyapunov exponent (FTLE) field. This raises the issue of characterization of attracting LCSs from forward time FTLE analysis. First, we extend recent results of Haller & Sapsis (2011) [11] on the relation between forward and backward maximal and minimal stretching rates to the whole finite-time Lyapunov spectrum and to stretching directions by considering the singular value decomposition (SVD) of the deformation gradient. We show two significant advantages of the SVD compared to the usual eigendecomposition of the Cauchy-Green strain tensor: (1) one gains theoretical insight into local deformation under a finite-time dynamical system, and (2) one obtains both complete forward and backward strain information from a single grid advection. Furthermore, we give a short and direct proof of t...
Time-Dependent Lagrangian Biomechanics
Ivancevic, Tijana T
2009-01-01
In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. On this extended configuration space we develop time-dependent biomechanical Lagrangian dynamics, using derived jet spaces of velocities and accelerations, as well as the underlying geometric evolution of the mass-inertia matrix. Keywords: Human time-dependent biomechanics, configuration manifold, jet spaces, geometric evolution
Critical Point Theory for Lagrangian Systems
Mazzucchelli, Marco
2012-01-01
Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange's reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more spec
Lagrangian Space Nonlinear $E$-mode clustering
Yu, Hao-Ran; Zhu, Hong-Ming
2016-01-01
We study the nonlinear $E$-mode clustering in Lagrangian space by using large scale structure (LSS) $N$-body simulations and use the displacement field information in Lagrangian space to recover the primordial linear density field. We find that, compared to Eulerian nonlinear density fields, the $E$-mode displacement fields in Lagrangian space improves the cross-correlation scale $k$ with initial density field by factor of 6 $\\sim$ 7, containing 2 orders of magnitude more primordial information. This illustrates ability of potential density reconstruction algorithms, to improve the baryonic acoustic oscillation (BAO) measurements from current and future large scale structure surveys.
An Augmented Lagrangian Approach for Scheduling Problems
Nishi, Tatsushi; Konishi, Masami
The paper describes an augmented Lagrangian decomposition and coordination approach for solving single machine scheduling problems to minimize the total weighted tardiness. The problem belongs to the class of NP-hard combinatorial optimization problem. We propose an augmented Lagrangian decomposition and coordination approach, which is commonly used for continuous optimization problems, for solving scheduling problems despite the fact that the problem is nonconvex and non-differentiable. The proposed method shows a good convergence to a feasible solution without heuristically constructing a feasible solution. The performance of the proposed method is compared with that of an ordinary Lagrangian relaxation.
Measuring And Explaining The Supersymmetric Lagrangian
Wang, L
2002-01-01
The issues of measuring the supersymmetric Lagrangian once data is available, and making the connections between the low energy effective Lagrangian and fundamental theory, are considered. After a brief introduction to the fundamentals of supersymmetry and overview of Minimal Supersymmetric Standard Model (MSSM), case studies in ways of measuring different parameters in the low energy MSSM Lagrangian are presented. They include: measuring CP violation phases and LSP masses in gluino decay; Higgs production and detection; flavor and CP violation in b → sγ processes; signature of cold dark matter in the cosmic rays. Potential ambiguities in the process of recovering the high energy effective Lagrangian from low energy data are discussed. A new basis, which is explicitly independent of unphysical parameters, is proposed to write the renormalization group equations. After a brief survey of some basic issues of string theory phenomenology, a string theory motivated Pati-Salam like model is const...
Multi-Lagrangians for Integrable Systems
Nutku, Y
2001-01-01
We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear 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. Furthermore we construct a new Lagrangian for polytropic gas dynamics in 1+1 dimensions which is a {\\it local} functional of the physical field variables, namely density and velocity.
Effective Lagrangians and Light Gravitino Phenomenology
Luty, M A; Luty, Markus A.; Ponton, Eduardo
1998-01-01
We construct the low-energy effective lagrangian for supersymmetry breaking models with a light gravitino. Our effective lagrangian is written in terms of the spin-1/2 Goldstino (the longitudinal component of the gravitino) transforming under a non-linear realization of supersymmetry. The Goldstino is derivatively coupled. We use this lagrangian to place bounds on the supersymmetry breaking scale \\sqrt{F} from Goldstino phenomenology. The most stringent bounds come from the coupling of a single photon to Goldstino pairs. For gauge-mediated models, this coupling arises at one loop in the effective lagrangian, and supernova cooling allows \\sqrt{F} > 610 GeV or \\sqrt{F} 140 GeV for tan\\beta = 2.
Detecting Lagrangian fronts with favourable fishery conditions
Prants, S V; Uleysky, M Yu
2012-01-01
Lagrangian fronts in the ocean delineate boundaries between surface waters with different Lagrangian properties. They can be accurately detected in a given velocity field by computing synoptic maps of the drift of synthetic tracers, their Lyapunov exponents, and other Lagrangian indicators. Using Russian ship's catch and location data for a number of commercial fishing seasons in the region of the northwest Pacific with one of the richest fishery in the world, it is shown that the saury fishing grounds with maximal catches are located mainly along those Lagrangian fronts 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 with the altimetric geostrophic velocity fields both in the years with the First and Second Oyashio Intrusions shows that in spite of different oceanographic conditions in both the cases the front locations may serve good indicators of potential fishing grou...
On invariant sets in Lagrangian graphs
无
2010-01-01
In this exposition, we show that the Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are sufficiently smooth. We also provide some counterexamples to show that if the Hamiltonian function is not smooth enough, then it may be non-constant on a compact invariant connected subset which lies in a Lagrangian graph.
Lagrangian Formulation of Todorov-Komar Model
Gomis, J.; Kamimura, K.; Pons, J. M.
1984-05-01
The multi-temporal Hamiltonian model of relativistic particle interaction (Todorov-Komar model) is studied from the viewpoint of the Lagrangian formalism. The action is constructed and the gauge structure is clarified.The mathematical coordinates used to describe the Lagrangian are not gauge invariant and are disqualified as the physical coordinates of the interacting particles. The position of the particles is defined as the function of the canonical variables so that the world lines are invariant under the gauge transformations.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding
Krause, Katharina; Klopper, Wim, E-mail: klopper@kit.edu [Karlsruhe Institute of Technology (KIT), Institute of Physical Chemistry, Theoretical Chemistry Group, KIT Campus South, P.O. Box 6980, 76049 Karlsruhe (Germany)
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.
Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.
Holm, Darryl D.
2002-06-01
We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.
Lagrangian Methods Of Cosmic Web Classification
Fisher, J D; Johnson, M S T
2015-01-01
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. (2012) is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or halos) 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 straight forward inclusion of the Hubble flow negating the necessity of a visually defined thresh...
Forecasting for a Lagrangian aircraft campaign
A. Stohl
2004-01-01
Full Text Available A forecast system has been developed in preparation for an upcoming aircraft measurement campaign, where the same air parcels polluted by emissions over North America shall be sampled repeatedly as they leave the continent, during transport over the Atlantic, and upon their arrival over Europe. This paper describes the model system in advance of the campaign, in order to make the flight planners familiar with the novel model output. The aim of a Lagrangian strategy is to infer changes in the chemical composition and aerosol distribution occurring en route by measured upwind/downwind differences. However, guiding aircraft repeatedly into the same polluted air parcels requires careful forecasting, for which no suitable model system exists to date. This paper describes a procedure using both Eulerian-type (i.e. concentration fields and Lagrangian-type (i.e. trajectories model output from the Lagrangian particle dispersion model FLEXPART to predict the best opportunities for a Lagrangian experiment. The best opportunities are defined as being highly polluted air parcels which receive little or no emission input after the first measurement, which experience relatively little mixing, and which are reachable by as many aircraft as possible. For validation the system was applied to the period of the NARE 97 campaign where approximately the same air masses were sampled on different flights. Measured upwind/downwind differences in carbon monoxide (CO and ozone (O3 decreased significantly as the threshold values used for accepting cases as Lagrangian were tightened. This proves that the model system can successfully identify Lagrangian opportunities.
Forecasting for a Lagrangian aircraft campaign
A. Stohl
2004-05-01
Full Text Available A forecast system has been developed in preparation for an upcoming aircraft measurement campaign, where the same air parcels polluted by emissions over North America shall be sampled repeatedly as they leave the continent, during transport over the Atlantic, and upon their arrival over Europe. This paper describes the model system in advance of the campaign, in order to make the flight planners familiar with the novel model output. The aim of a Lagrangian strategy is to infer changes in the chemical composition and aerosol distribution occurring en route by measured upwind/downwind differences. However, guiding aircraft repeatedly into the same polluted air parcels requires careful forecasting, for which no suitable model system exists to date. This paper describes a procedure using both Eulerian-type (i.e. concentration fields and Lagrangian-type (i.e. trajectories model output from the Lagrangian particle dispersion model FLEXPART to predict the best opportunities for a Lagrangian experiment. The best opportunities are defined as being highly polluted air parcels which receive little or no emission input after the first measurement, which experience relatively little mixing, and which are reachable by as many aircraft as possible. For validation the system was applied to the period of the NARE 97 campaign where approximately the same air masses were sampled on different flights. Measured upwind/downwind differences in carbon monoxide (CO and ozone (O_{3} decreased significantly as the threshold values used for accepting cases as Lagrangian were tightened. This proves that the model system can successfully identify Lagrangian opportunities.
Euler-Lagrangian computation for estuarine hydrodynamics
Cheng, Ralph T.
1983-01-01
The transport of conservative and suspended matter in fluid flows is a phenomenon of Lagrangian nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an Eulerian formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an Eulerian reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the Eulerian and Lagrangian computational techniques.
Lagrangians for the W-Algebra Models
Gaite, J C
1994-01-01
The field algebra of the minimal models of W-algebras is amenable to a very simple description as a polynomial algebra generated by few elementary fields, corresponding to order parameters. Using this description, the complete Landau-Ginzburg lagrangians for these models are obtained. Perturbing these lagrangians we can explore their phase diagrams, which correspond to multicritical points with $D_n$ symmetry. In particular, it is shown that there is a perturbation for which the phase structure coincides with that of the IRF models of Jimbo et al.
Effective Lagrangian in de Sitter Spacetime
Kitamoto, Hiroyuki
2016-01-01
Scale invariant fluctuations of metric are universal feature of quantum gravity in de Sitter spacetime. We construct an effective Lagrangian which summarizes their implications on local physics by integrating super-horizon 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.
Maxwell-like Lagrangians for higher spins
Campoleoni, Andrea
2012-01-01
We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless fields produce single-particle actions, while whenever trace constraints can be dispensed with the resulting Lagrangians display the same reducible, multi-particle spectra as those emerging from the tensionless limit of free open-string field theory. For all explored options the corresponding kinetic operators take essentially the same form as in the spin-one, Maxwell case.
The Mather problem for lower semicontinuous Lagrangians
Gomes, Diogo A.
2013-08-01
In this paper we develop the Aubry-Mather theory for Lagrangians in which the potential energy can be discontinuous. Namely we assume that the Lagrangian is lower semicontinuous in the state variable, piecewise smooth with a (smooth) discontinuity surface, as well as coercive and convex in the velocity. We establish existence of Mather measures, various approximation results, partial regularity of viscosity solutions away from the singularity, invariance by the Euler-Lagrange flow away from the singular set, and further jump conditions that correspond to conservation of energy and tangential momentum across the discontinuity. © 2013 Springer Basel.
Learn the Lagrangian: A Vector-Valued RKHS Approach to Identifying Lagrangian Systems.
Cheng, Ching-An; Huang, Han-Pang
2016-12-01
We study the modeling of Lagrangian systems with multiple degrees of freedom. Based on system dynamics, canonical parametric models require ad hoc derivations and sometimes simplification for a computable solution; on the other hand, due to the lack of prior knowledge in the system's structure, modern nonparametric models in machine learning face the curse of dimensionality, especially in learning large systems. In this paper, we bridge this gap by unifying the theories of Lagrangian systems and vector-valued reproducing kernel Hilbert space. We reformulate Lagrangian systems with kernels that embed the governing Euler-Lagrange equation-the Lagrangian kernels-and show that these kernels span a subspace capturing the Lagrangian's projection as inverse dynamics. By such property, our model uses only inputs and outputs as in machine learning and inherits the structured form as in system dynamics, thereby removing the need for the mundane derivations for new systems as well as the generalization problem in learning from scratches. In effect, it learns the system's Lagrangian, a simpler task than directly learning the dynamics. To demonstrate, we applied the proposed kernel to identify the robot inverse dynamics in simulations and experiments. Our results present a competitive novel approach to identifying Lagrangian systems, despite using only inputs and outputs.
Lagrangian theoretical framework of dynamics of nonholonomic systems
无
2007-01-01
@@ By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.
Lagrangian theoretical framework of dynamics of nonholonomic systems
LIANG; LiFu
2007-01-01
By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right. ……
On Stability of the Mechanical Lagrangian Systems
Valer Niminet
2011-12-01
Full Text Available
We consider MLS (mechanical Lagrangian systems with
external forces. We give some conditions of stability and dissipativity and show that the energy of the system decreases on the integral curves.
Key words: LMS, stability, dissipative system.
Lagrangian tetragons and instabilities in Hamiltonian dynamics
Entov, Michael; Polterovich, Leonid
2017-01-01
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.
Experimental design for drifting buoy Lagrangian test
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.
Towards effective Lagrangians for adelic strings
Dragovich, Branko
2009-01-01
p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By this way, one can consider adelic strings as a very useful instrument in the further investigation of modern string theory. It is remarkable that for some scalar p-adic strings exist effective Lagrangians, which are based on real instead of p-adic numbers and describe not only four-point scattering amplitudes but also all higher ones at the tree level. In this work, starting from p-adic Lagrangians, we consider some approaches to construction of effective field Lagrangians for p-adic sector of adelic strings. It yields Lagrangians for nonlinear and nonlocal scalar field theory, where spacetime nonlocality is determined by an infinite number of derivatives contained in the operator-valued Riemann zeta function. Owing to the Riemann zeta function in the dynamics of these sca...
A new semi-Lagrangian difference scheme
季仲贞; 陈嘉滨
2001-01-01
A new completely energy-conserving semi-Lagrangian scheme is constructed. The numerical solution of shallow water equation shows that this conservative scheme preserves the total energy in twelve significant digits, while the traditional scheme does only in five significant digits.
Lagrangian duality and cone convexlike functions
J.B.G. Frenk (Hans); G. Kassay
2005-01-01
textabstractIn this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation s
Lagrangian duality and cone convexlike functions
J.B.G. Frenk (Hans); G. Kassay
2005-01-01
textabstractIn this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation
Target Lagrangian kinematic simulation for particle-laden flows
Murray, S.; Lightstone, M. F.; Tullis, S.
2016-09-01
The target Lagrangian kinematic simulation method was motivated as a stochastic Lagrangian particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target Lagrangian integral timescale. In addition to recovering the expected Lagrangian properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark.
Classification of Lagrangian Fibrations over a Klein Bottle
Sepe, D
2009-01-01
This paper completes the classification of regular Lagrangian fibratiopns over compact surfaces. \\cite{misha} classifies regular Lagrangian fibrations over $\\mathbb{T}^2$. The main theorem in \\cite{hirsch} is used in order to classify integral affine structures on the Klein bottle $K^2$ and, hence, regular Lagrangian fibrations over this space.
Lagrangian multiplier and massive Yang-Mills fields
Li, Z.P.
1982-09-01
If we give appropriate constraint to the gauge invariant Lagrangian, the variation principle of the action convert to the variational problems with subsidiary condition. The effective Lagrangian which contains Lagrangian multiplier may have the mass term of the mesons. In that case we obtain naturally the massive Yang-Mills fields which was discussed by Nakanishi.
Lagrangian statistics in turbulent channel flow: implications for Lagrangian stochastic models
Stelzenmuller, Nickolas; Polanco, Juan Igancio; Vinkovic, Ivana; Mordant, Nicolas
2016-11-01
Lagrangian acceleration and velocity correlations in statistically one-dimesional turbulence are presented in the context of the development of Lagrangian stochastic models of inhomogeneous turbulent flows. These correlations are measured experimentally by 3D PTV in a high aspect ratio water channel at Reτ = 1450 , and numerically from DNS performed at the same Reynolds number. Lagrangian timescales, key components of Lagrangian stochastic models, are extracted from acceleration and velocity autocorrelations. The evolution of these timescales as a function of distance to the wall is presented, and compared to similar quantities measured in homogeneous isotropic turbulence. A strong dependance of all Lagrangian timescales on wall distance is present across the width of the channel. Significant cross-correlations are observed between the streamwise and wall-normal components of both acceleration and velocity. Lagrangian stochastic models of this flow must therefore retain dependance on the wall-normal coordinate and the components of acceleration and velocity, resulting in significantly more complex models than those used for homogeneous isotropic turbulence. We gratefully acknowledge funding from the Agence Nationale de la Recherche, LabEx Tec 21, and CONICYT Becas Chile.
Classification of Flat Lagrangian Surfaces in Complex Lorentzian Plane
Bang-Yen CHEN; Johan FASTENAKELS
2007-01-01
One of the most fundamental problems in the study of Lagrangian submanifolds fromRiemannian geometric point of view is to classify Lagrangian immersions of real space forms intocomplex space forms. The main purpose of this paper is thus to classify flat Lagrangian surfaces inthe Lorentzian complex plane C12. Our main result states that there are thirty-eight families of flatLagrangian surfaces in C12. Conversely, every flat Lagrangian surface in C12 is locally congruent to oneof the thirty-eight families.
Synchronous Lagrangian variational principles in General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in relativistic classical field theory which are either asynchronous or synchronous. The historical Einstein-Hilbert and Palatini variational formulations are found to belong to the first category. Nevertheless, it is shown that an alternative route exists which permits one to cast these principles in terms of equivalent synchronous Lagrangian variational formulations. The advantage is twofold. First, synchronous approaches allow one to overcome the lack of gauge symmetry of the asynchronous principles. Second, the property of manifest covariance of the theory is also restored at all levels, including the symbolic Euler-Lagrange equations, with the variational Lagrangian density being now identified with a $4-$scalar. As an application, a joint synchronous variational principle...
A Lagrangian particle level set method
Hieber, Simone E.; Koumoutsakos, Petros
2005-11-01
We present a novel particle level set method for capturing interfaces. The level set equation is solved in a Lagrangian frame using particles that carry the level set information. A key aspect of the method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field. The Lagrangian description of the level set method is inherently adaptive and exact in the case of solid body motions. The efficiency and accuracy of the method is demonstrated in several benchmark problems in two and three dimensions involving pure advection and curvature induced motion of the interface. The simplicity of the particle description is shown to be well suited for real time simulations of surfaces involving cutting and reconnection as in virtual surgery environments.
Multiloop Information from the QED Effective Lagrangian
Dunne, G V; Dunne, Gerald V.; Schubert, Christian
2006-01-01
We obtain information on the QED photon amplitudes at high orders in perturbation theory starting from known results on the QED effective Lagrangian in a constant electric field. A closed-form all-order result for the weak field limit of the imaginary part of this Lagrangian has been given years ago by Affleck, Alvarez and Manton (for scalar QED) and by Lebedev and Ritus (for spinor QED). We discuss the evidence for its correctness, and conjecture an analogous formula for the case of a self-dual field. From this extension we then obtain, using Borel analysis, the leading asymptotic growth for large N of the maximally helicity violating component of the L - loop N - photon amplitude in the low energy limit. The result leads us to conjecture that the perturbation series converges for the on-shell renormalized QED N - photon amplitudes in the quenched approximation.
A hybrid Eulerian-Lagrangian flow solver
Palha, Artur; Ferreira, Carlos Simao; van Bussel, Gerard
2015-01-01
Currently, Eulerian flow solvers are very efficient in accurately resolving flow structures near solid boundaries. On the other hand, they tend to be diffusive and to dampen high-intensity vortical structures after a short distance away from solid boundaries. The use of high order methods and fine grids, although alleviating this problem, gives rise to large systems of equations that are expensive to solve. Lagrangian solvers, as the regularized vortex particle method, have shown to eliminate (in practice) the diffusion in the wake. As a drawback, the modelling of solid boundaries is less accurate, more complex and costly than with Eulerian solvers (due to the isotropy of its computational elements). Given the drawbacks and advantages of both Eulerian and Lagrangian solvers the combination of both methods, giving rise to a hybrid solver, is advantageous. The main idea behind the hybrid solver presented is the following. In a region close to solid boundaries the flow is solved with an Eulerian solver, where th...
Lagrangian Vortices in Developing Tropical Cyclones
2015-06-25
cyclones B. Rutherford,a* T. J. Dunkertona and M. T. Montgomeryb aNorthwest Research Associates, Redmond, WA, USA bNaval Postgraduate School, Monterey...article has been contributed to by a US Government employee and his work is in the public domain in the USA. Tracking pre-genesis tropical cyclones is...season. All of the Lagrangian coherent structures that can be identified by this field are shown for developing disturbances and mature cyclones . The
Equivalent Lagrangians: Generalization, Transformation Maps, and Applications
N. Wilson
2012-01-01
Full Text Available Equivalent Lagrangians are used to find, via transformations, solutions and conservation laws of a given differential equation by exploiting the possible existence of an isomorphic algebra of Lie point symmetries and, more particularly, an isomorphic Noether point symmetry algebra. Applications include ordinary differential equations such as the Kummer equation and the combined gravity-inertial-Rossbywave equation and certain classes of partial differential equations related to multidimensional wave equations.
Ocean Model Assessment with Lagrangian Metrics
2016-06-07
Ocean Model Assessment With Lagrangian Metrics” Pearn P. Niiler Scripps Institution of Oceanography 9500 Gilman Drive MC 0213 La Jolla, CA...project are to aid in the development of accurate modeling of upper ocean circulation by using data on circulation observations to test models . These tests...or metrics, will be statistical measures of model and data comparisons. It is believed that having accurate models of upper ocean currents will
Introduction to Focus Issue: Lagrangian Coherent Structures.
Peacock, Thomas; Dabiri, John
2010-03-01
The topic of Lagrangian coherent structures (LCS) has been a rapidly growing area of research in nonlinear dynamics for almost a decade. It provides a means to rigorously define and detect transport barriers in dynamical systems with arbitrary time dependence and has a wealth of applications, particularly to fluid flow problems. Here, we give a short introduction to the topic of LCS and review the new work presented in this Focus Issue.
Lagrangian Observations and Modeling of Marine Larvae
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.
Lagrangian methods of cosmic web classification
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.
Inverse Variational Problem for Nonstandard Lagrangians
Saha, A.; Talukdar, B.
2014-06-01
In the mathematical physics literature the nonstandard Lagrangians (NSLs) were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of the equation of motion and solve the associated inverse problem to obtain some of the existing results for NSLs. In addition, we provide a number of alternative Lagrangian representations. The case studies envisaged by us include (i) the usual modified Emden-type equation, (ii) Emden-type equation with dissipative term quadratic in velocity, (iii) Lotka-Volterra model and (vi) a number of the generic equations for dissipative-like dynamical systems. Our method works for nonstandard Lagrangians corresponding to the usual action integral of mechanical systems but requires modification for those associated with the modified actions like S =∫abe L(x ,x˙ , t) dt and S =∫abL 1 - γ(x ,x˙ , t) dt because in the latter case one cannot construct expressions for the Jacobi integrals.
Lagrangian approach and dissipative magnetic systems
Bose, Thomas, E-mail: thomas.bose@physik.uni-halle.de [Martin-Luther-University, Physics Department, Von-Seckendorff-Platz 1, 06114 Halle (Germany); Trimper, Steffen, E-mail: steffen.trimper@physik.uni-halle.de [Martin-Luther-University, Physics Department, Von-Seckendorff-Platz 1, 06114 Halle (Germany)
2011-06-13
A Lagrangian is introduced which includes the coupling between magnetic moments m and the degrees of freedom σ of a reservoir. In case the system-reservoir coupling breaks the time reversal symmetry the magnetic moments perform a damped precession around an effective field which is self-organized by the mutual interaction of the moments. The resulting evolution equation has the form of the Landau-Lifshitz-Gilbert equation. In case the bath variables are constant vector fields the moments m fulfill the reversible Landau-Lifshitz equation. Applying Noether's theorem we find conserved quantities under rotation in space and within the configuration space of the moments. -- Highlights: → We propose a new approach for describing magnetic systems with dissipation on a mesoscopic scale. → The Lagrangian consists of an active magnetic system and a bath. → The coupling between both subsystems breaks the time reversal symmetry. → The suggested Lagrangian leads to the Landau-Lifshitz equation with damping. → We consider symmetry operations by means of Noether's theorem.
Applications the Lagrangian description in aperiodic flows
Mendoza, Carolina; Mancho, Ana Maria
2012-11-01
We use several recently developed Lagrangian tools for describing transport in general aperiodic flows. In our approach the first step is based in a Lagrangian descriptor (the so called function M). It measures the length of particle trajectories on the ocean surface over a given interval of time. We describe its output over satellite altimetry data on the Kuroshio current. The technique is combined with the direct computation of manifolds of Distinguished Hyperbolic trajectories and a very detailed description of transport is achieved across an eddy and a jet on the Kuroshio current,. A second velocity data set is examined with the M function tool. These are obtained from the HYCOM project on the Gulf of Mexico during the time of the oil-spill. We have identified underlying Lagrangian structures and dynamics. We acknowledge to the hospitality of the university of Delaware and the assistance of Bruce Lipphardt and Helga Huntley in accessing the model data sets. We acknowledge to the grants: UPM-AL12-PAC-09, Becas de Movilidad de Caja Madrid 2011, MTM2011-26696 and ILINK-0145.
A Lagrangian-Lagrangian Model for Two-Phase Bubbly Flow around Circular Cylinder
M. Shademan
2014-06-01
Full Text Available A Lagrangian-Lagrangian model is developed using an in-house code to simulate bubble trajectory in two-phase bubbly flow around circular cylinder. Random Vortex Method (RVM which is a Lagrangian approach is used for solving the liquid phase. The significance of RVM relative to other RANS/LES methods is its capability in directly modelling the turbulence. In RVM, turbulence is modeled by solving the vorticity transport equation and there is no need to use turbulence closure models. Another advantage of RVM relative to other CFD approaches is its independence from mesh generation. For the bubbles trajectory, equation of motion of bubbles which takes into account effect of different forces are coupled with the RVM. Comparison of the results obtained from current model with the experimental data confirms the validity of the model. Effect of different parameters including flow Reynolds number, bubble diameter and injection point on the bubbles' trajectory are investigated. Results show that increase in the Reynolds number reduces the rising velocity of the bubbles. Similar behavior is observed for the bubbles when their diameter was decreased. According to the analysis carried out, present Lagrangian-Lagrangian model solves the issues of mesh generation and turbulence modelling which exist in common two phase flow modelling schemes.
Dynamics of Multibody Systems Near Lagrangian Points
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
Continuous Time Random Walks for the Evolution of Lagrangian Velocities
Dentz, Marco; Comolli, Alessandro; Borgne, Tanguy Le; Lester, Daniel R
2016-01-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have non-stationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and non-stationary conditions. We provide explicit expressions for the Lagrangian velocity statistics, and determine the behaviors of...
Lagrangian Coherent Structures in the Trieste Gulf
Besio, G.; Enrile, F.; Magaldi, M. G.; Mantovani, C.; Cosoli, S.; Gerin, R.; Poulain, P. M.
2013-12-01
One serious issue in Environmental Science and Engineering concerns the prediction of the fate of contaminants released in a water body. A possible way to tackle this problem consists in forecasting pollutant trajectories from velocity-field data sets obtained by measurements or numerical simulations. A shortcoming of such a traditional approach is the high sensitivity to initial conditions. Another way to understand transport in complex fluid flows comes from a new mathematical tool: Lagrangian Coherent Structures (LCS). The idea of using Lagrangian Structures rose as a meeting point between non-linear dynamics and fluid mechanics. It provides the means to identify material lines that shape trajectory patterns, dividing the flow field into regions with different dynamical behaviours. The objective of this study is the detection of Lagrangian Coherent Structures in the Gulf of Trieste. LCS are calculated from the 2D surface velocity field measured by the coastal radars of the TOSCA (Tracking Oil Spills & Coastal Awareness network) project. Blobs of simulated particles are subjected to chaotic stirring (transport and stretching) that is in agreement with the detected LCS. In the TOSCA project drifters were deployed, too. Therefore, a simple simulation of some of these drifters was carried out. The trajectory of the simulated drifters diverge from the real one: this result is due to the chaotic transport of passive tracers. However, the separation becomes more evident when velocity fields are less accurate because of lack of measurements, previously filled with nearest neighbourhood interpolation. In the light of such results, the use of LCS could be helpful in understanding the trajectory followed by drifters and passive tracers in general, because they can point out the directions along which transport is likely to develop.
Lagrangian form of Schrödinger equation
Arsenović, D.; Burić, N.; Davidović, D. M.; Prvanović, S.
2014-07-01
Lagrangian formulation of quantum mechanical Schrödinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein-Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schrödinger equation.
Webs of Lagrangian Tori in Projective Symplectic Manifolds
Hwang, Jun-Muk
2012-01-01
For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.
New Terms for Compact Form of Electroweak Chiral Lagrangian
YE Wei; ZHANG Hong-Hao; YANG Hong-Wei; YAN Wen-Bin; CHEN Na; J.K. Parry; LI Xue-Song
2008-01-01
The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add several new chiral invariant terms to it and discuss the contributions of these terms to the original electroweak chiral Lagrangian.
Towards Lagrangian approach to quantum computations
Vlasov, A Yu
2003-01-01
In this work is discussed possibility and actuality of Lagrangian approach to quantum computations. Finite-dimensional Hilbert spaces used in this area provide some challenge for such consideration. The model discussed here can be considered as an analogue of Weyl quantization of field theory via path integral in L. D. Faddeev's approach. Weyl quantization is possible to use also in finite-dimensional case, and some formulas may be simply rewritten with change of integrals to finite sums. On the other hand, there are specific difficulties relevant to finite case. This work has some allusions with phase space models of quantum computations developed last time by different authors.
Hamiltonian and Lagrangian theory of viscoelasticity
Hanyga, A.; Seredyńska, M.
2008-03-01
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
Trivial Lagrangians in the Causal Approach
Grigore, Dan-Radu
2015-01-01
We prove the non-uniqueness theorem for the chronological products of a gauge model. We use a cohomological language where the cochains are chronological products, gauge invariance means a cocycle restriction and coboundaries are expressions producing zero sandwiched between physical states. Suppose that we have gauge invariance up to order n of the perturbation theory and we modify the first-order chronological products by a coboundary (a trivial Lagrangian). Then the chronological products up to order n get modified by a coboundary also.
Laboratori aperti anche ai fan della fisica
2005-01-01
"Masterclasses" is supported from the Infn and involves 18 nations of the Union. In a closed past, the game "the small chemist" had a great success, a game that allowed to realise a common aspiration: put the hands in the chemistry
Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs
X. X. HUANG; K. L. TEO; X. Q. YANG
2006-01-01
In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.
Relativistic Lagrangians for the Lorentz–Dirac equation
Deguchi, Shinichi, E-mail: deguchi@phys.cst.nihon-u.ac.jp [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan); Nakano, Kunihiko [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan); Suzuki, Takafumi [Junior College Funabashi Campus, Nihon University, Narashinodai, Funabashi, Chiba 274-8501 (Japan)
2015-09-15
We present two types of relativistic Lagrangians for the Lorentz–Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz–Dirac equation with a source-like term.
Lagrangian Transport Through Surfaces in Volume-Preserving Flows
Karrasch, Daniel
2015-01-01
Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The recent development of highly accurate semi-Lagrangian methods for solving scalar conservation laws and of Lagrangian approaches to coherent structures in turbulent (geophysical) fluid flows necessitate a new approach to transport from the (Lagrangian) material perspective. We present a Lagrangian framework for calculating transport of conserved quantities through a given surface in $n$-dimensional, fully aperiodic, volume-preserving flows. Our approach does not involve any dynamical assumptions on the surface or its boundary.
The Dirac Conjecture and the Non-uniqueness of Lagrangian
Wang, Yong-Long; Jiang, Hua; Lu, Wei-Tao; Pan, Hong-Zhe
2013-01-01
We prove the validity of the Dirac conjecture generally by adding the total time derivatives of all constraints to the Lagrangian step by step. It is worthy to state that the total time derivatives added to the original Lagrangian can turn up some constraints, and discover the symmetries hidden in the original Lagrangian. For a constrained system, the extended Hamiltonian $H_E$ contains more constraints, and shows more symmetries. We discuss the Cawley's counterexample, and prove it not a real one to the Dirac conjecture. And we offer an example, its extended Hamiltonian is better that its total Hamiltonian for its Lagrangian.
Parallel algorithms for semi-lagrangian advection
Malevsky, A. V.; Thomas, S. J.
1997-08-01
Numerical time step limitations associated with the explicit treatment of advection-dominated problems in computational fluid dynamics are often relaxed by employing Eulerian-Lagrangian methods. These are also known as semi-Lagrangian methods in the atmospheric sciences. Such methods involve backward time integration of a characteristic equation to find the departure point of a fluid particle arriving at a Eulerian grid point. The value of the advected field at the departure point is obtained by interpolation. Both the trajectory integration and repeated interpolation influence accuracy. We compare the accuracy and performance of interpolation schemes based on piecewise cubic polynomials and cubic B-splines in the context of a distributed memory, parallel computing environment. The computational cost and interprocessor communication requirements for both methods are reported. Spline interpolation has better conservation properties but requires the solution of a global linear system, initially appearing to hinder a distributed memory implementation. The proposed parallel algorithm for multidimensional spline interpolation has almost the same communication overhead as local piecewise polynomial interpolation. We also compare various techniques for tracking trajectories given different values for the Courant number. Large Courant numbers require a high-order ODE solver involving multiple interpolations of the velocity field.
Variational Contact Symmetries of Constraint Lagrangians
Terzis, Petros A; Christodoulakis, T; Paliathanasis, A; Tsamparlis, M
2015-01-01
The investigation of contact symmetries of re--parametrization invariant Lagrangians of finite degrees of freedom and quadratic in the velocities is presented. The main concern of the paper is those symmetry generators which depend linearly in the velocities. A natural extension of the symmetry generator along the lapse function $N(t)$, with the appropriate extension of the dependence in $\\dot{N}(t)$ of the gauge function, is assumed; this action yields new results. The central finding is that the integrals of motion are either linear or quadratic in velocities and are generated, respectively by the conformal Killing vector fields and the conformal Killing tensors of the configuration space metric deduced from the kinetic part of the Lagrangian (with appropriate conformal factors). The freedom of re--parametrization allows one to appropriately scale $N(t)$, so that the potential becomes constant; in this case the integrals of motion can be constructed from the Killing fields and Killing tensors of the scaled ...
Sigma decomposition: the CP-odd Lagrangian
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.
Generating functionals and Lagrangian partial differential equations
Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)
2013-08-15
The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.
Evaluation of the Lagrangian Marker Method in CTH: Taylor Impact
2015-03-01
ARL-TR-7235•MAR 2015 US Army Research Laboratory Evaluation of the Lagrangian Marker Method in CTH: Taylor Impact by Stephen Schraml Approved for...Research Laboratory Evaluation of the Lagrangian Marker Method in CTH: Taylor Impact by Stephen Schraml Weapons and Materials Research Directorate, ARL...
Deformations of log-Lagrangian submanifolds of Poisson manifolds
2013-01-01
We consider Lagrangian-like submanifolds in certain even-dimensional 'symplectic-like' Poisson manifolds. We show, under suitable transversality hypotheses, that the pair consisting of the ambient Poisson manifold and the submanifold has unobstructed deformations and that the deformations automatically preserve the Lagrangian-like property.
Parallel Lagrangian models for turbulent transport and chemistry
Crone, Gilia Cornelia
1997-01-01
In this thesis we give an overview of recent stochastic Lagrangian models and present a new particle model for turbulent dispersion and chemical reactions. Our purpose is to investigate and assess the feasibility of the Lagrangian approach for modelling the turbulent dispersion and chemistry
Flux form Semi-Lagrangian methods for parabolic problems
Bonaventura, Luca
2015-01-01
A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and convergence analysis are proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection--diffusion and nonlinear parabolic problems.
Lagrangian supersymmetries depending on derivatives. Global analysis and cohomology
Giachetta, G; Sardanashvily, G
2004-01-01
Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed. In particular, the first variational formula and conservation laws for Lagrangian systems on graded manifolds using contact supersymmetries are obtained.
Geometric Lagrangians for massive higher-spin fields
Francia, D
2007-01-01
Lagrangians for massive, unconstrained, higher-spin bosons and fermions are proposed. The idea is to modify the geometric, gauge invariant Lagrangians describing the corresponding massless theories by the addition of suitable quadratic polynomials. These polynomials provide generalisations of the Fierz-Pauli mass term containing all possible traces of the basic field. No auxiliary fields are needed.
Numerical methods for Eulerian and Lagrangian conservation laws
Després, Bruno
2017-01-01
This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.
Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics
Miron, Radu
2012-01-01
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries. More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author. The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order. For short, in this text we aim to solve some difficult problems: The problem of geometrization of classical non conservative mechanical systems; The foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;To determine the evolution equations of the classical mechanical systems for whose external forces depend on the hig...
Multi-Scale Analysis of Lagrangian Properties of Turbulence
Wilczek, Michael; Lalescu, Cristian
2016-11-01
Turbulence is a multi-scale problem in space and time with a broad range of strongly interacting degrees of freedom. Lagrangian tracer particles advected with the flow sample this spatio-temporal complexity. This naturally leads to the question of how Lagrangian properties are affected by the scales of turbulence. We attempt to answer this question numerically and theoretically adopting a coarse-graining approach. In an extensive DNS (direct numerical simulation) study, we track tracer particles advected by spatially coarse-grained velocity fields. This allows to distinguish the impact of large-scale sweeping effects and small-scale intermittency on Lagrangian aspects of turbulence. In this presentation we will present results on Lagrangian particle dispersion and velocity fluctuations for various coarse-graining scales. The results will furthermore be discussed in the context of Eulerian-Lagrangian bridging relations.
Lagrangian and Hamiltonian two-scale reduction
Giannoulis, Johannes; Mielke, Alexander
2008-01-01
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave...
Lagrangian coherent structures and plasma transport processes
Falessi, M V; Schep, T J
2015-01-01
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\\'e map provides a splitting of the phase space into regions where particles have different kinds of motion: periodic, quasi-periodic or chaotic. The boundaries of these regions are transport barriers; i.e., a trajectory cannot cross such boundaries during the whole evolution of the system. Lagrangian Coherent Structure (LCS) generalize this method to systems with the most general time dependence, splitting the phase space into regions with different qualitative behaviours. This leads to the definition of finite-time transport barriers, i.e. trajectories cannot cross the barrier for a finite amount of time. This methodology can be used to identify fast recirculating regions in the dynamical system and to characterize the transport between them.
Instantons in a Lagrangian model of turbulence
Grigorio, Leonardo S; Pereira, Rodrigo M; Chevillard, Laurent
2016-01-01
The role of instantons is investigated in the Lagrangian model for the velocity gradient evolution known as the Recent Fluid Deformation approximation. After recasting the model into the path-integral formalism, the probability distribution function is computed along with the most probable path in the weak noise limit through the saddle-point approximation. Evaluation of the instanton solution is implemented numerically by means of the iteratively Chernykh-Stepanov method. In the case of the longitudinal velocity gradient statistics, due to symmetry reasons, the number of degrees of freedom can be reduced to one, allowing the pdf to be evaluated analytically as well, thereby enabling a prediction of the scaling of the moments as a function of Reynolds number. It is also shown that the instanton solution lies on the Vieillefosse line concerning the RQ-plane. We illustrate how instantons can be unveiled in the stochastic dynamics performing a conditional statistics.
Holography, chiral Lagrangian and form factor relations
Zuo, Fen
2013-01-01
We perform a detailed study of mesonic properties in a class of holographic models of QCD, which is described by the Yang-Mills plus Chern-Simons action. By decomposing the 5 dimensional gauge field into resonances and integrating out the massive ones, we reproduce the Chiral Perturbative Theory Lagrangian up to ${\\cal O}(p^6)$ and obtain all the relevant low energy constants (LECs). The numerical predictions of the LECs show minor model dependence, and agree reasonably with the determinations from other approaches. Interestingly, various model-independent relations appear among them. Some of these relations are found to be the large-distance limits of universal relations between form factors of the anomalous and even-parity sectors of QCD.
Non-Lagrangian theories from brane junctions
Bao, Ling [Chalmers Univ. of Technology, Goeteborg (Sweden); Mitev, Vladimir [Humboldt Univ., Berlin (Germany). Inst. fuer Mathematik und Inst. fuer Physik; Pomoni, Elli [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany). Theory Group; Taki, Masato [RIKEN Nishina Center, Saitama (Japan). Mathematical Physics Lab.; Yagi, Futoshi [International School of Advanced Studies (SISSA), Trieste (Italy); INFN, Trieste (Italy); Korea Institute for Advanced Study (KIAS), Seoul (Korea, Republic of)
2013-10-15
In this article we use 5-brane junctions to study the 5D T{sub N} SCFTs corresponding to the 5D N=1 uplift of the 4D N=2 strongly coupled gauge theories, which are obtained by compactifying N M5 branes on a sphere with three full punctures. Even though these theories have no Lagrangian description, by using the 5-brane junctions proposed by Benini, Benvenuti and Tachikawa, we are able to derive their Seiberg-Witten curves and Nekrasov partition functions. We cross-check our results with the 5D superconformal index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss the relations between 5D superconformal indices and n-point functions of the q-deformed W{sub N} Toda theories.
A perturbative approach to Lagrangian flow networks
Fujiwara, Naoya; Donges, Jonathan F; Donner, Reik V
2016-01-01
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (a...
Lagrangian Coherent Structures: Introduction and Applications
Haller, George
2008-11-01
Lagrangian Coherent Structures (LCS) are distinguished material surfaces that organize the global mixing and transport of fluid particles. While these surfaces define a skeleton that governs all mixing events even in turbulent flows, LCS remain hidden to traditional coherent structure detecting methods based on vorticity, pressure, streamlines, or other frame-dependent quantities. Here we review the mathematical foundations of LCS and discuss how they can be located in an objective (frame-independent) way in complex flows. We also highlight applications to experimental and numerical flow data analysis. Examples include two-dimensional rotating turbulence, hairpin vortices in three-dimensional numerical simulations, passive ocean pollution control and atmospheric clear-air turbulence detection. Some of these examples will be discussed in more detail in later talks within this minisymposium.
Lagrangian mixing in an axisymmetric hurricane model
B. Rutherford
2009-09-01
Full Text Available This paper discusses the extension of established Lagrangian mixing measures to make them applicable to data extracted from a 2-D axisymmetric hurricane simulation. Because of the non-steady and unbounded characteristics of the simulation, the previous measures are extended to a moving frame approach to create time-dependent mixing rates that are dependent upon the initial time of particle integration, and are computed for nonlocal regions. The global measures of mixing derived from finite-time Lyapunov exponents, relative dispersion, and a measured mixing rate are applied to distinct regions representing different characteristic feautures within the model. It is shown that these time-dependent mixing rates exhibit correlations with maximal tangential winds during a quasi-steady state, establishing a connection between mixing and hurricane intensity.
On Active Current Selection for Lagrangian Profilers
J. Jouffroy
2013-01-01
Full Text Available Autonomous Lagrangian profilers are now widely used as measurement and monitoring platforms, notably in observation programs as Argo. In a typical mode of operation, the profilers drift passively at their parking depthbefore making a vertical profile to go back to the surface. This paperpresents simple and computationally-efficient control strategies to activelyselect and use ocean currents so that a profiler can autonomously reach adesired destination. After briefly presenting a typical profiler andpossible mechanical modifications for a coastal environment, we introducesimple mathematical models for the profiler and the currents it will use. Wethen present simple feedback controllers that, using the direction of thecurrents and taking into account the configuration of the environment(coastal or deep-sea, is able to steer the profiler to any desiredhorizontal location. To illustrate the approach, a few results are presentedusing both simulated currents and real current velocity profiles from theNorth Sea.
HybridN-order Lagrangian Interpolation Eulerian-Lagrangian Method for Salinity Calculation
吴炎成; 朱首贤; 周林; 游小宝; 张文静
2016-01-01
The Eulerian−Lagrangian method (ELM) has been used by many ocean models as the solution of the advection equation, but the numerical error caused by interpolation imposes restriction on its accuracy. In the present study, hybrid N-order Lagrangian interpolation ELM (LiELM) is put forward in which theN-order Lagrangian interpolation is used at first, then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower. The calculation results of a step-shaped salinity advection model are analyzed, which show that higher order (N=3−8) LiELM can reduce the mean numerical error of salinity calculation, but the numerical oscillation error is still significant. Even number order LiELM makes larger numerical oscillation error than its adjacent odd number order LiELM. HybridN-order LiELM can remove numerical oscillation, and it significantly reduces the mean numerical error whenN is even and the current is in fixed direction, while it makes less effect on mean numerical error whenNis odd or the current direction changes periodically. Hybrid odd number order LiELM makes less mean numerical error than its adjacent even number order LiELM when the current is in the fixed direction, while the mean numerical error decreases asN increases when the current direction changes periodically, so odd number ofN may be better for application. Among various types of HybridN-order LiELM, the scheme reducingN-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.
A reduction of order two for infinite-order Lagrangians
Jaén, X.; Llosa, J.; Molina, A.
1986-10-01
Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.
In defence of naivete The conceptual status of Lagrangian QFT
Wallace, D
2001-01-01
I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the "naive" quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work.
Lagrangian Volume Deformations around Simulated Galaxies
Robles, S; Oñorbe, J; Martínez-Serrano, F J
2015-01-01
We present a detailed analysis of the local evolution of 206 Lagrangian Volumes (LVs) selected at high redshift around galaxy seeds, identified in a large-volume $\\Lambda$CDM hydrodynamical simulation. The LVs have a mass range of $1 - 1500 \\times 10^{10} M_\\odot$. We follow the dynamical evolution of the density field inside these initially spherical LVs from $z=10$ up to $z_{\\rm low}= 0.05$, witnessing highly non-linear, anisotropic mass rearrangements within them, leading to the emergence of the local cosmic web (CW). These mass arrangements have been analysed in terms of the reduced inertia tensor $I_{ij}^r$, focusing on the evolution of the principal axes of inertia and their corresponding eigen directions, and paying particular attention to the times when the evolution of these two structural elements declines. In addition, mass and component effects along this process have also been investigated. We have found that deformations are led by DM dynamics and they transform most of the initially spherical L...
One-loop effective lagrangians after matching
Aguila, F. del; Santiago, J. [Universidad de Granada, Departamento de Fisica Teorica y del Cosmos and CAFPE, Granada (Spain); Kunszt, Z. [ETH Zuerich, Institute for Theoretical Physics, Zuerich (Switzerland)
2016-05-15
We discuss the limitations of the covariant derivative expansion prescription advocated to compute the one-loop Standard Model (SM) effective lagrangian when the heavy fields couple linearly to the SM. In particular, one-loop contributions resulting from the exchange of both heavy and light fields must be explicitly taken into account through matching because the proposed functional approach alone does not account for them. We review a simple case with a heavy scalar singlet of charge -1 to illustrate the argument. As two other examples where this matching is needed and this functional method gives a vanishing result, up to renormalization of the heavy sector parameters, we re-evaluate the one-loop corrections to the T-parameter due to a heavy scalar triplet with vanishing hypercharge coupling to the Brout-Englert-Higgs boson and to a heavy vector-like quark singlet of charged 2/3 mixing with the top quark, respectively. In all cases we make use of a new code for matching fundamental and effective theories in models with arbitrary heavy field additions. (orig.)
Lagrangian based methods for coherent structure detection
Allshouse, Michael R., E-mail: mallshouse@chaos.utexas.edu [Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, Texas 78712 (United States); Peacock, Thomas, E-mail: tomp@mit.edu [Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2015-09-15
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.
Sigma Decomposition: The CP-Odd Lagrangian
Hierro, I M; Rigolin, and S
2015-01-01
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-$\\theta$ term linked to non-perturbative sources of CP viola- tion, 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 $SU(3)/(SU(2)\\times U(1))$ model, which intrinsically breaks cus- todial symmetry. Moreover, the projection of the high-energy electroweak effective theory to the low-ener...
High Order Semi-Lagrangian Advection Scheme
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2014-11-01
In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
Sea Fog Forecasting with Lagrangian Models
Lewis, J. M.
2014-12-01
In 1913, G. I. Taylor introduced us to a Lagrangian view of sea fog formation. He conducted his study off the coast of Newfoundland in the aftermath of the Titanic disaster. We briefly review Taylor's classic work and then apply these same principles to a case of sea fog formation and dissipation off the coast of California. The resources used in this study consist of: 1) land-based surface and upper-air observations, 2) NDBC (National Data Buoy Center) observations from moored buoys equipped to measure dew point temperature as well as the standard surface observations at sea (wind, sea surface temperature, pressure, and air temperature), 3) satellite observations of cloud, and 4) a one-dimensional (vertically directed) boundary layer model that tracks with the surface air motion and makes use of sophisticated turbulence-radiation parameterizations. Results of the investigation indicate that delicate interplay and interaction between the radiation and turbulence processes makes accurate forecasts of sea fog onset unlikely in the near future. This pessimistic attitude stems from inadequacy of the existing network of observations and uncertainties in modeling dynamical processes within the boundary layer.
Lagrangian Hydrocode Simulations of Tsunamigenic, Subaerial Landslides
Schwaiger, H. F.; Parsons, J.; Higman, B.
2006-12-01
The interaction of debris flows, both subaqueous and subaerial, with bodies of water can produce tsunamis with a locally devastating impact. When debris flows begin above the water surface, the impact can produce a large air cavity, significantly increasing the effective volume of water displaced and complicating efforts to model the resulting tsunami. Because grid-based, Eulerian numerical methods have an inherent difficulty tracking material boundaries, we have implemented a particle-based, Lagrangian model (Smoothed Particle Hydrodynamics). The use of a particle model removes the common numerical difficulties associated with large deformation, multi-phase flows such as the numerical diffusion of material boundaries. We treat the debris flow as an incompressible, viscous fluid and the body of water as inviscid. Other rheologies of the debris flow (Mohr-Coulomb or Bingham plastic) can be included through the use of a non-linear viscosity. We apply this model to study the 1958 Lituya Bay landslide and resulting tsunami. Our simulation results compare favorably with field observations as well as a scaled laboratory experiment and a numerical study using an AMR Eulerian compressible fluid model.
Disentangling the Cosmic Web with Lagrangian Submanifold
Shandarin, Sergei F.; Medvedev, Mikhail V.
2016-10-01
The Cosmic Web is a complicated highly-entangled geometrical object. Remarkably it has formed from practically Gaussian initial conditions, which may be regarded as the simplest departure from exactly uniform universe in purely deterministic mapping. The full complexity of the web is revealed neither in configuration no velocity spaces considered separately. It can be fully appreciated only in six-dimensional (6D) phase space. However, studies of the phase space is complicated by the fact that every projection of it on a three-dimensional (3D) space is multivalued and contained caustics. In addition phase space is not a metric space that complicates studies of geometry. We suggest to use Lagrangian submanifold i.e., x = x(q), where both x and q are 3D vectors instead of the phase space for studies the complexity of cosmic web in cosmological N-body dark matter simulations. Being fully equivalent in dynamical sense to the phase space it has an advantage of being a single valued and also metric space.
Top marine predators track Lagrangian coherent structures.
Tew Kai, Emilie; Rossi, Vincent; Sudre, Joel; Weimerskirch, Henri; Lopez, Cristobal; Hernandez-Garcia, Emilio; Marsac, Francis; Garçon, Veronique
2009-05-19
Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great Frigatebird. Using a newly developed dynamic concept, the finite-size Lyapunov exponent (FSLE), we identified Lagrangian coherent structures (LCSs) present in the surface flow in the channel over a 2-month observation period (August and September 2003). By comparing seabird satellite positions with LCS locations, we demonstrate that frigatebirds track precisely these structures in the Mozambique Channel, providing the first evidence that a top predator is able to track these FSLE ridges to locate food patches. After comparing bird positions during long and short trips and different parts of these trips, we propose several hypotheses to understand how frigatebirds can follow these LCSs. The birds might use visual and/or olfactory cues and/or atmospheric current changes over the structures to move along these biologic corridors. The birds being often associated with tuna schools around foraging areas, a thorough comprehension of their foraging behavior and movement during the breeding season is crucial not only to seabird ecology but also to an appropriate ecosystemic approach to fisheries in the channel.
A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints
de Leon, M. [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); de Diego, D.M. [Departamento de Economia Aplicada Cuantitativa, Facultad de Ciencias Economicas y Empresariales, UNED, 28040 Madrid (Spain)
1997-06-01
We construct a constraint algorithm for singular Lagrangian systems subjected to nonholonomic constraints which generalizes that of Dirac for constrained Hamiltonian systems. {copyright} {ital 1997 American Institute of Physics.}
A Dynamic Job Shop Scheduling Method Based on Lagrangian Relaxation
无
1999-01-01
Due to the complexity of dynamic job shop scheduling in flexible manufacturing s ystem(FMS), many heuristic rules are still used today. A dynamic scheduling appr oach based on Lagrangian relaxation is proposed to improve the quality and guara ntee the real-time capability of dynamic scheduling. The proposed method makes use of the dynamic predictive optimal theory combined with Lagrangian relaxation to obtain a good solution that can be evaluated quantitatively. The Lagrangian multipliers introduced here are capable of describing machine predictive states and system capacity constraints. This approach can evaluate the suboptimality of the scheduling systems. It can also quickly obtain high quality feasible schedu les, thus enabling Lagrangian relaxation to be better used in the dynamic schedu ling of manufacturing system. The efficiency and effectiveness of this method ar e verified by numerical experiments.
Remarks on the Lagrangian representation of bi-Hamiltonian equations
Pavlov, M. V.; Vitolo, R. F.
2017-03-01
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2 =LτA1. We use this result in order to find the Lagrangian representation when A2 is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components.
Second post-Newtonian Lagrangian dynamics of spinning compact binaries
Huang, Li; Wu, Xin [Nanchang University, Department of Physics and Institute of Astronomy, Nanchang (China); Ma, DaZhu [Hubei University for Nationalities, School of Science, Enshi (China)
2016-09-15
The leading-order spin-orbit coupling is included in a post-Newtonian Lagrangian formulation of spinning compact binaries, which consists of the Newtonian term, first post-Newtonian (1PN) and 2PN non-spin terms and 2PN spin-spin coupling. This leads to a 3PN spin-spin coupling occurring in the derived Hamiltonian. The spin-spin couplings are mainly responsible for chaos in the Hamiltonians. However, the 3PN spin-spin Hamiltonian is small and has different signs, compared with the 2PN spin-spin Hamiltonian equivalent to the 2PN spin-spin Lagrangian. As a result, the probability of the occurrence of chaos in the Lagrangian formulation without the spin-orbit coupling is larger than that in the Lagrangian formulation with the spin-orbit coupling. Numerical evidences support this claim. (orig.)
Construction of Lagrangians and Hamiltonians from the Equation of Motion
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)
A discrete Lagrangian based direct approach to macroscopic modelling
Sarkar, Saikat; Nowruzpour, Mohsen; Reddy, J. N.; Srinivasa, A. R.
2017-01-01
A direct discrete Lagrangian based approach, designed at a length scale of interest, to characterize the response of a body is proposed. The main idea is to understand the dynamics of a deformable body via a Lagrangian corresponding to a coupled interaction of rigid particles in the reduced dimension. We argue that the usual practice of describing the laws of a deformable body in the continuum limit is redundant, because for most of the practical problems, analytical solutions are not available. Since continuum limit is not taken, the framework automatically relaxes the requirement of differentiability of field variables. The discrete Lagrangian based approach is illustrated by deriving an equivalent of the Euler-Bernoulli beam model. A few test examples are solved, which demonstrate that the derived non-local model predicts lower deflections in comparison to classical Euler-Bernoulli beam solutions. We have also included crack propagation in thin structures for isotropic and anisotropic cases using the Lagrangian based approach.
Don't worry. Lagrangian drift kinetics is OK
Burby, Joshua
2015-11-01
I show that standard Lagrangian (i.e. variational) drift kinetics with uE × B ~vth and Hgc =Ho + ɛH1 +ɛ2H2 has an unphysically-large phase space; where a valid initial condition ought to consist of (F , E , B) specified at t = 0 , Lagrangian drift kinetics requires initial time derivatives of the electromagnetic field to be specified as well. This phenomenon occurs because the guiding center coordinate transformation depends on time derivatives of the electromagnetic field, and this leads to the appearance of a time derivative of E in H2. I also show how to ``renormalize'' the Lagrangian approach to drift kinetics in a way that manifestly preserves the correct structure of the initial value problem. Starting from this modified Lagrangian procedure, I derive the drift kinetic system's Poisson bracket. Work supported by DOE contract # DE-AC02-09CH11466.
Geometry of Lagrangian First-order Classical Field Theories
Echeverría-Enríquez, A; Román-Roy, N; Echeverr\\'ia-Enr\\'iquez, Arturo; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso
1996-01-01
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the {\\sl Euler-Lagrange equations} in two equivalent ways: as the result of a variational problem and developing the {\\sl jet field formalism} (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied.
The complete HEFT Lagrangian after the LHC Run I
Brivio, I; Gonzalez-Garcia, M C; Merlo, L
2016-01-01
The complete effective chiral Lagrangian for a dynamical Higgs is presented and constrained by means of a global analysis including electroweak precision data together with Higgs and triple gauge boson coupling data from the LHC Run~I. The operators' basis up to next-to-leading order in the expansion consists of 148 (188 considering right-handed neutrinos) flavour universal terms and it is presented here making explicit the custodial nature of the operators. This effective Lagrangian provides the most general description of the physical Higgs couplings once the electroweak symmetry is assumed, and it allows for deviations from the $SU(2)_L$ doublet nature of the Standard Model Higgs. The comparison with the effective linear Lagrangian constructed with an exact $SU(2)_L$ doublet Higgs and considering operators with at most canonical dimension six is presented. A promising strategy to disentangle the two descriptions consists in analysing i) anomalous signals present only in the chiral Lagrangian and not expect...
Classical Nonminimal Lagrangians and Kinematic Tests of Special Relativity
Schreck, M
2016-01-01
This article gives a brief summary on recently obtained classical lagrangians for the nonminimal fermion sector of the Standard-Model Extension (SME). Such lagrangians are adequate descriptions of classical particles that are subject to a Lorentz-violating background field based on the SME. Explicitly, lagrangians were obtained for the leading nonminimal contributions of the m, a, c, e, and f coefficients. These results were then used to interpret classical, kinematic tests of Special Relativity in the framework of the nonminimal SME. This led to new constraints on certain nonminimal controlling coefficients. Although the experiments were very sophisticated in the era when they were carried out, their sensitivities for detecting Lorentz violation were still far away from the Planck scale. Obtaining the novel constraints can be considered as a proof-of-principle demonstrating the applicability of the classical lagrangians computed.
Simultaneous temperature and velocity Lagrangian measurements in turbulent thermal convection
Liot, O; Zonta, F; Chibbaro, S; Coudarchet, T; Gasteuil, Y; Pinton, J -F; Salort, J; Chillà, F
2015-01-01
We report joint Lagrangian velocity and temperature measurements in turbulent thermal convection. Measurements are performed using an improved version (extended autonomy) of the neutrally-buoyant instrumented particle that was used by to performed experiments in a parallelepipedic Rayleigh-Benard cell. The temperature signal is obtained from a RFtransmitter. Simultaneously, we determine particle's position and velocity with one camera, which grants access to the Lagrangian heat flux. Due to the extended autonomy of the present particle, we obtain well converged temperature and velocity statistics, as well as pseudo-eulerian maps of velocity and heat flux. Present experimental results have also been compared with the results obtained by a corresponding campaign of Direct Numerical Simulations and Lagrangian Tracking of massless tracers. The comparison between experimental and numerical results show the accuracy and reliability of our experimental measurements. Finally, the analysis of lagrangian velocity and t...
Flux form Semi-Lagrangian methods for parabolic problems
Bonaventura Luca
2016-09-01
Full Text Available A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and stability analysis is proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection diffusion and nonlinear parabolic problems.
Integration over families of Lagrangian submanifolds in BV formalism
Mikhailov, Andrei
2016-01-01
Gauge fixing is interpreted in BV formalims as a choice of Lagrangian submanifold in an odd symplectic manifold. 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 this way. We discuss the role of symmetries in this construction. We also discuss its applications to string worldsheet sigma-model, in particular to the construction of vertex operators.
Addendum to "Coherent Lagrangian vortices: The black holes of turbulence"
Haller, G.; Beron-Vera, F. J.
2014-01-01
In Haller and Beron-Vera (2013) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null-geodesics of the Lorentzian metric associated with a generalized Green-Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here we give an improved discussion on this analogy.
Merging matter and geometry in the same Lagrangian
Hendrik Ludwig
2015-12-01
Full Text Available We show that a Lagrangian density proportional to −gLm2/R reduces to a pressuron theory of gravity that is indistinguishable from General Relativity in the dust limit. The combination of matter and geometry in the same Lagrangian density intrinsically satisfies Mach's Principle — since matter cannot exist without curvature and vice versa — while it may have the correct phenomenology in order to describe actual gravity.
Lagrangian formulation of continuum with internal long-range interactions
无
2011-01-01
Based on a new definition of nonlocal variable,this paper establishes the Lagrangian formulation for continuum with internal long-range interactions.Distinguished from the existing theories,the nonlocal term in the Lagrangian formulation automatically satisfies the zero mean condition determined by the action and reaction law.By this formulation,elastic wave in a rod with the internal long-range interactions is investigated.The dispersion of the elastic wave is predicted.
BRST Lagrangian construction for spin-2 field in Einstein space
Buchbinder, I.L., E-mail: joseph@tspu.edu.r [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation); Krykhtin, V.A., E-mail: krykhtin@tspu.edu.r [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation); Laboratory of Mathematical Physics, Tomsk Polytechnic University, Tomsk 634034 (Russian Federation); Lavrov, P.M., E-mail: lavrov@tspu.edu.r [Department of Mathematical Analysis, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation)
2010-03-01
We explore a new possibility of BRST construction in higher spin field theory to obtain a consistent Lagrangian for massive spin-2 field in Einstein space. Such approach automatically leads to gauge invariant Lagrangian with suitable auxiliary and Stueckelberg fields. It is proved that in this case a propagation of spin-2 field is hyperbolic and causal. Also we extend notion of partial masslessness for spin-2 field in the background under consideration.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2002-10-19
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. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2004-01-28
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. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
Forecasting Future Sea Ice Conditions: A Lagrangian Approach
2014-09-30
that survives the summer melt season in each of the Arctic peripheral seas. The Lagrangian Model is forced with weekly mean satellite-derived sea- ice ...GCM to drive the Lagrangian code and map the regions for the multi-year ice surviving the summer melt in each of the Arctic peripheral seas in todays...1995, Emery et al. 1997, Meier et al. 2000, Tschudi et al. 2010) 3- Assess whether the source region of sea ice melting in peripheral seas in the
Interactive Lagrangian density between massive photons and gravitons
DENG Yan-bin
2006-01-01
The interactive Lagrangian density of massive photons and gravitons is proposed after an investigation into the interaction between photons with or without mass under the influence of gravity either as classical field, gravitational wave, or gravitons from a perspective of quantum field. This interactive Lagrangian density can provide a step-stone for further research of gravitational wave and the possible rest mass of photon.
Generalized Lagrangian dynamics of physical and non-physical systems
Sandler, U.
2014-12-01
In this paper, we show how to study the evolution of a complex system, given imprecise knowledge about the state of the system and the dynamics laws. It will be shown that dynamics of these systems is equivalent to Lagrangian (or Hamiltonian) mechanics in a n+1-dimensional space, where n is a system's dimensionality. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's equations gain a non-zero right side proportional to the derivative of the Lagrangian with respect to the action. Examples of such systems are unstable systems, systems with dissipation and systems which can remember their history. Moreover, in certain situations, the Lagrangian could be a set-valued function. The corresponding equations of motion then become differential inclusions instead of differential equations. We will also show that the principal of least action is a consequence of the causality principle and the local topology of the state space and not an independent axiom of classical mechanics. We emphasize that our adaptation of Lagrangian mechanics does not use or depend on specific properties of the physical system being modeled. Therefore, this Lagrangian approach may be equally applied to non-physical systems. An example of such an application is presented as well.
Lagrangian structures in time-periodic vortical flows
S. V. Kostrykin
2006-01-01
Full Text Available The Lagrangian trajectories of fluid particles are experimentally studied in an oscillating four-vortex velocity field. The oscillations occur due to a loss of stability of a steady flow and result in a regular reclosure of streamlines between the vortices of the same sign. The Eulerian velocity field is visualized by tracer displacements over a short time period. The obtained data on tracer motions during a number of oscillation periods show that the Lagrangian trajectories form quasi-regular structures. The destruction of these structures is determined by two characteristic time scales: the tracers are redistributed sufficiently fast between the vortices of the same sign and much more slowly transported into the vortices of opposite sign. The observed behavior of the Lagrangian trajectories is quantitatively reproduced in a new numerical experiment with two-dimensional model of the velocity field with a small number of spatial harmonics. A qualitative interpretation of phenomena observed on the basis of the theory of adiabatic chaos in the Hamiltonian systems is given. The Lagrangian trajectories are numerically simulated under varying flow parameters. It is shown that the spatial-temporal characteristics of the Lagrangian structures depend on the properties of temporal change in the streamlines topology and on the adiabatic parameter corresponding to the flow. The condition for the occurrence of traps (the regions where the Lagrangian particles reside for a long time is obtained.
Toscano, G. [Ancona Univ., Ancona (Italy). Dipt. di Biotecnologie agrarie ed ambientali
2001-06-01
di primaria importanza per l'economia del processo che, peraltro, deve affrontare anche le restrizioni imposte dalla politica agricola dell'UE. Piu' in dettaglio, il settore sta vivendo negli ultimi anni una fase di trasformazione dovuta alla riduzione delle quantita' di zucchero esportate (impegno preso dall'UE a seguito degli accordi del GATT del 1994) e alla diminuzione dei sostegni finanziari alla produzione agricola. In aggiunta i sottoprodotti di processo soffrono sempre piu' della concorrenza di altre materie prime oggi rese disponibili a prezzi competitivi dal mercato internazionale. E' quindi necessario trovare per questi ultimi anni - unitamente ai residui di scarso interesse pratico - degli sbocchi alternativi che possono soddisfare al difficile equilibrio tra una destinazione ambientalmente corretta e la riduzione dei costi di produzione. Con questo contributo si vuole quindi analizzare la problematica, con l'intento di fornire degli elementi utili per l'eventuale definizione di nuove tecniche di smaltimento. L'analisi e' impostata facendo riferimento a uno zuccherificio del centro Italia caratterizzato da una potenzialita' produttiva superiore alle 10.000 t/d di barbabietole.
Geometric deviation modeling by kinematic matrix based on Lagrangian coordinate
Liu, Weidong; Hu, Yueming; Liu, Yu; Dai, Wanyi
2015-09-01
Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it's expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.
Multi-symplectic, Lagrangian, one-dimensional gas dynamics
Webb, G. M.
2015-05-01
The equations of Lagrangian, ideal, one-dimensional, compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate m and time t as independent variables, and in which the Eulerian position of the fluid element x = x(m, t) is one of the dependent variables. This approach differs from the Eulerian, multi-symplectic approach using Clebsch variables. Lagrangian constraints are used to specify equations for xm, xt, and St consistent with the Lagrangian map, where S is the entropy of the gas. We require St = 0 corresponding to advection of the entropy S with the flow. We show that the Lagrangian Hamiltonian equations are related to the de Donder-Weyl multi-momentum formulation. The pullback conservation laws and the symplecticity conservation laws are discussed. The pullback conservation laws correspond to invariance of the action with respect to translations in time (energy conservation) and translations in m in Noether's theorem. The conservation law due to m-translation invariance gives rise to a novel nonlocal conservation law involving the Clebsch variable r used to impose ∂S(m, t)/∂t = 0. Translation invariance with respect to x in Noether's theorem is associated with momentum conservation. We obtain the Cartan-Poincaré form for the system, and use it to obtain a closed ideal of two-forms representing the equation system.
A Lagrangian fluctuation-dissipation relation for scalar turbulence
Drivas, Theodore D
2016-01-01
An exact relation is derived between the dissipation of scalar fluctuations and the variance of the scalar inputs (due to initial scalar values, scalar sources, and boundary fluxes) as those are sampled by stochastic Lagrangian trajectories. Previous work on the Kraichnan (1968) model of turbulent scalar advection has shown that anomalous scalar dissipation, non-vanishing in the limit of vanishing viscosity and diffusivity, is in that model due to Lagrangian spontaneous stochasticity, or non-determinism of the Lagrangian particle trajectories in the limit. We here extend this result to scalars advected by any incompressible velocity field. For fluid flows in domains without walls (e.g. periodic boxes) and for insulating/impermeable walls with zero scalar fluxes, we prove that anomalous scalar dissipation and spontaneous stochasticity are completely equivalent. For flows with imposed scalar values or non-vanishing scalar fluxes at the walls, spontaneous stochasticity still implies anomalous scalar dissipation ...
The semi-Lagrangian method on curvilinear grids
Hamiaz Adnane
2016-09-01
Full Text Available We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.
A new approach to Lagrangian investigations of isotropic turbulence
Barjona, Manuel; B. da Silva, Carlos; Idmec Team
2016-11-01
A new numerical approach is used in conjunction with direct numerical simulations (DNS) of statistically stationary (forced) isotropic turbulence to investigate the high Reynolds number scaling properties of turbulence characteristics in a Lagrangian frame. The new method provides an alternative route to the determination of the classical Lagrangian turbulence quantities, such as the second order Lagrangian velocity structure function and two point particle separation, at a much higher Reynolds number than as obtained in previous numerical simulations, and displays excellent agreement with the classical theoretical predictions and existing numerical simulations and experimental data. The authors acknowledge the Laboratory for Advanced Computing at University of Coimbra for providing HPC, computing, consulting resources that have contributed to the research results reported within this paper. URL http://www.lca.uc.pt.
Tracing the Cosmic Web substructure with Lagrangian submanifold
Shandarin, Sergei F
2014-01-01
A new computational paradigm for the analysis of substructure of the Cosmic Web in cosmological cold dark matter simulations is proposed. We introduce a new data-field --- the flip-flop field ---which carries wealth of information about the history and dynamics of the structure formation in the universe. The flip-flop field is an ordered data set in Lagrangian space representing the number of turns inside out sign reversals of an elementary volume of each collisionless fluid element represented by a computational particle in a N-body simulation. This field is computed using the Lagrangian submanifold, i.e. the three-dimensional dark matter sheet in the six-dimensional space formed by three Lagrangian and three Eulerian coordinates of the simulation particles. It is demonstrated that the very rich substructure of dark matter haloes and the void regions can be reliably and unambiguously recovered from the flip-flop field.
Does a Functional Integral Really Need a Lagrangian?
D. Kochan
2010-01-01
Full Text Available Path integral formulation of quantum mechanics (and also other equivalent formulations depends on a Lagrangian and/or Hamiltonian function that is chosen to describe the underlying classical system. The arbitrariness presented in this choice leads to a phenomenon called Quantization ambiguity. For example both L1 = ˙q2 and L2 = eq˙ are suitable Lagrangians on a classical level (δL1 = δL2, but quantum mechanically they are diverse. This paper presents a simple rearrangement of the path integral to a surface functional integral. It is shown that the surface functional integral formulation gives transition probability amplitude which is free of any Lagrangian/Hamiltonian and requires just the underlying classical equations of motion. A simple example examining the functionality of the proposed method is considered.
Collaborative production planning between supply chain partners by Lagrangian relaxation
无
2007-01-01
A collaborative planning framework based on the Lagrangian Relaxation was developed to coordinate and optimize the production planning of independent partners in multiple tier supply chains. Linking constraints and dependent demand constraints were added to the monolithic Multi-Level, multi-item Capacitated Lot Sizing Problem (MLCLSP). MLCLSP was Lagrangian relaxed and decomposed into facility-separable subproblems.Surrogate gradient algorithm was used to update Lagrangian multipliers, which coordinate decentralized decisions of the facilities. Production planning of independent partners could be appropriately coordinated and optimized by this framework without intruding their decision authorities and private information. Experimental results show that the proposed coordination mechanism and procedure come close to optimal results as obtained by central coordination.
Local Lagrangian Formalism and Discretization of the Heisenberg Magnet Model
Karpeev, D
2004-01-01
In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global Lagrangian density, a local variational formulation allows one to derive local conservation laws using a version of N\\"other's theorem from the formal variational calculus of Gelfand-Dikii. Using the local Lagrangian form we extend the method of Marsden, Patrick and Schkoller to derive local multisymplectic discretizations directly from the variational principle. We employ a version of the finite element method to discretize the space of sections of the trivial magnetic spin bundle $N = M\\times S^2$ over an appropriate space-time $M$. Since sections do not form a vector space, the usual FEM bases can be used only locally with coordinate transformations intervening on element boundaries, and conservation properties are guaranteed only within an element. We discuss possible w...
Minimal Local Lagrangians for Higher-Spin Geometry
Francia, D
2005-01-01
The Fronsdal Lagrangians for free totally symmetric rank-s tensors rest on suitable trace constraints for their gauge parameters and gauge fields. Only when these constraints are removed, however, the resulting equations reflect the expected free higher-spin geometry. We show that geometric equations, in both their local and non-local forms, can be simply recovered from local Lagrangians with only two additional fields, a rank-(s-3) compensator and a rank-(s-4) Lagrange multiplier. In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n-2) compensator and a rank-(n-3) Lagrange multiplier.
Lagrangian statistics and flow topology in forced 2-D turbulence
Kadoch, B. [Universite d' Aix-Marseille; Del-Castillo-Negrete, Diego B [ORNL; Bos, W.J.T. [CNRS, Ecole Centrale de Lyon, Universite Claude Bernard Lyon; Schneider, Kai [Universite d' Aix-Marseille
2011-01-01
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.
New Lagrangian diagnostics for characterizing fluid flow mixing
Mundel, Ruty; Gildor, Hezi; Rom-Kedar, Vered
2014-01-01
A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two- (and potentially three-) dimensional unsteady flows in both bounded and open domains. Its computation is much easier than all other Lagrangian diagnostics known to us and provides new insights regarding the mixing properties on both short and long time scales and on both spatial plots and distribution diagrams. We demonstrate its applicability to two dimensional flows using two toy models and a data set of surface currents from the Mediterranean Sea.
Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations
Deriglazov, Alexei A
2015-01-01
We obtain Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body with given values of spin and momentum starting from Lagrangian action without auxiliary variables. MPTD-equations correspond to minimal interaction of our spinning particle with gravity. We shortly discuss some novel properties deduced from the Lagrangian form of MPTD-equations: emergence of an effective metric instead of the original one, non-commutativity of coordinates of representative point of the body, spin corrections to Newton potential due to the effective metric as well as spin corrections to the expression for integrals of motion of a given isometry.
Using Upper Tolerances in Lagrangian Relaxation for the DCMSTP
Turkensteen, Marcel
-constraints, the Minimum Spanning Tree Problem (MSTP), is polynomially solvable. We solve the DCMSTP using Lagrangian relaxation. This is the approach in which constraint violations are penalized in the objective function. In an iterative process, the penalty values of violated constraints are increased...... used to approximate the optimal solution value. We present a Lagrangian approach that, as in Volgenant (1989), penalizes violations of the degree-constraints of each vertex. The penalty of a vertex is added to the costs of all edges adjacent to the vertex. Our approach uses upper tolerances...
An extended Lagrangian support vector machine for classifications
YANG Xiaowei; SHU Lei; HAO Zhifeng; LIANG Yanchun; LIU Guirong; HAN Xu
2004-01-01
Lagrangian support vector machine (LSVM) cannot solve large problems for nonlinear kernel classifiers. In order to extend the LSVM to solve very large problems, an extended Lagrangian support vector machine (ELSVM) for classifications based on LSVM and SVMlight is presented in this paper. Our idea for the ELSVM is to divide a large quadratic programming problem into a series of subproblems with small size and to solve them via LSVM. Since the LSVM can solve small and medium problems for nonlinear kernel classifiers, the proposed ELSVM can be used to handle large problems very efficiently. Numerical experiments on different types of problems are performed to demonstrate the high efficiency of the ELSVM.
A truly noninterpolating semi-Lagrangian Lax-Wendroff method
Olim, M.
1994-06-01
A truly noninterpolating semi-Lagrangian method has been developed. It is based upon a modification of a standard Lax-Wendroff scheme and is unconditionally stable on a regular rectangular grid. The method is explicit and second-order accurate in both time and space. It is suggested that the computational cost and memory allocation required by this method are the least possible for a semi-Lagrangian algorithm of this order of accuracy. The numerical experiments presented indicate that the algorithm is very accurate indeed.
The anomalous chiral Lagrangian of order $p^6$
Bijnens, J; Talavera, P
2002-01-01
We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$. The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavors, 23 terms for three and five for two flavors. In the two flavor case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well.
Experimental investigation of Lagrangian structure functions in turbulence
Berg, Jacob; Ott, Søren; Mann, Jakob
2009-01-01
Lagrangian properties obtained from a particle tracking velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian structure functions and to measure intermittency at small...... temporal scales. The finiteness of the measurement volume can bias the results significantly. We present a robust way to overcome this obstacle. Despite no fully developed inertial range, we observe strong intermittency at the scale of dissipation. The multifractal model is only partially able to reproduce...
Lagrangian Approach to Dispersionless KdV Hierarchy
Amitava Choudhuri
2007-09-01
Full Text Available We derive a Lagrangian based approach to study the compatible Hamiltonian structure of the dispersionless KdV and supersymmetric KdV hierarchies and claim that our treatment of the problem serves as a very useful supplement of the so-called r-matrix method. We suggest specific ways to construct results for conserved densities and Hamiltonian operators. The Lagrangian formulation, via Noether's theorem, provides a method to make the relation between symmetries and conserved quantities more precise. We have exploited this fact to study the variational symmetries of the dispersionless KdV equation.
Large N duality, lagrangian cycles, and algebraic knots
Diaconescu, D -E; Vafa, C
2011-01-01
We consider knot invariants in the context of large $N$ transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicity constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.
Large N Duality, Lagrangian Cycles, and Algebraic Knots
Diaconescu, D.-E.; Shende, V.; Vafa, C.
2013-05-01
We consider knot invariants in the context of large N transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicitly constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.
Unifying Ghost-Free Lorentz-Invariant Lagrangians
Li, Wenliang
2015-01-01
We present the details of the novel framework for Lagrangian field theories that are Lorentz-invariant and lead to at most second order equations of motion. The use of antisymmetric structure is of crucial importance. The general ghost-free Lagrangians are constructed and then translated into the language of differential forms. The ghost-freeness has a geometric nature. A novel duality is proposed which generalizes the Hodge duality in Maxwell's theory. We discuss how the well-established theories are reformulated and propose many new theories.
Particles within extended-spin space: Lagrangian connection
Besprosvany, J
2015-01-01
A spin-space extension is reviewed, which provides information on the standard model. Its defining feature is a common matrix space that describes symmetries and representations, and leads to limits on these, for given dimension. The model provides additional information on the standard model, whose interpretation requires an interactive formulation. Within this program, we compare the model's lepton-W generated interactive Lagrangian in (5+1)-dimensions, and that of the standard model. We derive the conditions for this matching, which apply to other Lagrangian terms. We also discuss the advantages of this extension, as compared to others.
Upper Tolerances and Lagrangian Relaxation for the DCMSTP
Turkensteen, Marcel
The Degree-Constrained Minimum Spanning Tree Problem (DCMSTP) is the problem of connecting a set of vertices against minimum cost, where no more than a prespecified number of edges may enter or leave each vertex. The DCMSTP is an NP-hard problem with many practical applications in the design...... of networks. Many efficient solution methods for the DCMSTP rely on Lagrangian relaxation for the tight lower bounds needed to solve instances. Lagrangian procedures for the DCMSTP solve a modified version of the regular Minimum Spanning Tree Problem (MSTP) in which the degree constraint violations...
Lagrangian Fuzzy Dynamics of Physical and Non-Physical Systems
Sandler, Uziel
2014-01-01
In this paper, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the \\emph{Fuzzy Dynamics} of a $n$-dimensional system is equivalent to Lagrangian (or Hamiltonian) mechanics in a $n+1$-dimensional space. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's eq...
Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems
CHEN Jing; BAI Yuzhen
2006-01-01
Ma(n)é conjectured that every minimal measure in the generic Lagrangian systems is by analyzing the structure of the supports of minimal probability measures for some kinds of the Lagrangian systems.
Low energy effective Lagrangians in open superstring theory
Medina, Ricardo [Universidade Federal de Itajuba, MG (Brazil). Inst. de Ciencias Exatas
2008-07-01
The low energy effective Lagrangian describes the interactions of the massless modes of String Theory. Present work is being done to obtain all alpha'{sup 3} terms (bosonic and fermionic) by means of the known 5-point amplitudes and SUSY.
Towards Selective Tidal-Stream Transport for Lagrangian profilers
Jouffroy, Jerome; Zhou, Qiuyang; Zielinski, Oliver
2011-01-01
Autonomous Lagrangian profilers are widely used as measurement and monitoring platforms. In their current mode of operation, the profilers usually drift passively at their parking depth before making a vertical profile to go back to the surface. This paper presents a control strategy to actively...
Structure of Lanczos-Lovelock Lagrangians in critical dimensions
Yale, Alexandre; Padmanabhan, T.
2011-06-01
The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D-dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general covariance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension D = 2 m and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in D = 2 m. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, {R √{-g} = partial_j R^j} for a doublet of functions R j = ( R 0, R 1) which depends only on the metric and its first derivatives. We explicitly construct families of such R j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in D = 4. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.
Lagrangianity for log extendable overconvergent $F$-isocrystals
Caro, Daniel
2015-01-01
In the framework of Berthelot's theory of arithmetic $\\mathcal{D}$-modules, we prove that Berthelot's characteristic variety associated with a holonomic $\\mathcal{D}$-modules endowed with a Frobenius structure has pure dimension. As an application, we get the lagrangianity of the characteristic variety of a log extendable overconvergent $F$-isocrystal.
Extended Lagrangian formalism for rheonomic systems with variable mass
Mušicki Đorđe
2017-01-01
Full Text Available In this paper the extended Lagrangian formalism for the rheonomic systems (Dj. Mušicki, 2004, which began with the modification of the mechanics of such systems (V. Vujičić, 1987, is extended to the systems with variable mass, with emphasis on the corresponding energy relations. This extended Lagrangian formalism is based on the extension of the set of chosen generalized coordinates by new quantities, suggested by the form of nonstationary constraints, which determine the position of the frame of reference in respect to which these generalized coordinates refer. As a consequence, an extended system of the Lagrangian equations is formulated, accommodated to the variability of the masses of particles, where the additional ones correspond to the additional generalized coordinates. By means of these equations, the energy relations of such systems have been studied, where it is demonstrated that here there are four types of energy conservation laws. The obtained energy laws are more complete and natural than the corresponding ones in the usual Lagrangian formulation for such systems. It is demonstrated that the obtained energy laws, are in full accordance with the energy laws in the corresponding vector formulation, if they are expressed in terms of the quantities introduced in this formulation of mechanics. The obtained results are illustrated by an example: the motion of a rocket, which ejects the gasses backwards, while this rocket moves up a straight line on an oblique plane, which glides uniformly in a horizontal direction.
Kepler Problem in Lagrangian Formulation Discussed from Topological Viewpoint
XU Gong-Ou; XU Ming-Jie
2005-01-01
@@ The Kepler problem in Lagrangian formulation is discussed from the topological viewpoint. Essential points are analysed. Along the same line of thoughts, it is possible to study the Kepler problem in Hamiltonian formulation as well as in quantum mechanics from the topological viewpoint for showing quantum-classical correspondence.
Effective weak Lagrangians in the Standard Model and B decays
Grozin, Andrey
2013-01-01
Weak processes (e.g., B decays) with characteristic energies <
Some Three-body force cancellations in Chiral Lagrangians
Arriola, E Ruiz
2016-01-01
The cancellation between off-shell two body forces and three body forces implies a tremendous simplification in the study of three body resonances in two meson-one baryon systems. While this can be done by means of Faddeev equations we provide an alternative and simpler derivation using just the chiral Lagrangian and the field re-parametrization invariance.
The 3D Lagrangian Integral Method. Henrik Koblitz Rasmussen
Rasmussen, Henrik Koblitz
2003-01-01
. This are processes such as thermo-forming, gas-assisted injection moulding and all kind of simultaneous multi-component polymer processing operations. Though, in all polymer processing operations free surfaces (or interfaces) are present and the dynamic of these surfaces are of interest. In the "3D Lagrangian...
Physical unitarity in the lagrangian Sp(2)-symmetric formalism
Lavrov, P M
1996-01-01
The structure of state vector space for a general (non-anomalous) gauge theory is studied within the Lagrangian version of the Sp(2)-symmetric quantization method. The physical {\\it S}-matrix unitarity conditions are formulated. The general results are illustrated on the basis of simple gauge theory models.
A remapped particle-mesh semi-Lagrangian advection scheme
Cotter, C.J.; Frank, J.E.; Reich, S.
2007-01-01
We describe the remapped particle-mesh advection method, a new mass-conserving method for solving the density equation which is suitable for combining with semi-Lagrangian methods for compressible flow applied to numerical weather prediction. In addition to the conservation property, the remapped pa
Bohr--Sommerfeld Lagrangians of moduli spaces of Higgs bundles
Biswas, Indranil; Gammelgaard, Niels Leth; Logares, Marina
Let $X$ be a compact connected Riemann surface of genus at least two. Let $M_H(r,d)$ denote the moduli space of semistable Higgs bundles on $X$ of rank $r$ and degree $d$. We prove that the compact complex Bohr-Sommerfeld Lagrangians of $M_H(r,d)$ are precisely the irreducible components of the n...
Classical dynamical variables for the Wess-Zumino matter Lagrangian
Domenech, G.; Levinas, M.; Umerez, N.
1989-05-01
We study the macroscopic behaviour of the Wess-Zumino matter multiplet. The Lagrangian and the energy-momentum tensor are obtained in terms of densities and velocities of an interacting fluid in N=1 supergravity background. Equations of motion and conditions for consistency are found.
Baryon magnetic moments in the effective quark Lagrangian approach
Simonov, YA; Tjon, JA; Weda, J; Simonov, Yu A.
2002-01-01
An effective quark Lagrangian is derived from first principles through bilocal gluon field correlators. It is used to write down equations for baryons, containing both perturbative and nonperturbative fields. As a result one obtains magnetic moments of octet and decuplet baryons without the introduc
Using Lagrangian Coherent Structures to understand coastal water quality
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 composition at high density by effective scaled lagrangian
Hyun, Chang Ho; Min, Dong Pil [Dept. of Physics, Seoul National Univ., Seoul (Korea, Republic of)
1998-06-01
We investigate the matter composition at around the neutron star densities with a model lagrangian satisfying Brown-Rho scaling law. We calculate the neutron star properties such as maximum mass, radius, hyperon compositions and central density. We compare our results with those of Walecka model. (orig.)
Lagrangian Fuzzy Dynamics of Physical and Non-Physical Systems
Sandler, Uziel
2014-01-01
In this paper, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the \\emph{Fuzzy Dynamics} of a $n$-dimensional system is equivalent to Lagrangian (or Hamiltonian) mechanics in a $n+1$-dimensional space. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's equations gain a non-zero right side proportional to the derivative of the Lagrangian with respect to the action. Examples of such systems are unstable systems, systems with dissipation and systems which can remember their history. Moreover, in certain situations, the Lagrangian could be a set-valued function. The corresponding equations of motion then become differential inclusions instead of differential equations. We will also show that the principal of least action is a consequence of the causality principle and the loc...
Three dimensional Lagrangian structures in the Antarctic Polar Vortex.
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
Evaluation of the Eulerian-Lagrangian spray atomisation (ELSA) in spray simulations
Hoyas, S.; Pastor Enguídanos, José Manuel; KHUONG, ANH DUNG; MOMPÓ LABORDA, JUAN MANUEL; Ravet, Frederic
2011-01-01
Many approaches have been used to simulate the spray structure especially in modelling fuel sprays, i.e., Eulerian, Lagrangian, Lagrangian- Eulerian, Eulerian-Eulerian and Eulerian-Lagrangian approaches. The present study uses an Eulerian-Lagrangian spray atomisation (ELSA) method which is an integrated model for capturing the whole spray evolution starting directly from injector nozzle still the end. Our goal in this study is to evaluate the ELSA model which is implementing into the commerci...
An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems Techniques
2016-06-07
An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems Techniques Christopher K. R. T. Jones Department of... technology for assimilating Lagrangian data. This new Lagrangian data assimilation platform is expected to be particularly effective in ocean regions where...COVERED 00-00-2006 to 00-00-2006 4. TITLE AND SUBTITLE An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems
High-Order Hamilton's Principle and the Hamilton's Principle of High-Order Lagrangian Function
ZHANG Ming-Jiang; ZHAO Hong-Xia; FANG Jian-Hui; MA Shan-Jun; LU Kai
2008-01-01
In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton's principle. Finally, the Hamilton's principle of high-order Lagrangian function is given.
Ames, Thomas L.; Farnsworth, Grant V.; Ketcheson, David Isaac; Robinson, Allen Conrad
2009-09-01
The modeling of solids is most naturally placed within a Lagrangian framework because it requires constitutive models which depend on knowledge of the original material orientations and subsequent deformations. Detailed kinematic information is needed to ensure material frame indifference which is captured through the deformation gradient F. Such information can be tracked easily in a Lagrangian code. Unfortunately, not all problems can be easily modeled using Lagrangian concepts due to severe distortions in the underlying motion. Either a Lagrangian/Eulerian or a pure Eulerian modeling framework must be introduced. We discuss and contrast several Lagrangian/Eulerian approaches for keeping track of the details of material kinematics.
The existence of Hamiltonian stationary Lagrangian tori in Kahler manifolds of any dimension
Lee, Yng-Ing
2010-01-01
Hamiltonian stationary Lagrangians are Lagrangian submanifolds that are critical points of the volume functional under Hamiltonian deformations. They can be considered as a generalization of special Lagrangians or Lagrangian and minimal submanifolds. Joyce, Schoen and the author show that given any compact rigid Hamiltonian stationary Lagrangian in $\\C^n$, one can always find a family of Hamiltonian stationary Lagrangians of the same type in any compact symplectic manifolds with a compatible metric. The advantage of this result is that it holds in very general classes. But the disadvantage is that we do not know where these examples locate and examples in this family might be far apart. In this paper, we derive a local condition on Kahler manifolds which ensures the existence of one family of Hamiltonian stationary Lagrangian tori near a point with given frame satisfying the criterion. Butscher and Corvino ever proposed a condition in n=2. But our condition appears to be different from theirs. The condition d...
A Discrete Approach to Meshless Lagrangian Solid Modeling
Matthew Marko
2017-07-01
Full Text Available The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles apply stresses expected with Hooke’s law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke’s law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with smoothed particle hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for fluid–solid interactions.
Lagrangian tools to monitor transport and mixing in the ocean
Prants, S V; Uleysky, M Yu
2012-01-01
We apply the Lagrangian approach to study surface transport and mixing in the ocean. New tools have been developed to track the motion of water masses, their origin and fate and to quantify transport and mixing. To illustrate the methods used we compute the Lagrangian synoptic maps a comparatively small marine bay, the Peter the Great Bay in the Japan Sea near Vladivostok city (Russia), and in a comparatively large region in the North Pacific, the Kuroshio Extension system. In the first case we use velocity data from a Japan Sea circulation numerical model and in the second one the velocity data are derived from satellite altimeter measurements of anomalies of the sea height distributed by AVISO.
Finite Spectral Semi-Lagrangian Method for Incompressible Flows
LI Shao-Wu; WANG Jian-Ping
2012-01-01
A new semi-Lagrangian (SL) scheme is proposed by using finite spectral regional interpolation and adequate numerical dissipation to control the nonlinear instability. The finite spectrai basis function is C1 continuous at the boundary and is easy to construct. Comparison between numerical and experimental results indicates that the present method works well in solving incompressible Navier-Stokes equations for unsteady Sows around airfoil with different angles of attack.%A new semi-Lagrangian (SL) scheme is proposed by using finite spectral regional interpolation and adequate numerical dissipation to control the nonlinear instability.The finite spectral basis function is C1 continuous at the boundary and is easy to construct.Comparison between numerical and experimental results indicates that the present method works well in solving incompressible Navier-Stokes equations for unsteady flows around airfoil with different angles of attack.
Acoustic Streaming: An Arbitrary Lagrangian-Eulerian Perspective
Nama, Nitesh; Costanzo, Francesco
2016-01-01
We analyze acoustic streaming flows using an 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 microacosutofluidic devices. After the formulation's exposition, we present numerical re...
Unambiguous formalism for higher order Lagrangian field theories
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain); Vankerschaver, Joris [Control and Dynamical Systems, California Institute of Technology, CA (United States)], E-mail: cedricmc@imaff.cfmac.csic.es, E-mail: mdeleon@imaff.cfmac.csic.es, E-mail: d.martin@imaff.cfmac.csic.es, E-mail: jv@caltech.edu
2009-11-27
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Bohr--Sommerfeld Lagrangians of moduli spaces of Higgs bundles
Biswas, Indranil; Gammelgaard, Niels Leth; Logares, Marina
Let $X$ be a compact connected Riemann surface of genus at least two. Let $M_H(r,d)$ denote the moduli space of semistable Higgs bundles on $X$ of rank $r$ and degree $d$. We prove that the compact complex Bohr-Sommerfeld Lagrangians of $M_H(r,d)$ are precisely the irreducible components of the n......Let $X$ be a compact connected Riemann surface of genus at least two. Let $M_H(r,d)$ denote the moduli space of semistable Higgs bundles on $X$ of rank $r$ and degree $d$. We prove that the compact complex Bohr-Sommerfeld Lagrangians of $M_H(r,d)$ are precisely the irreducible components...
Chiral lagrangian approach to exchange vector currents in nuclei
Park, T S; Rho, M; Park, Tae Sun; Min, Dong Pil; Rho, Mannque
1995-01-01
Exchange vector currents are calculated up to one-loop order (corresponding to next-to-next-to-leading order) in chiral perturbation theory. As an illustration of the power of the approach, we apply the formalism to the classic nuclear process n+p\\rightarrow d +\\gamma at thermal energy. The exchange current correction comes out to be (4.5 \\pm 0.3) \\% in amplitude giving a predicted cross section \\sigma= (334\\pm 3)\\ {\\mbox mb} in excellent agreement with the experimental value (334.2\\pm 0.5)\\ {\\mbox mb}. Together with the axial charge transitions computed previously, this result provides a strong support for the power of chiral Lagrangians in nuclear physics. As a by-product of our results, we suggest an open problem in the application of chiral Lagrangian approach to nuclear processes that has to do with giving a physical meaning to the short-range correlations that play an important role in nuclei.
Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics.
Busse, Angela; Müller, Wolf-Christian; Gogoberidze, Grigol
2010-12-01
For the phenomenological description of magnetohydrodynamic turbulence competing models exist, e.g., Boldyrev [Phys. Rev. Lett. 96, 115002 (2006)] and Gogoberidze [Phys. Plasmas 14, 022304 (2007)], which predict the same Eulerian inertial-range scaling of the turbulent energy spectrum although they employ fundamentally different basic interaction mechanisms. A relation is found that links the Lagrangian frequency spectrum with the autocorrelation time scale of the turbulent fluctuations τ(ac) and the associated cascade time scale τ(cas). Thus, the Lagrangian energy spectrum can serve to identify weak (τ(ac) ≪ τ(cas)) and strong (τ(ac) ∼ τ(cas)) interaction mechanisms providing insight into the turbulent energy cascade. The new approach is illustrated by results from direct numerical simulations of two- and three-dimensional incompressible MHD turbulence.
An algorithm for discovering Lagrangians automatically from data
Daniel J.A. Hills
2015-11-01
Full Text Available An activity fundamental to science is building mathematical models. These models are used to both predict the results of future experiments and gain insight into the structure of the system under study. We present an algorithm that automates the model building process in a scientifically principled way. The algorithm can take observed trajectories from a wide variety of mechanical systems and, without any other prior knowledge or tuning of parameters, predict the future evolution of the system. It does this by applying the principle of least action and searching for the simplest Lagrangian that describes the system’s behaviour. By generating this Lagrangian in a human interpretable form, it can also provide insight into the workings of the system.
Statistical Decoupling of Lagrangian Fluid Parcel in Newtonian Cosmology
Wang, Xin
2016-01-01
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the non-linear evolution of various cosmic objects, e.g. dark matter halos, in the context of Lagrangian fluid dynamics, since a fluid parcel with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the probability distribution evolution equation of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (PDF). Consequently it is guaranteed that the one-point PDF would be preserved by evolving these...
Lagrangian intersection Floer theory anomaly and obstruction, part I
Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru
2009-01-01
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A_\\infty-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A_\\infty algebras and A_\\infty bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-co...
Lagrangian intersection Floer theory anomaly and obstruction, part II
Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru
2009-01-01
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A_\\infty-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A_\\infty algebras and A_\\infty bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-co...
Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
Ruiz, D E
2015-01-01
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". Both phenomena are governed by an effective gauge Hamiltonian, which vanishes 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 lead to equations for the wave spin, which happens to be a $(N^2-1)$-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 Lagrangi...
Singular Lorentz-Violating Lagrangians and Associated Finsler Structures
Colladay, Don
2015-01-01
Several lagrangians associated to classical limits of lorenz-violating fermions in the Standard Model extension (SME) have been shown to yield Finsler functions when the theory is expressed in Euclidean space. When spin-couplings are present, the lagrangian can develop singularities that obstruct the construction of a globally defined Legendre transformation, leading to singular Finsler spaces. A specific sector of the SME where such problems arise is studied. It is found that the singular behavior can be eliminated by an appropriate lifting of the problem to an associated algebraic variety. This provides a smooth classical model for the singular problem. In Euclidean space, the procedure involves combining two related singular Finsler functions into a single smooth function with a semi-positive definite quadratic form defined on a desingularized variety.
Yasutake, Nobutoshi; Fujisawa, Kotaro; Yamada, Shoichi
2016-12-01
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.
Inertial-particle accelerations in turbulence: a Lagrangian closure
Vajedi, S; Mehlig, B; Biferale, L
2016-01-01
The distribution of particle accelerations in turbulence is intermittent, with non-Gaussian tails that are quite different for light and heavy particles. In this article we analyse a closure scheme for the acceleration fluctuations of light and heavy inertial particles in turbulence, formulated in terms of Lagrangian correlation functions of fluid tracers. We compute the variance and the flatness of inertial particle accelerations and we discuss their dependency on the Stokes number. The closure incorporates effects induced by the Lagrangian correlations along the trajectories of fluid tracers, and its predictions agree well with results of direct numerical simulations of inertial particles in turbulence, provided that the effects induced by the inertial preferential sampling of heavy/light particles outside/inside vortices are negligible. In particular, the scheme predicts the correct functional behaviour of the acceleration variance, as a function of Stokes, as well as the presence of a minimum/maximum for ...
Chiral Lagrangian and chiral quark model from confinement in QCD
Simonov, Yu A
2015-01-01
The effective chiral Lagrangian in both nonlocal form $L_{ECCL}$ and standard local form $L_{ECL}$ are derived in QCD using the confining kernel, obtained in the vacuum correlator formalism. As a result all coefficients of $L_{ECL}$ can be computed via $q\\bar q$ Green's functions. In the $p^2$ order of $L_{ECL}$ one obtains GOR relations and quark decay constants $f_a$ are calculated $a=1,...8$, while in the $p^4$ order the coefficients $L_1, L_2, L_3,L_4, L_5, L_6$ are obtained in good agreement with the values given by data. The chiral quark model is shown to be a simple consequence of $L_{ECCL}$ with defined coefficients. It is demonstrated that $L_{ECCL}$ gives an extension of the limiting low-energy Lagrangian $L_{ECL}$ to arbitrary momenta.
Low-spin models for higher-spin Lagrangians
Francia, Dario
2011-01-01
Higher-spin theories are most commonly modelled on the example of spin 2. While this is appropriate for the description of free irreducible spin-s particles, alternative options could be equally interesting. In particular Maxwell's equations provide the effective model for maximally reducible theories of higher spins inspired by the tensionless limit of the open string. For both options, as well as for their fermionic counterparts, one can extend the analogy beyond the equations for the gauge potentials, formulating the corresponding Lagrangians in terms of higher-spin curvatures. The associated non-localities are effectively due to the elimination of auxiliary fields and do not modify the spectrum. Massive deformations of these theories are also possible, and in particular in this contribution we propose a generalisation of the Proca Lagrangian for the Maxwell-inspired geometric theories.
The Lagrangian Deformation Structure of Three-Dimensional Steady Flow
Lester, Daniel R; Borgne, Tanguy Le; de Barros, Felipe P J
2016-01-01
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures (LCSs). To understand and model these processes it is necessary to quantify Lagrangian deformation in terms of Eulerian flow properties, currently an open problem. To elucidate this link we develop a Protean (streamline) coordinate transform for steady three-dimensional (3D) flows which renders both the velocity gradient and deformation gradient upper triangular. This frame not only simplifies computation of fluid deformation metrics such as fi?nite-time Lyapunov exponents (FTLEs) and elucidates the deformation structure of the flow, but moreover explicitly recovers kinematic and topological constraints upon deformation such as those related to helicity density and the Poincar\\'{e}-Bendixson theorem. We apply this transform to several classes of steady 3D flow, including helical ...
A non-conventional discontinuous Lagrangian for viscous flow
Scholle, M.; Marner, F.
2017-02-01
Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier-Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier-Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.
Proof of the equivalence theorem in the chiral lagrangian formalism
He, H J; Li, X; Hong-Jian He; He, Hong-Jian; Kuang, Yu-Ping; Li, Xiaoyuan; Xiaoyuan Li
1994-01-01
A general proof of the equivalence theorem in electroweak theories with the symmetry breaking sector described by the chiral Lagrangian is given in the $R_{\\xi}$ gauge by means of the Ward-Takahashi identities. The precise form of the theorem contains a modification factor $C_{mod}$ associated with each external Goldstone boson similar to that in the standard model. $C_{mod}$ is exactly unity in our previously proposed renormalization scheme, {\\it Scheme-II}.
Lagrangian model for oil spill diffusion at sea
Lonin, Serguei A. [Centro de Investigaciones Oceanograficas e Hidrograficas, Escuela Naval, Cartagena de Indias (Colombia)
1999-07-01
The Eulerian and Lagrangian methods for oil spill simulations are discussed. A mathematical description of the vertical movement of an oil droplet in the ocean is proposed based on the Langeven equation and the analytical test results are presented to compare the results. The results are that the buoyant effect and the vertical turbulent variations are very important mechanisms for vertical movement of oil in the water column. (Author)
Tsunami intrusion in wide meandering channels: a Lagrangian numerical experiment
Couston, L. A.; Alam, M. R.
2015-12-01
Among the many difficulties of tsunami forecast, wave runup on sloped beaches remains a major obstacle in numerical simulations. Traditional Eulerian models must adjust the fluid flow domain continuously due to the moving shorelines, which can significantly affect the computational cost and results accuracy. An efficient though uncommon alternative for accurate runup predictions still exists, consisting in using a Lagrangian model as recently shown by e.g. Couston et al. (2015) who studied the runup of landslide tsunamis in lakes with a non-dispersive Lagrangian model. Here we introduce a fully-nonlinear Boussinesq-type model derived in the Lagrangian framework to investigate various cases of long-wave runup on curved beaches and meandering channels. The governing equations are expressed in terms of curvilinear Lagrangian coordinates, making the model suitable for accurate runup computations at shorelines of arbitrary geometry while retaining the inherent simplicity of a physical model discretized on a fixed and structured grid. We implement an elliptic grid generation algorithm to map the physical space to the computational space, and a high-order finite-difference scheme for time integration. The numerical model has a linear complexity in the number of unknowns when neglecting dispersive effects. We show that the formation of edge waves due to the sloped banks of a wide channel has a significant influence on the capability of a meander or constriction in reflecting the intruding tsunami, and we investigate the effect of dispersion. Reference: Couston, L.-A., Mei, C. C., & Alam, M.-R. (2015). Landslide tsunamis in lakes. Journal of Fluid Mechanics, 772, 784-804.
A Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
Torrieri, Giorgio
2016-01-01
We rederive relativistic hydrodynamics as a Lagrangian effective theory using the doubled coordinates technique, allowing us to include dissipative terms. We include Navier-Stokes shear and bulk terms, as well as Israel-Stewart relaxation time terms, within this formalism. We show how the inclusion of shear viscosity, and the requirement of a bounded energy-momentum "vacuum", forces the inclusion of the Israel-Stewart term into the theory, thereby providing a justification for the origin and uniqueness of these terms.
Lagrangian Data Analysis in Mesoscale Prediction and Model Validation Studies
2016-06-21
Department Rosenstiel School of Marine and Atmospheric Science 4600 Rickenbacker Causeway, Miami, Florida 33149 phone: (305) 361 4892, fax: (305) 361...of Marine and Atmospheric Science ,4600 Rickenbacker Causeway,Miami,FL,33149 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY...stratification and direct wind forcing. Second, a stochastic Lagrangian model of transport has been implemented, and tested with positive results against
Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
Montenegro, David; Torrieri, Giorgio
2016-09-01
We rederive relativistic hydrodynamics as a Lagrangian effective theory using the doubled coordinates technique, allowing us to include dissipative terms. We include Navier-Stokes shear and bulk terms, as well as Israel-Stewart relaxation time terms, within this formalism. We show how the inclusion of shear dissipation forces the inclusion of the Israel-Stewart term into the theory, thereby providing an additional justification for the form of this term.
Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds
Yau, S-T
2002-01-01
The collection of articles in this volume are based on lectures presented during the Winter School on Mirror Symmetry held at Harvard University. There are many new directions suggested by mirror symmetry which could potentially have very rich connections in physics and mathematics. This book brings together the latest research in a major area of mathematical physics, including the recent progress in mirror manifolds and Lagrangian submanifolds. In particular, several articles describing homological approach and related topics are included.
The hybrid Eulerian Lagrangian numerical scheme tested with Chemistry
A. B. Hansen
2012-11-01
Full Text Available A newly developed advection scheme, the Hybrid Eulerian Lagrangian (HEL scheme, has been tested, including a module for atmospheric chemistry, including 58 chemical species, and compared to two other traditional advection schemes; a classical pseudospectral Eulerian method the Accurate Space Derivative (ASD scheme and the bi-cubic semi-Lagrangian (SL scheme using classical rotation tests. The rotation tests have been designed to test and compare the advection schemes for different spatial and temporal resolutions in different chemical conditions (rural and urban and for different shapes (cone and slotted cylinder giving the advection schemes different challenges with respect to relatively slow or fast chemistry and smooth or sharp gradients, respectively. In every test, error measures have been calculated and used for ranking of the advection schemes with respect to performance, i.e. lowest overall errors for all chemical species. Furthermore, the HEL and SL schemes have been compared in a shallow water model, demonstrating the performance in a more realistic non-linear deformation flow.
The results in this paper show that the new advection scheme, HEL, by far outperforms both the Eulerian and semi-Lagrangian schemes with very low error estimates compared to the two other schemes. Although no analytic solution can be obtained for the performance in the non-linear shallow water model flow, the tracer distribution appears realistic as compared to LMCSL when a mixing between local parcel concentrations is introduced in HEL.
Geometric Time and Causal Time in Relativistic Lagrangian Mechanics
Brunet, Olivier
2016-01-01
In this article, we argue that two distinct types of time should be taken into account in relativistic physics: a geometric time, which emanates from the structure of spacetime and its metrics, and a causal time, indicating the flow from the past to the future. A particularity of causal times is that its values have no intrinsic meaning, as their evolution alone is meaningful. In the context of relativistic Lagrangian mechanics, causal times corresponds to admissible parameterizations of paths, and we show that in order for a langragian to not depend on any particular causal time (as its values have no intrinsic meaning), it has to be homogeneous in its velocity argument. We illustrate this property with the example of a free particle in a potential. Then, using a geometric Lagrangian (i.e. a parameterization independent Lagrangian which is also manifestly covariant), we introduce the notion of ageodesicity of a path which measures to what extent a path is far from being a geodesic, and show how the notion ca...
Bounded fractional diffusion in geological media: Definition and Lagrangian approximation
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.
Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices
Huhn, F.; van Rees, W. M.; Gazzola, M.; Rossinelli, D.; Haller, G.; Koumoutsakos, P.
2015-08-01
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
Connections between chiral Lagrangians and QCD sum-rules
Fariborz, Amir H; Steele, T G
2016-01-01
It is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g., quark-antiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that are particularly effective in studies of the substructure of light scalar mesons with multiple complicated resonance shapes and substantial underlying mixings. The validity of these connections is demonstrated for the example of the isotriplet $a_0(980)$-$a_0(1450)$ system, resulting in an unambiguous determination of the scale factors from the combined inputs of QCD sum-rules and chiral Lagrangians. These scale factors ...
Currents in the Dead Sea: Lagrangian and Eulerian observations
Ozer, Tal; Gertman, Isaac; Katsenelson, Boris; Bodzin, Raanan; Lensly, Nadav
2015-04-01
The Dead Sea is a terminal hypersaline lake located in the lowest surface on Earth (currently -429 m bsl). The physical properties of the brine are significantly different than in common marine systems: the DS brine density is ~1.24 gr/cc and its viscosity ~3 times higher than marine systems. We present observational data on wind and currents in the Dead Sea. The observation setup includes a few fixed (Eulerian) stations which are equipped with wind meter and current meter profiler that covers the entire water column (ADCP). Thermal stratification is continuously measured in some of the stations using a thermistor chain. Lagrangian drifters that record the shallow water currents were released in liner array of single drifters between the fixed stations, and also in triplets (15 m triangle). The results include the measured time series data of wind (atmospheric forcing) and the measured current profiles from the fixed stations. Data of the Lagrangian drifters is presented as trajectories along with vector time series. Quality control check included comparison of drifter data and ADCP data whenever the drifters passed by the fixed stations; a very good agreement was found between the different measuring approaches. We discuss the following issues : (i) the relation between the wind and current data, (ii) the Lagrangian trajectories and transport aspects.
The effective Lagrangian of dark energy from observations
Jimenez, Raul; Verde, Licia [ICREA and ICC, Institut de Ciencies del Cosmos, Universitat de Barcelona (IEEC-UB), Marti i Franques 1, Barcelona 08028 (Spain); Talavera, P. [DFEN and ICC, Universitat Politècnica de Catalunya, Comte Urgell 187, Barcelona (Spain); Moresco, Michele; Cimatti, Andrea [Dipartimento di Astronomia, Università di Bologna, via Ranzani 1, 40127 Bologna (Italy); Pozzetti, Lucia, E-mail: raul.jimenez@icc.ub.edu, E-mail: pere.talavera@icc.ub.edu, E-mail: liciaverde@icc.ub.edu, E-mail: michele.moresco@unibo.it, E-mail: a.cimatti@unibo.it, E-mail: lucia.pozzetti@oabo.inaf.it [INAF — Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna (Italy)
2012-03-01
Using observational data on the expansion rate of the universe (H(z)) we constrain the effective Lagrangian of the current accelerated expansion. Our results show that the effective potential is consistent with being flat i.e., a cosmological constant; it is also consistent with the field moving along an almost flat potential like a pseudo-Goldstone boson. We show that the potential of dark energy does not deviate from a constant at more than 6% over the redshift range 0 < z < 1. The data can be described by just a constant term in the Lagrangian and do not require any extra parameters; therefore there is no evidence for augmenting the number of parameters of the LCDM paradigm. We also find that the data justify the effective theory approach to describe accelerated expansion and that the allowed parameters range satisfy the expected hierarchy. Future data, both from cosmic chronometers and baryonic acoustic oscillations, that can measure H(z) at the % level, could greatly improve constraints on the flatness of the potential or shed some light on possible mechanisms driving the accelerated expansion. Besides the above result, it is shown that the effective Lagrangian of accelerated expansion can be constrained from cosmological observations in a model-independent way and that direct measurements of the expansion rate H(z) are most useful to do so.
On the Lagrangian Biduality of Sparsity Minimization Problems
Singaraju, Dheeraj; Tron, Roberto; Yang, Allen Y; Sastry, S Shankar
2012-01-01
Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of the original problem. In this work, we present a novel primal-dual analysis on a class of sparsity minimization problems. We show that the Lagrangian bidual (i.e., the Lagrangian dual of the Lagrangian dual) of the sparsity minimization problems can be used to derive interesting convex relaxations: the bidual of the $\\ell_0$-minimization problem is the $\\ell_1$-minimization problem; and the bidual of the $\\ell_{0,1}$-minimization problem for enforcing group sparsity on structured data is the $\\ell_{1,\\infty}$-minimization problem. The analysis provides a means to compute per-instance non-trivial lower bounds on the (group) sparsity of the desired solutions. In a real-world application, the bidual relaxation improves the performance of a sparsity-based classification framewor...
Lagrangian chaos in three- dimensional steady buoyancy-driven flows
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 Pr1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).
Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices.
Huhn, F; van Rees, W M; Gazzola, M; Rossinelli, D; Haller, G; Koumoutsakos, P
2015-08-01
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
A lagrangian dynamical theory for the mass function of cosmic structures; 1, dynamics
Monaco, P
1996-01-01
A new theory for determining the mass function of cosmic structures is presented. It relies on a realistic treatment of collapse dynamics. Gravitational collapse is analyzed in the Lagrangian perturbative framework. Lagrangian perturbations provide an approximation of truncated type, i.e. small-scale structure is filtered out. The collapse time is suitably defined as the instant at which orbit crossing takes place. The convergence of the Lagrangian series in predicting the collapse time of a homogeneous ellipsoid is demonstrated; it is also shown that third-order calculations are necessary in predicting collapse. Then, the Lagrangian prediction, with a correction for quasi-spherical perturbations, can be used to determine the collapse time of a homogeneous ellipsoid in a very fast and precise way. Furthermore, ellipsoidal collapse can be considered as a particular truncation of the Lagrangian series. Gaussian fields with scale-free power spectra are then considered. The Lagrangian series for the collapse time...
Differential geometry based solvation model II: Lagrangian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2011-12-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of
An unconditionally stable fully conservative semi-Lagrangian method
Lentine, Michael
2011-04-01
Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had. © 2011 Elsevier Inc.
Comparing High-latitude Ionospheric and Thermospheric Lagrangian Coherent Structures
Wang, N.; Ramirez, U.; Flores, F.; Okic, D.; Datta-Barua, S.
2015-12-01
Lagrangian Coherent Structures (LCSs) are invisible boundaries in time varying flow fields that may be subject to mixing and turbulence. The LCS is defined by the local maxima of the finite time Lyapunov exponent (FTLE), a scalar field quantifying the degree of stretching of fluid elements over the flow domain. Although the thermosphere is dominated by neutral wind processes and the ionosphere is governed by plasma electrodynamics, we can compare the LCS in the two modeled flow fields to yield insight into transport and interaction processes in the high-latitude IT system. For obtaining thermospheric LCS, we use the Horizontal Wind Model 2014 (HWM14) [1] at a single altitude to generate the two-dimensional velocity field. The FTLE computation is applied to study the flow field of the neutral wind, and to visualize the forward-time Lagrangian Coherent Structures in the flow domain. The time-varying structures indicate a possible thermospheric LCS ridge in the auroral oval area. The results of a two-day run during a geomagnetically quiet period show that the structures are diurnally quasi-periodic, thus that solar radiation influences the neutral wind flow field. To find the LCS in the high-latitude ionospheric drifts, the Weimer 2001 [2] polar electric potential model and the International Geomagnetic Reference Field 11 [3] are used to compute the ExB drift flow field in ionosphere. As with the neutral winds, the Lagrangian Coherent Structures are obtained by applying the FTLE computation. The relationship between the thermospheric and ionospheric LCS is analyzed by comparing overlapping FTLE maps. Both a publicly available FTLE solver [4] and a custom-built FTLE computation are used and compared for validation [5]. Comparing the modeled IT LCSs on a quiet day with the modeled IT LCSs on a storm day indicates important factors on the structure and time evolution of the LCS.
Bounded fractional diffusion in geological media: Definition and Lagrangian approximation
Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang
2016-01-01
Spatiotemporal Fractional-Derivative Models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and non-zero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing non-zero-value spatial-nonlocal boundary conditions with directional super-diffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eularian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the non-local and non-symmetric fractional diffusion. For a non-zero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite do mains to those with any size and boundary conditions.
Zhang, Y.; Dioos, B.; Hu, Z.; Vrancken, L.; Wang, X.
2016-10-01
In this paper, we study the Lagrangian submanifolds in the homogeneous nearly Kähler S3 ×S3 with parallel second fundamental form. We first prove that every Lagrangian submanifold with parallel second fundamental form in any 6-dimensional strict nearly Kähler manifold is totally geodesic. Then we give a complete classification of the totally geodesic Lagrangian submanifolds in the homogeneous nearly Kähler S3 ×S3.
Comment on Pauli-Villars Lagrangian on the Lattice
Haga, K; Okuyama, K; Suzuki, H; Haga, Kazunobu; Igarashi, Hiroshi; Okuyama, Kiyoshi; Suzuki, Hiroshi
1997-01-01
It is interesting to superimpose the Pauli--Villars regularization on the lattice regularization. We illustrate how this scheme works by evaluating the axial anomaly in a simple lattice fermion model, the Pauli--Villars Lagrangian with a gauge non-invariant Wilson term. The gauge non-invariance of the axial anomaly, caused by the Wilson term, is remedied by a compensation between Pauli--Villars regulators in the continuum limit. A subtlety in Frolov--Slavnov's scheme for an {\\it odd\\/} number of chiral fermions in an anomaly free complex gauge representation, which requires an infinite number of regulators, is briefly mentioned.
Inflation, bifurcations of nonlinear curvature Lagrangians and dark energy
Mielke, Eckehard W; Schunck, Franz E
2008-01-01
A possible equivalence of scalar dark matter, the inflaton, and modified gravity is analyzed. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einsteinian spaces, distinguished only by a different effective gravitational strength and cosmological constant. A swallow tail catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This `triple unification' may shed new light on the nature and large scale distribution not only of dark matter but also on `dark energy', regarded as an effective cosmological constant, and inflation.
Attraction-Based Computation of Hyperbolic Lagrangian Coherent Structures
Karrasch, Daniel; Haller, George
2014-01-01
Recent advances enable the simultaneous computation of both attracting and repelling families of Lagrangian Coherent Structures (LCS) at the same initial or final time of interest. Obtaining LCS positions at intermediate times, however, has been problematic, because either the repelling or the attracting family is unstable with respect to numerical advection in a given time direction. Here we develop a new approach to compute arbitrary positions of hyperbolic LCS in a numerically robust fashion. Our approach only involves the advection of attracting material surfaces, thereby providing accurate LCS tracking at low computational cost. We illustrate the advantages of this approach on a simple model and on a turbulent velocity data set.
Radiative neutron-proton capture in effective chiral lagrangians
Park, T S; Rho, M; Park, Tae Sun; Min, Dong Pil; Rho, Mannque
1994-01-01
We calculate the cross-section for the thermal n+p\\rightarrow d+\\gamma process in chiral perturbation theory to next-to-next-to-leading order using heavy-fermion formalism. The exchange current correction is found to be (4.5\\pm 0.3)~\\% in amplitude and the chiral perturbation at one-loop order gives the cross section \\sigma_{th}^{np}=(334\\pm 2)\\ {\\mbox mb} which is in agreement with the experimental value (334.2\\pm 0.5)\\ {\\mbox mb}. Together with the axial charge transitions, this provides a strong support for the power of chiral Lagrangians for nuclear physics.
Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics.
Ilinskii, Yurii A; Hamilton, Mark F; Zabolotskaya, Evgenia A
2007-02-01
Two models of interacting bubble dynamics are presented, a coupled system of second-order differential equations based on Lagrangian mechanics, and a first-order system based on Hamiltonian mechanics. Both account for pulsation and translation of an arbitrary number of spherical bubbles. For large numbers of interacting bubbles, numerical solution of the Hamiltonian equations provides greater stability. The presence of external acoustic sources is taken into account explicitly in the derivation of both sets of equations. In addition to the acoustic pressure and its gradient, it is found that the particle velocity associated with external sources appears in the dynamical equations.
On Problems of the Lagrangian Quantization of W3-gravity
Geyer, B; Lavrov, P M; Moshin, P Y
2003-01-01
We consider the two-dimensional model of W3-gravity within Lagrangian quantization methods for general gauge theories. We use the Batalin-Vilkovisky formalism to study the arbitrariness in the realization of the gauge algebra. We obtain a one-parametric non-analytic extension of the gauge algebra, and a corresponding solution of the classical master equation, related via an anticanonical transformation to a solution corresponding to an analytic realization. We investigate the possibility of closed solutions of the classical master equation in the Sp(2)-covariant formalism and show that such solutions do not exist in the approximation up to the third order in ghost and auxiliary fields.
Lagrangian chaos and small scale structure of passive scalars
Vulpiani, Angelo
1989-09-01
We revise the classical theory of Batchelor, which gives a k-1 law for the power spectrum of a passive scalar at wavenumbers k, for which the molecular diffusion is unimportant and much smaller than the fluid viscosity. Using some ideas borrowed from the theory of dynamical systems, we show that this power law is related to the chaotic motion of marker particles (Lagrangian chaos) and to the incompressibility constraint. Moreover our approach permits showing that the k-1 regime is present in fluids which are not turbulent and it is valid for all dimensionalities d⩾2.
k Spectrum of Passive Scalars in Lagrangian Chaotic Fluid Flows
Antonsen, Thomas M., Jr.; Fan, Zhencan Frank; Ott, Edward
1995-08-01
An eikonal-type description for the evolution of k spectra of passive scalars convected in a Lagrangian chaotic fluid flow is shown to accurately reproduce results from orders of magnitude more time consuming computations based on the full passive scalar partial differential equation. Furthermore, the validity of the reduced description, combined with concepts from chaotic dynamics, allows new theoretical results on passive scalar k spectra to be obtained. Illustrative applications are presented to long-time passive scalar decay, and to Batchelor's law k spectrum and its diffusive cutoff.
Hilbert series for constructing Lagrangians: Expanding the phenomenologist's toolbox
Lehman, Landon; Martin, Adam
2015-05-01
This paper presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a given field content and is a useful cross-check on more well-known group theoretical methods. In addition, at least when restricted to invariants without derivatives, the Hilbert series technique supplies a robust way of counting invariants in scenarios which, due to the large number of fields involved or to high-dimensional group representations, are intractable by traditional methods. We work out several practical examples.
Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
Lehman, Landon
2015-01-01
This note presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a given field content, and is a useful cross check on more well-known group theoretical methods. In addition, at least when restricted to invariants without derivatives, the Hilbert series technique supplies a robust way of counting invariants in scenarios which, due to the large number of fields involved or to high dimensional group representations, are intractable by traditional methods. We work out several practical examples.
A hybrid Eulerian Lagrangian numerical scheme for solving prognostic equations in fluid dynamics
E. Kaas
2013-07-01
Full Text Available A new hybrid Eulerian Lagrangian numerical scheme (HEL for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place, i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.
A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
Li, Wenliang
2015-01-01
We develop a general framework for Lorentz-invariant Lagrangian field theories that leads to second order equations of motion. The key ingredient is the antisymmetric Kronecker delta. Then we reformulate the general ghost-free Lagrangians in the language of differential forms. The absence of higher order equations of motion stems from the basic fact that every exact form is closed. All known ghost-free Lagrangian theories for spin-0, spin-1, spin-2 fields have natural formulations in this framework. We propose new ghost-free Lagrangians, for example, novel nonlinear kinetic terms for graviton.
Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions
Yale, Alexandre
2010-01-01
The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general co-variance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension $D = 2m$ and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in $D = 2m$. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In parti...
Lagrangian Floer Superpotentials and Crepant Resolutions for Toric Orbifolds
Chan, Kwokwai; Cho, Cheol-Hyun; Lau, Siu-Cheong; Tseng, Hsian-Hua
2014-05-01
We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold and that of its toric crepant resolution Y coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we find that the change of variable formula which appears in closed CRC can be explained by relations between open (orbifold) Gromov-Witten invariants. We also discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appears in Ruan's original CRC (Gromov-Witten theory of spin curves and orbifolds, contemp math, Amer. Math. Soc., Providence, RI, pp 117-126, 2006). We prove the open CRC for the weighted projective spaces using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.
The initial value problem in Lagrangian drift kinetic theory
Burby, J. W.
2016-06-01
> Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low orders. These unphysical modes, which may be rapidly oscillating, damped or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model's initial value problem. In short, the (infinite dimensional) system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, `renormalized' variational approach to drift kinetic theory that manifestly respects the parent model's initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase-space Lagrangian instead of the usual `field particle' Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dimensional toy model of high-order variational drift kinetics; the analogous full-on drift kinetic story is discussed subsequently. The renormalized drift kinetic system, while variational and just as formally accurate as conventional formulations, does not support the troublesome rapidly varying modes.
The initial value problem in Lagrangian drift kinetic theory
Burby, J W
2015-01-01
Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low-orders. These unphysical modes, which may be rapidly oscillating, damped, or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model's initial value problem (Vlasov-Poisson for electrostatics, Vlasov-Darwin or Vlasov-Maxwell for electromagnetics.) In short, the system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, "renormalized" variational approach to drift kinetic theory that manifestly respects the parent model's initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase space Lagrangian instead of the usual "field+particle" Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dime...
Linear wave equations and effective lagrangians for Wigner supermultiplets
Dahm, R
1995-01-01
The relevance of the contracted SU(4) group as a symmetry group of the pion nucleon scattering amplitudes in the large N_c limit of QCD raises the problem on the construction of effective Lagrangians for SU(4) supermultiplets. In the present study we suggest effective Lagrangians for selfconjugate representations of SU(4) in exploiting isomorphism between so(6) and ist universal covering su(4). The model can be viewed as an extension of the linear \\sigma model with SO(6) symmetry in place of SO(4) and generalizes the concept of the linear wave equations for particles with arbitrary spin. We show that the vector representation of SU(4) reduces on the SO(4) level to a complexified quaternion. Its real part gives rise to the standard linear \\sigma model with a hedgehog configuration for the pion field, whereas the imaginary part describes vector meson degrees of freedom via purely transversal \\rho mesons for which a helical field configuration is predicted. As a minimal model, baryonic states are suggested to ap...
The effective Lagrangian of dark energy from observations
Jimenez, Raul; Verde, Licia; Moresco, Michele; Cimatti, Andrea; Pozzetti, Lucia
2012-01-01
Using observational data on the expansion rate of the universe (H(z)) we constrain the effective Lagrangian of the current accelerated expansion. Our results show that the effective potential is consistent with being flat i.e., a cosmological constant; it is also consistent with the field moving along an almost flat potential like a pseudo-Goldstone boson. We show that the potential of dark energy does not deviate from a constant at more than 6% over the redshift range 0 < z < 1. The data can be described by just a constant term in the Lagrangian and do not require any extra parameters; therefore there is no evidence for augmenting the number of parameters of the LCDM paradigm. We also find that the data justify the effective theory approach to describe accelerated expansion and that the allowed parameters range satisfy the expected hierarchy. Future data, both from cosmic chronometers and baryonic acoustic oscillations, that can measure H(z) at the % level, could greatly improve constraints on the flat...
Lagrangian transported MDF methods for compressible high speed flows
Gerlinger, Peter
2017-06-01
This paper deals with the application of thermochemical Lagrangian MDF (mass density function) methods for compressible sub- and supersonic RANS (Reynolds Averaged Navier-Stokes) simulations. A new approach to treat molecular transport is presented. This technique on the one hand ensures numerical stability of the particle solver in laminar regions of the flow field (e.g. in the viscous sublayer) and on the other hand takes differential diffusion into account. It is shown in a detailed analysis, that the new method correctly predicts first and second-order moments on the basis of conventional modeling approaches. Moreover, a number of challenges for MDF particle methods in high speed flows is discussed, e.g. high cell aspect ratio grids close to solid walls, wall heat transfer, shock resolution, and problems from statistical noise which may cause artificial shock systems in supersonic flows. A Mach 2 supersonic mixing channel with multiple shock reflection and a model rocket combustor simulation demonstrate the eligibility of this technique to practical applications. Both test cases are simulated successfully for the first time with a hybrid finite-volume (FV)/Lagrangian particle solver (PS).
The Gaussian streaming model and Lagrangian effective field theory
Vlah, Zvonimir; White, Martin
2016-01-01
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 to 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 int...
The Gaussian streaming model and convolution Lagrangian effective field theory
Vlah, Zvonimir; Castorina, Emanuele; White, Martin
2016-12-01
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 to 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.
Hamiltonian and Lagrangian Dynamical Matrix Approaches Applied to Magnetic Nanostructures
Roberto Zivieri
2012-01-01
Full Text Available Two micromagnetic tools to study the spin dynamics are reviewed. Both approaches are based upon the so-called dynamical matrix method, a hybrid micromagnetic framework used to investigate the spin-wave normal modes of confined magnetic systems. The approach which was formulated first is the Hamiltonian-based dynamical matrix method. This method, used to investigate dynamic magnetic properties of conservative systems, was originally developed for studying spin excitations in isolated magnetic nanoparticles and it has been recently generalized to study the dynamics of periodic magnetic nanoparticles. The other one, the Lagrangian-based dynamical matrix method, was formulated as an extension of the previous one in order to include also dissipative effects. Such dissipative phenomena are associated not only to intrinsic but also to extrinsic damping caused by injection of a spin current in the form of spin-transfer torque. This method is very accurate in identifying spin modes that become unstable under the action of a spin current. The analytical development of the system of the linearized equations of motion leads to a complex generalized Hermitian eigenvalue problem in the Hamiltonian dynamical matrix method and to a non-Hermitian one in the Lagrangian approach. In both cases, such systems have to be solved numerically.
Fingerprints of heavy scales in electroweak effective Lagrangians
Pich, Antonio; Santos, Joaquin; Sanz-Cillero, Juan Jose
2016-01-01
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 $SU(2)_L\\otimes SU(2)_R\\to SU(2)_{L+R}$, which couples the known particle fields to heavier states with bosonic quantum numbers $J^P=0^\\pm$ and $1^\\pm$. 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 equiva...
Lagrangian structures, integrability and chaos for 3D dynamical equations
Bustamante, M D; Bustamante, Miguel D.; Hojman, Sergio A.
2003-01-01
In this paper we consider the general setting for constructing Action Principles for three-dimensional first order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and we show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behavior or homoclinic orbits have not been verified up to now. The Euler-Lagrange equations we get for these systems usually present "time reparameterization" symmetry, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrabi...
A few words about resonances in the electroweak effective Lagrangian
Rosell, Ignasi [Departamento de Ciencias Físicas, Matemáticas y de la Computación, Universidad CEU Cardenal Herrera, c/ Sant Bartomeu 55, 46115 Alfara del Patriarca, València (Spain); Pich, Antonio; Santos, Joaquín [Departament de Física Teòrica, IFIC, Universitat de València – CSIC, Apt. Correus 22085, 46071 València (Spain); Sanz-Cillero, Juan José [Departamento de Física Teórica and Instituto Física Teórica, IFT-UAM/CSIC, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain)
2016-01-22
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 calculation 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.
Wang, Dake
2011-01-01
We construct singular solutions to special Lagrangian equa- tions with subcritical phases and minimal surface systems. A priori estimate breaking families of smooth solutions are also produced cor- respondingly. A priori estimates for special Lagrangian equations with certain convexity are largely known by now.
On nonlinear controllability and series expansions for Lagrangian systems with dissipative forces
Cortes, J.; Martinez, S.; Bullo, F.
2002-01-01
This paper presents series expansions and nonlinear controllability results for Lagrangian systems subject to dissipative forces. The treatment relies on the assumption of dissipative forces of linear isotropic nature. The approach is based on the affine connection formalism for Lagrangian control s
Modified Lagrangian and Least Root Approaches for General Nonlinear Optimization Problems
W. Oettli; X.Q. Yang
2002-01-01
In this paper we study nonlinear Lagrangian methods for optimization problems with side constraints.Nonlinear Lagrangian dual problems are introduced and their relations with the original problem are established.Moreover, a least root approach is investigated for these optimization problems.
Simulation of Steady Laser Hardening by an Arbitrary Lagrangian Eulerian Method
Geijselaers, H.J.M.; Huetink, J.
2004-01-01
One of the most practical methods for simulation of steady state thermal processing is the Arbitrary Lagrangian- Eulerian method. Each calculation step is split into two phases. In the first phase, the Lagrangian phase, the element mesh remains attached to the material. The evolution of the state va
Simulation of Steady Laser Hardening by an Arbitrary Lagrangian Eulerian Method
Geijselaers, Hubertus J.M.; Huetink, Han
2004-01-01
One of the most practical methods for simulation of steady state thermal processing is the Arbitrary Lagrangian- Eulerian method. Each calculation step is split into two phases. In the first phase, the Lagrangian phase, the element mesh remains attached to the material. The evolution of the state
Roode, S.R. de; Duynkerke, P.G.
2001-01-01
Aircraft measurements made during the "First Lagrangian" of the Atlantic Stratocumulus Transition Experiment (ASTEX) between 12 and 14 June 1992 are presented. During this Lagrangian experiment an air mass was followed that was advected southward by the mean wind. Five aircraft flights were undertak
LOOP GROUP ACTIONS AND THE RIBAUCOUR TRANSFORMATIONS FOR FLAT LAGRANGIAN SUBMANIFOLDS
XIA QIAOLING; SHEN YIBING
2005-01-01
The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.
The S-Lagrangian and a theory of homeostasis in living systems
Sandler, U.; Tsitolovsky, L.
2017-04-01
A major paradox of living things is their ability to actively counteract degradation in a continuously changing environment or being injured through homeostatic protection. In this study, we propose a dynamic theory of homeostasis based on a generalized Lagrangian approach (S-Lagrangian), which can be equally applied to physical and nonphysical systems. Following discoverer of homeostasis Cannon (1935), we assume that homeostasis results from tendency of the organisms to decrease of the stress and avoid of death. We show that the universality of homeostasis is a consequence of analytical properties of the S-Lagrangian, while peculiarities of the biochemical and physiological mechanisms of homeostasis determine phenomenological parameters of the S-Lagrangian. Additionally, we reveal that plausible assumptions about S-Lagrangian features lead to good agreement between theoretical descriptions and observed homeostatic behavior. Here, we have focused on homeostasis of living systems, however, the proposed theory is also capable of being extended to social systems.
Particle Paths of Lagrangian Velocity Distribution Simulating the Spiral Arms of Galaxy M51
Tzu-Fang Chen; Georgios H. Vatistas; Sui Lin
2008-01-01
Galaxies are huge families of stars held together by their own gravities. The system M51 is a spiral galaxy. It possesses billions of stars. The range of the spiral arms extends hundred thousand light years. The present study is in an attempt in using the particle paths of the Lagrangian flow field to simulate the spiral arms of Galaxy M51.The Lagrangian flow field is introduced. The initial locations of fluid particles in the space between two concentric cylinders are first specified. Then a linear velocity distribution of the fluid particles is used with different angle rotations of the particles to obtain the particle paths in the Lagrangian diagram. For simulating the spiral arms of Galaxy M51, the Lagrangian M51 diagram is developed. The particle paths of the Lagrangian M51 diagram agree quite well with the spiral arms of Galaxy M51.
Yue Yang
2016-01-01
The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed. The quasi-Lagrangian structures, e.g., vortex surfaces in vis-cous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition, they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution. The improving understanding of the quasi-Lagrangian struc-tures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.
What if we had a magnetograph at Lagrangian L5?
Pevtsov, Alexei A.; Bertello, Luca; MacNeice, Peter; Petrie, Gordon
2016-11-01
Synoptic Carrington charts of magnetic field are routinely used as an input for modelings of solar wind and other aspects of space weather forecast. However, these maps are constructed using only the observations from the solar hemisphere facing Earth. The evolution of magnetic flux on the "farside" of the Sun, which may affect the topology of coronal field in the "nearside," is largely ignored. It is commonly accepted that placing a magnetograph in Lagrangian L5 point would improve the space weather forecast. However, the quantitative estimates of anticipated improvements have been lacking. We use longitudinal magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) to investigate how adding data from L5 point would affect the outcome of two major models used in space weather forecast.
Lagrangian Relaxation Applied to Sparse Global Network Alignment
El-Kebir, Mohammed; Klau, Gunnar W
2011-01-01
Data on molecular interactions is increasing at a tremendous pace, while the development of solid methods for analyzing this network data is lagging behind. This holds in particular for the field of comparative network analysis, where one wants to identify commonalities between biological networks. Since biological functionality primarily operates at the network level, there is a clear need for topology-aware comparison methods. In this paper we present a method for global network alignment that is fast and robust, and can flexibly deal with various scoring schemes taking both node-to-node correspondences as well as network topologies into account. It is based on an integer linear programming formulation, generalizing the well-studied quadratic assignment problem. We obtain strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach and introduce the software tool natalie 2.0, a publicly available implementation of our method. In an extensive computational study on protein inte...
On the Nonlinear Evolution of Cosmic Web: Lagrangian Dynamics Revisited
Wang, Xin
2014-01-01
We investigate the nonlinear evolution of cosmic morphologies of the large-scale structure by examining the Lagrangian dynamics of various tensors of a cosmic fluid element, including the velocity gradient tensor, the Hessian matrix of the gravitational potential as well as the deformation tensor. Instead of the eigenvalue representation, the first two tensors, which associate with the "kinematic" and "dynamical" cosmic web classification algorithm respectively, are studied in a more convenient parameter space. These parameters are defined as the rotational invariant coefficients of the characteristic equation of the tensor. In the nonlinear local model (NLM) where the magnetic part of Weyl tensor vanishes, these invariants are fully capable of characterizing the dynamics. Unlike the Zeldovich approximation (ZA), where various morphologies do not change before approaching a one-dimensional singularity, the sheets in NLM are unstable for both overdense and underdense perturbations. While it has long been known...
Parametrized Ring-Spectra and the Nearby Lagrangian Conjecture
Kragh, Thomas
2011-01-01
We prove that any closed connected exact Lagrangian manifold L in a connected cotangent bundle T*N is up to a finite covering space lift a homology equivalence. We prove this by constructing a fibrant parametrized family of ring spectra FL parametrized by the manifold N. The homology of FL will be (twisted) symplectic cohomology of T*L. The fibrancy property will imply that there is a Serre spectral sequence converging to the homology of FL and the product combined with intersection product on N induces a product on this spectral sequence. This product structure and its relation to the intersection product on L is then used to obtain the result. Combining this result with work of Abouzaid we arrive at the conclusion that L -> N is always a homotopy equivalence.
Novikov-symplectic cohomology and exact Lagrangian embeddings
Ritter, Alexander F
2007-01-01
We prove that if N is a closed simply connected manifold and j:L \\to T^*N is an exact Lagrangian embedding, then H^2(N) \\to H^2(L) is injective and the image of \\pi_2(L) in \\pi_2(N) has finite index. Viterbo proved that there is a transfer map on free loopspaces which commutes under the inclusion of constant loops with the ordinary transfer map H_*(N) \\to H_*(L). This commutative diagram still holds if one introduces a Novikov bundle of local coefficients induced by the transgression t(\\beta) of a non-zero class \\beta in H^2(N). By proving the vanishing of the Novikov homology of the free loopspace of N with respect to t(\\beta) we obtain a contradiction to Viterbo functoriality if t(j^*\\beta) vanished. This yields the above obstructions to the existence of j.
Domingues M. O.
2013-12-01
Full Text Available We present a new adaptive multiresoltion method for the numerical simulation of ideal magnetohydrodynamics. The governing equations, i.e., the compressible Euler equations coupled with the Maxwell equations are discretized using a finite volume scheme on a two-dimensional Cartesian mesh. Adaptivity in space is obtained via Harten’s cell average multiresolution analysis, which allows the reliable introduction of a locally refined mesh while controlling the error. The explicit time discretization uses a compact Runge–Kutta method for local time stepping and an embedded Runge-Kutta scheme for automatic time step control. An extended generalized Lagrangian multiplier approach with the mixed hyperbolic-parabolic correction type is used to control the incompressibility of the magnetic field. Applications to a two-dimensional problem illustrate the properties of the method. Memory savings and numerical divergences of magnetic field are reported and the accuracy of the adaptive computations is assessed by comparing with the available exact solution.
Chaotic Lagrangian transport and mixing in the ocean
Prants, S V
2015-01-01
Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of chaotic advection in fluids, an analogue of dynamical Hamiltonian chaos in mechanics. The starting point for analysis is a velocity field obtained by this or that way. Being motivated by successful applications of that approach to simplified analytic models of geophysical fluid flows, researchers now work with satellite-derived velocity fields and outputs of sophisticated numerical models of ocean circulation. This review article gives an introduction to some of the basic concepts and methods used to study chaotic mixing and transport in the ocean and a brief overview of recent results with some practical applications of Lagrangian tools to monitor spreading of Fukushima-derived radionuclides in the ocean.
Relativistic Lagrangian model of a nematic liquid crystal
Obukhov, Yuri N; Rubilar, Guillermo F
2012-01-01
We develop a relativistic variational model for a nematic liquid crystal interacting with the electromagnetic field. The constitutive relation for an anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss light wave propagation in this moving uniaxial medium, for which the corresponding optical metrics are identified explicitly. A Lagrangian for the coupled system of a nematic liquid crystal and the electromagnetic field is constructed. We derive a complete set of equations of motion for the system. The canonical energy-momentum and spin tensors are systematically obtained. We compare our results with those within the non-relativistic models. As an application of our general formalism, we discuss the so-called Abraham-Minkowski controversy on the momentum of light in a medium.
Chaotic Lagrangian transport and mixing in the ocean
Prants, S. V.
2014-12-01
Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of chaotic advection in fluids, an analogue of dynamical Hamiltonian chaos in mechanics. The starting point for analysis is a velocity field obtained by this or that way. Being motivated by successful applications of that approach to simplified analytic models of geophysical fluid flows, researchers now work with satellite-derived velocity fields and outputs of sophisticated numerical models of ocean circulation. This review article gives an introduction to some of the basic concepts and methods used to study chaotic mixing and transport in the ocean and a brief overview of recent results with some practical applications of Lagrangian tools to monitor spreading of Fukushima-derived radionuclides in the ocean.
Lagrangian formulation of symmetric space sine-Gordon models
Bakas, Ioannis; Shin, H J; Park, Q Han
1996-01-01
The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim \\sigma-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F \\supset G \\supset H. We show that for every symmetric space F/G, the generalized sine-Gordon models can be derived from the G/H WZW action, plus a potential term that is algebraically specified. Thus, the symmetric space sine-Gordon models describe certain integrable perturbations of coset conformal field theories at the classical level. We also briefly discuss their vacuum structure, Backlund transformations, and soliton solutions.
Noether Symmetries of the Area-Minimizing Lagrangian
Adnan Aslam
2012-01-01
Full Text Available It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an (n-1-area enclosing a constant n-volume in a Euclidean space is so(n⊕sℝn and in a space of constant curvature the Lie algebra is so(n. Furthermore, if the space has one section of constant curvature of dimension n1, another of n2, and so on to nk and one of zero curvature of dimension m, with n≥∑j=1knj+m (as some of the sections may have no symmetry, then the Lie algebra of Noether symmetries is ⊕j=1kso(nj+1⊕(so(m⊕sℝm.
Effective Lagrangian Approach to pion photoproduction from the nucleon
Fernandez-Ramirez, C; Udias, J M
2006-01-01
We present a pion photoproduction model on the free nucleon based on an Effective Lagrangian Approach (ELA) which includes the nucleon resonances ($\\Delta(1232)$, N(1440), N(1520), N(1535), $\\Delta (1620)$, N(1650), and $\\Delta (1700)$), in addition to Born and vector meson exchange terms. The model incorporates a new theoretical treatment of spin-3/2 resonances, first introduced by Pascalutsa, avoiding pathologies present in previous models. Other main features of the model are chiral symmetry, gauge invariance, and crossing symmetry. We use the model combined with modern optimization techniques to assess the parameters of the nucleon resonances on the basis of world data on electromagnetic multipoles. We present results for electromagnetic multipoles, differential cross sections, asymmetries, and total cross sections for all one pion photoproduction processes on free nucleons. We find overall agreement with data from threshold up to 1 GeV in laboratory frame.
An augmented Lagrangian multi-scale dictionary learning algorithm
Ye Meng
2011-01-01
Full Text Available Abstract Learning overcomplete dictionaries for sparse signal representation has become a hot topic fascinated by many researchers in the recent years, while most of the existing approaches have a serious problem that they always lead to local minima. In this article, we present a novel augmented Lagrangian multi-scale dictionary learning algorithm (ALM-DL, which is achieved by first recasting the constrained dictionary learning problem into an AL scheme, and then updating the dictionary after each inner iteration of the scheme during which majorization-minimization technique is employed for solving the inner subproblem. Refining the dictionary from low scale to high makes the proposed method less dependent on the initial dictionary hence avoiding local optima. Numerical tests for synthetic data and denoising applications on real images demonstrate the superior performance of the proposed approach.
LAGRANGIAN MICROMIXING MODELS FOR CONCENTRATION FLUCTUATIONS: AN OVERVIEW
Andrea Amicarelli
2012-01-01
Full Text Available This study presents a brief overview of the main features, theoretical formulations and validation tests of some Lagrangian micromixing models, currently used for estimations of the ensemble mean and the turbulent fluctuations of concentration. Their application fields regards several pollutant dispersion phenomena such as: accidents (power or production plants, terroristic attacks, hydrocarbons storage and transport, extraordinary emissions, odours (power plants and energy production from waste resources-compost, dumps, incinerators, biogas storage and smokes-, high enthalpy geothermic plants-sulfide hydrogen-, animal farms, micro-scale dispersion from continuous or spot emissions (traffic pollutants, power and production plants, dispersion in aquatic environmentsâ¦, industrial processes (combustion, pollutant treatment,â¦, strong non-linear relationship between concentration and damage (inflammable substances, explosions,.., reactions depending on instantaneous concentrations.
Lagrangian hydrocode simulations of the 1958 Lituya Bay tsunamigenic rockslide
Schwaiger, H. F.; Higman, B.
2007-07-01
The interaction of debris flows, whether subaqueous or subaerial, with bodies of water can produce tsunamis with a locally devastating impact. When debris flows begin above the water surface, the impact can produce a large air cavity, corresponding to a large effective volume of water displaced and complicating efforts to model the resulting tsunami. Because grid-based, Eulerian numerical methods have an inherent difficulty tracking material boundaries, we have implemented a particle-based, Lagrangian model (Smoothed Particle Hydrodynamics). We treat the debris flow as an incompressible, viscous fluid and the body of water as inviscid. We use this model to simulate the 1958 Lituya Bay rockslide and resulting tsunami. Our simulation results compare favorably with field observations as well as a scaled laboratory experiment and numerical studies.
Coupled Eulerian-Lagrangian transport of large debris by tsunamis
Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos
2016-04-01
Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-Eulerian coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian and Eulerian solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed Eulerian-Lagrangian formulation and the resolution of the mesh used in the Eulerian solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the
Mimetic Methods for Lagrangian Relaxation of Magnetic Fields
Candelaresi, Simon; Hornig, Gunnar
2014-01-01
We present a new code that performs a relaxation of a magnetic field towards a force-free state (Beltrami field) using a Lagrangian numerical scheme. Beltrami fields are of interest for the dynamics of many technical and astrophysical plasmas as they are the lowest energy states that the magnetic field can reach. The numerical method strictly preserves the magnetic flux and the topology of magnetic field lines. In contrast to other implementations we use mimetic operators for the spatial derivatives in order to improve accuracy for high distortions of the grid. Compared with schemes using direct derivatives we find that the final state of the simulation approximates a force-free state with a significantly higher accuracy. We implement the scheme in a code which runs on graphical processing units (GPU), which leads to an enhanced computing speed compared to previous relaxation codes.
Poisson structures in BRST-antiBRST invariant Lagrangian formalism
Geyer, B; Nersessian, A P; Geyer, Bodo; Lavrov, Petr; Nersessian, Armen
2001-01-01
We show that the specific operators V^a appearing in the triplectic formalism can be viewed as the anti-Hamiltonian vector fields generated by a second rank irreducible Sp(2) tensor. This allows for an explicit realization of the triplectic algebra being constructed from an arbitrary Poisson bracket on the space of the fields only. We show that the whole space of fields and antifields can be equipped with an even supersymplectic structure when this Poisson bracket is non-degenerate. This observation opens the possibility to provide the BRST/antiBRST path integral by a well-defined integration measure, as well as to establish a direct link between the Sp(2) symmetric Lagrangian and Hamiltonian BRST quantization schemes.
Computing Lagrangian coherent structures from their variational theory.
Farazmand, Mohammad; Haller, George
2012-03-01
Using the recently developed variational theory of hyperbolic Lagrangian coherent structures (LCSs), we introduce a computational approach that renders attracting and repelling LCSs as smooth, parametrized curves in two-dimensional flows. The curves are obtained as trajectories of an autonomous ordinary differential equation for the tensor lines of the Cauchy-Green strain tensor. This approach eliminates false positives and negatives in LCS detection by separating true exponential stretching from shear in a frame-independent fashion. Having an explicitly parametrized form for hyperbolic LCSs also allows for their further in-depth analysis and accurate advection as material lines. We illustrate these results on a kinematic model flow and on a direct numerical simulation of two-dimensional turbulence.
Lagrangian Velocity Correlations and Absolute Dispersion in the Midlatitude Troposphere
Sukhatme, J
2004-01-01
Employing daily wind data from the ECMWF, we perform passive particle advection to estimate the Lagrangian velocity correlation functions (LVCF) associated with the midlatitude tropospheric flow. In particular we decompose the velocity field into time mean and transient (or eddy) components to better understand the nature of the LVCF's.A closely related quantity, the absolute dispersion (AD) is also examined. Given the anisotropy of the flow, meridional and zonal characteristics are considered separately. The zonal LVCF is seen to be non-exponential. In fact, for a broad set of intermediate timescales it is better described as a power law of the form $\\tau^{-\\alpha}$ with $ 0<\\alpha<1$. Indeed, the implied long time correlation in the zonal flow results in a superdiffusive zonal AD regime. On the other hand, the meridional LVCF decays rapidly to zero. Interestingly, before approaching to zero it shows a region of negative correlation. A physical argument based on the rotational inhibition of latitudinal...
Metriplectic Algebra for Dissipative Fluids in Lagrangian Formulation
Materassi, Massimo F D
2014-01-01
It is known that the dynamics of dissipative fluids in Eulerian variables can be derived from an algebra of Leibniz brackets of observables, the metriplectic algebra, that extends the Poisson algebra of the zero viscosity limit via a symmetric, semidefinite component. This metric bracket generates dissipative forces. The metriplectic algebra includes the conserved total Hamiltonian $H$, generating the non-dissipative part of dynamics, and the entropy $S$ of those microscopic degrees of freedom draining energy irreversibly, that generates dissipation. This $S$ is a Casimir of the Poisson algebra to which the metriplectic algebra reduces in the frictionless limit. In the present paper, the metriplectic framework for viscous fluids is re-written in the Lagrangian Formulation, where the system is described through material variables: this is a way to describe the continuum much closer to the discrete system dynamics than the Eulerian fields. Accordingly, the full metriplectic algebra is constructed in material va...
Using Upper Tolerances in Lagrangian Relaxation for the DCMSTP
Turkensteen, Marcel
We consider the NP-hard degree-constrained Minimum Spanning Tree Problem (DCMSTP). A solution, or spanning tree, is feasible if each vertex is connected to every other one and the number of edges adjacent to each vertex is not larger than a predefined number d. The problem without degree......-constraints, the Minimum Spanning Tree Problem (MSTP), is polynomially solvable. We solve the DCMSTP using Lagrangian relaxation. This is the approach in which constraint violations are penalized in the objective function. In an iterative process, the penalty values of violated constraints are increased...... of the ordinary MSTP, which are, roughly spoken, the increase in an edge's cost value needed to remove it from the solution. We show that, if the edge costs of at most d edges adjacent to a vertex do not increase by more than their respective upper tolerance values, the optimal tree with updated penalty values...
Coherent discrete embeddings for Lagrangian and Hamiltonian systems
Cresson, Jacky; Pierre, Charles
2011-01-01
The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with Lagrangian or Hamiltonian structures and thus with variational problems attached to a least action principle. Considering a partial differential equation (PDE) deriving from such a variational principle, a natural question is to know whether this structure at the continuous level is preserved at the discrete level when discretising the PDE. To address this question a concept of \\textit{coherence} is introduced. Both the differential equation (the PDE translating the least action principle) and the variational structure can be embedded at the discrete level. This provides two discrete embeddings for the original problem. In case these procedures finally provide the same discrete problem we will say that the discretisation is \\textit{coherent}. Our purpose is illustrated with the Poisson problem. Coherence for discrete embeddings of ...
Transport Theory from the Nambu-Jona-Lasinio Lagrangian
Marty, R; Bratkovskaya, E; Aichelin, J
2015-01-01
Starting from the (Polyakov-) Nambu-Jona-Lasinio Lagrangian, (P)NJL, we formulate a transport theory which allows for describing the expansion of a quark-antiquark plasma and the subsequent transition to the hadronic world --without adding any new parameter to the standard (P)NJL approach, whose parameters are fixed to vacuum physics. This transport theory can be used to describe ultrarelativistic heavy-ion reaction data as well as to study the (first-order) phase transition during the expansion of the plasma. (P)NJL predicts such a phase transition for finite chemical potentials. In this contribution we give an outline of the necessary steps to obtain such a transport theory and present first results.
An Hourglass Control Algorithm for Lagrangian Smooth Particle Hydrodynamics
Ganzenmüller, Georg C
2014-01-01
This paper presents a stabilization scheme which addresses the rank-deficiency problem in meshless collocation methods for solid mechanics. Specifically, Smooth-Particle Hydrodynamics (SPH) in the Total Lagrangian formalism is considered. This method is rank-deficient in the sense that the SPH approximation of the deformation gradient is not unique with respect to the positions of the integration points. The non-uniqueness can result in the formation of zero-energy modes. If undetected, these modes can grow and completely dominate the solution. Here, an algorithm is introduced, which effectively suppresses these modes in a fashion similar to hour-glass control mechanisms in Finite-Element methods. Simulations utilizing this control algorithm result exhibit much improved stability, accuracy, and error convergence properties. In contrast to an alternative method which eliminates zero-energy modes, namely the use of additional integration points, the here presented algorithm is easy to implement and computationa...
STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY
Wang, Xin; Szalay, Alex, E-mail: xwang@cita.utoronto.ca [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 (United States)
2016-03-20
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.
Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology
Wang, Xin; Szalay, Alex
2016-03-01
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.
Extending geometrical optics: A Lagrangian theory for vector waves
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.
Anche una nave alla fonda viaggia... - Anchored ships also travel...
Antonio Luigi Palmisano
2011-09-01
Full Text Available When travelling, reflections and considerations – more or less structured – are about being “elsewhere”. The subject finds himself physically, socially and politically in this “elsewhere” as an Ego and finds or maybe finds again another Ego, other Ego each of them being still the subject’s own but different from the previous. The structure of travelling is transition and the transitive structure of the Ego also comes to the fore. It is anyway a transition which stimulates reflections, a transition which complicates the Ego. Travelling is therefore the art of complicating the everyday life in order to reach the unexpected. Just as philosophy. But the relation between travelling and philosophy is still deeper: travelling is the praxis of philosophy. The encounter with the “Other” becomes an opportunity to communicate between Seienden which constitute themselves as such actually through the encounter. It is an encounter between men which does not exclude the encounter with Divinity.
Buchert, Thomas
2012-01-01
In this first paper we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a general-relativistic analogue of Zel'dovich's approximation for the description of structure formation in cosmology, and compare it with previous suggestions in the literature. This approximation is then investigated: paraphrasing the derivation in the Newtonian framework we provide general-relativistic analogues of the basic system of equations for a single dynamical field variable and recall the first-order perturbation solution of these equations. We then define a general-relativistic analogue of Zel'dovich's approximation and investigate consequences by functionally evaluating relevant variables. We so obtain a possibly powerful model that, although constructed through extrapolation of a perturbative solution, can be used to address non-perturbatively, e.g. problems of structu...
Lagrangian analysis. Modern tool of the dynamics of solids
Cagnoux, J.; Chartagnac, P.; Hereil, P.; Perez, M.; Seaman, L.
Explosive metal-working, material synthesis under shock loading, terminal ballistics, and explosive rock-blasting, are some of the civil and military fields of activity that call for a wider knowledge about the behavior of materials subjected to strong dynamic pressures. It is in these fields that Lagrangian analysis methods, the subject of this work, prove to be a useful investigative tool for the physicist. Lagrangian analysis was developed around 1970 by Fowles and Williams. The idea is based on the integration of the conservation equations of mechanics using stress or particle velocity records obtained by means of transducers placed in the path of a stress wave. In this way, all the kinematical and mechanical quantities contained in the conservation equations are obtained. In the first chapter the authors introduce the mathematical tools used to analyze plane and spherical one-dimensional motions. For plane motion, they describe the mathematical analysis methods pertinent to the three regimes of wave propagation encountered : the non-attenuating unsteady wave, the simple wave, and the attenuating unsteady wave. In each of these regimes, cases are treated for which either stress or particle velocity records are initially available. The authors insist that one or the other groups of data (stress and particle velocity) are sufficient to integrate the conservation equations in the case of the plane motion when both groups of data are necessary in the case of the spherical motion. However, in spite of this additional difficulty, Lagrangian analysis of the spherical motion remains particularly interesting for the physicist because it allows access to the behavior of the material under deformation processes other than that imposed by plane one-dimensional motion. The methods expounded in the first chapter are based on Lagrangian measurement of particle velocity and stress in relation to time in a material compressed by a plane or spherical dilatational wave. The
Lagrangian properties at the ocean submesoscales in presence of riverine outflows
Bracco, Annalisa; Choi, Jun
2017-04-01
A set of numerical simulations are used to characterize the impact of submesoscale circulations on surface Lagrangian statistics in the northern Gulf of Mexico over two months, February and August, representative of winter and summer. Whenever submesoscale circulations are resolved, the probability density functions (PDFs) of dynamical quantities such as vorticity and horizontal velocity divergence for Eulerian and Lagrangian fields differ, with particles preferentially mapping areas of elevated negative divergence and positive vorticity. The stronger are the submesoscale circulations the more skewed are the Lagrangian distributions and greater is the difference between Eulerian and Lagrangian PDFs. In winter Lagrangian distributions are modestly impacted by the presence of the riverine outflow, while increasing the model resolution from submesoscale permitting to submesoscale resolving has a more profound impact. In summer the presence of riverine induced buoyancy gradients is key to the development of submesoscale circulations and different Eulerian and Lagrangian PDFs. Finite Size Lyapunov Exponents (FSLEs) are used to characterize mixing rates. Whenever submesoscale circulations are resolved and riverine outflow is included, FSLEs slopes are broadly consistent with local stirring. Simulated slopes are close to -0.5 and support a velocity field where the ageostrophic and frontogenetic components are key to mixing for scales comprised between about 5-7 times the model resolution and 100 km. The robustness of Lagrangian statistics is further discussed in terms of their spatial and temporal variability, and of the number of particles used.
The Lagrangian Ensemble metamodel for simulating plankton ecosystems
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
COMPARISON OF THE EULERIAN AND LAGRANGIAN TIDAL RESIDUALS IN THE BOHAI SEA
无
2001-01-01
Tidal residual is very important to the transport of water particles, nutrients, plankton, etc. in the coastal sea. Eulerian scheme and Lagrangian scheme are two different ways to get the time averaged residual. Solution of the Bohai Sea's hydrodynamic system using a semi-implicit layer averaged numerical model yielded different direction Eulerian and Lagrangian tidal residuals. The latter were stronger than the former in most sea areas. Their different directions produced different circulation pattern in some areas. Compared with the Eulerian residual, the Lagrangian residual seemed to be more in accord with the observation.
The Lagrangian Formulation of Strong-Field QED in a Plasma
Raicher, Erez; Zigler, Arie
2013-01-01
The Lagrangian formulation of the scalar and spinor quantum electrodynamics (QED) in the presence of strong laser fields in a plasma medium is considered. We include the plasma influence in the free Lagrangian analogously to the "Furry picture" and obtain coupled equations of motion for the plasma particles and for the laser propagation. We demonstrate that the laser photons satisfy a massive dispersion relation and obtain their effective mass self-consistently. The Lagrangian formulation derived in this paper is the basis for the cross sections calculation of quantum processes taking place in the presence of a plasma.
Gauge invariant Lagrangian for non-Abelian tensor fauge Fields of fourth rank
Savvidy, G
2005-01-01
Using generalized field strength tensors for non-Abelian tensor gauge fields one can explicitly construct all possible Lorentz invariant quadratic forms for rank-4 non-Abelian tensor gauge fields and demonstrate that there exist only two linear combinations of them which form a gauge invariant Lagrangian. Together with the previous construction of independent gauge invariant forms for rank-2 and rank-3 tensor gauge fields this construction proves the uniqueness of early proposed general Lagrangian up to rank-4 tensor fields. Expression for the coefficients of the general Lagrangian is presented in a compact form.
On manifolds admitting the consistent Lagrangian formulation for higher spin fields
Buchbinder, I L; Lavrov, P M
2011-01-01
We study a possibility of Lagrangian formulation for free higher spin bosonic totally symmetric tensor field on the background manifold characterizing by the arbitrary metric, vector and third rank tensor fields in framework of BRST approach. Assuming existence of massless and flat limits in the Lagrangian and using the most general form of the operators of constraints we show that the algebra generated by these operators will be closed only for constant curvature space with no nontrivial coupling to the third rank tensor and the strength of the vector fields. This result finally proves that the consistent Lagrangian formulation at the conditions under consideration is possible only in constant curvature Riemann space.
Bridging from Eulerian to Lagrangian statistics in 3D hydro- and magnetohydrodynamic turbulent flows
Homann, H [CNRS, Universite de Nice-Sophia Antipolis, Observatoire de la Cote d' Azur, Lab. Cassiopee, Bd. de l' Observatoire, 06300 Nice (France); Kamps, O [Center for Nonlinear Science, Universitaet Muenster, 48149 Muenster (Germany); Friedrich, R [Theoretische Physik, Universitaet Muenster, 48149 Muenster (Germany); Grauer, R [Theoretische Physik I, Ruhr-Universitaet, 44780 Bochum (Germany)], E-mail: grauer@tp1.rub.de
2009-07-15
We present measurements of conditional probability density functions (PDFs) that allow one to systematically bridge from Eulerian to Lagrangian statistics in fully developed 3D turbulence. The transition is investigated for hydro- as well as magnetohydrodynamic flows and comparisons are drawn. Significant differences in the transition PDFs are observed for these flows and traced back to the differing coherent structures. In particular, we address the problem of an increasing degree of intermittency going from Eulerian to Lagrangian coordinates by means of the conditional PDFs involved in this transformation. First simple models of these PDFs are investigated in order to distinguish different contributions to the degree of Lagrangian intermittency.
A systematic method to enforce conservativity on semi-Lagrangian schemes
Cameron, Alexandre
2016-01-01
Semi-Lagrangian schemes have proven to be very efficient to model advection problems. However most semi-Lagrangian schemes are not conservative. Here, a systematic method is introduced in order to enforce the conservative property on a semi-Lagrangian advection scheme. This method is shown to generate conservative schemes with the same linear stability range and the same order of accuracy as the initial advection scheme from which they are derived. We used a criterion based on the column-balance property of the schemes to assess their conservativity property. We show that this approach can be used with large CFL numbers and third order schemes.
Stochastic Simulation of Lagrangian Particle Transport in Turbulent Flows
Sun, Guangyuan
This dissertation presents the development and validation of the One Dimensional Turbulence (ODT) multiphase model in the Lagrangian reference frame. ODT is a stochastic model that captures the full range of length and time scales and provides statistical information on fine-scale turbulent-particle mixing and transport at low computational cost. The flow evolution is governed by a deterministic solution of the viscous processes and a stochastic representation of advection through stochastic domain mapping processes. The three algorithms for Lagrangian particle transport are presented within the context of the ODT approach. The Type-I and -C models consider the particle-eddy interaction as instantaneous and continuous change of the particle position and velocity, respectively. The Type-IC model combines the features of the Type-I and -C models. The models are applied to the multi-phase flows in the homogeneous decaying turbulence and turbulent round jet. Particle dispersion, dispersion coefficients, and velocity statistics are predicted and compared with experimental data. The models accurately reproduces the experimental data sets and capture particle inertial effects and trajectory crossing effect. A new adjustable particle parameter is introduced into the ODT model, and sensitivity analysis is performed to facilitate parameter estimation and selection. A novel algorithm of the two-way momentum coupling between the particle and carrier phases is developed in the ODT multiphase model. Momentum exchange between the phases is accounted for through particle source terms in the viscous diffusion. The source term is implemented in eddy events through a new kernel transformation and an iterative procedure is required for eddy selection. This model is applied to a particle-laden turbulent jet flow, and simulation results are compared with experimental measurements. The effect of particle addition on the velocities of the gas phase is investigated. The development of
A Lagrangian Study of Southeast Pacific Boundary Layer Clouds
Painter, Gallia
Low clouds lie at the heart of climate feedback uncertainties. The representation of clouds in global climate models relies on parameterization of many sub-grid scale processes that are crucial to understanding cloud responses to climate; low clouds in particular exist as a result of tightly coupled microphysical, mesoscale, and synoptic mechanisms. The influence of anthropogenic aerosols on cloud properties could have important ramifications for our understanding of how clouds respond to a changing climate. The VAMOS Ocean-Cloud-Atmosphere-Land Study Regional Experiment (VOCALS REx) sampled the persistent stratocumulus cloud deck located off the coast of Peru and Chile in the southeastern Pacific ocean. Several cloud features found in the stratocumulus deck during VOCALS exhibit signs of interesting aerosol-cloud interactions, including pockets of open cells (POCs). POCs are regions of open-cellular convection surrounded by closed cell stratocumulus, exhibiting not only a marked transition in mesoscale organization and cloud morphology, but also sharp microphysical gradients (especially in droplet concentration) across the boundary between open-cellular and closed cellular convection. In addition, precipitation is often higher at the POC boundaries, hinting at the importance of precipitation in driving their formation. In order to evaluate the microphysical characteristics of POCs prior cloud breakup, we use Lagrangian trajectories coupled with geostationary satellite imagery and cloud retrievals, as well as observational data from VOCALS REx and model data. In three of our case studies, we found regions of anomalously low droplet concentration 18-24 hours prior to POC formation (coupled with liquid water path similar to or higher than surrounding cloud), supporting a precipitation driven mechanism for POC formation. Another group of features with interesting aerosol-cloud interactions observed during VOCALS were mesoscale hook-like features of high droplet
Matching effective chiral Lagrangians with dimensional and lattice regularization
Niedermayer, Ferenc
2016-01-01
We compute the free energy in the presence of a chemical potential coupled to a conserved charge in effective O($n$) scalar field theory (without explicit symmetry breaking terms) to NNL order for asymmetric volumes in general $d$--dimensions, using dimensional (DR) and lattice regularizations. This yields relations between the 4-derivative couplings appearing in the effective actions for the two regularizations, which in turn allows us to translate results, e.g. the mass gap in a finite periodic box in $d=3+1$ dimensions, from one regularization to the other. Consistency is found with a new direct computation of the mass gap using DR. For the case $n=4, d=4$ the model is the low-energy effective theory of QCD with $N_{\\rm f}=2$ massless quarks. The results can thus be used to obtain estimates of low energy constants in the effective chiral Lagrangian from measurements of the low energy observables, including the low lying spectrum of $N_{\\rm f}=2$ QCD in the $\\delta$--regime using lattice simulations, as pro...
Finite BRST–antiBRST transformations in Lagrangian formalism
Moshin, Pavel Yu., E-mail: moshin@rambler.ru [Department of Physics, Tomsk State University, 634050 (Russian Federation); Reshetnyak, Alexander A., E-mail: reshet@ispms.tsc.ru [Institute of Strength Physics and Materials Science, Siberian Branch of Russian Academy of Sciences, 634021, Tomsk (Russian Federation); Tomsk State Pedagogical University, 634061 (Russian Federation)
2014-12-12
We continue the study of finite BRST–antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [1], with a doublet λ{sub a}, a=1,2, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant λ{sub a}. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian (proved to be correct in [31]) for finite field-dependent BRST–antiBRST transformations with functionally-dependent parameters, λ{sub a}=s{sub a}Λ, induced by a finite even-valued functional Λ(ϕ,π,λ) and by the generators s{sub a} of BRST–antiBRST transformations, acting in the space of fields ϕ, antifields ϕ{sub a}{sup *},ϕ{sup ¯} and auxiliary variables π{sup a},λ. On the basis of this Jacobian, we present and solve a compensation equation for Λ, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities, containing the parameters λ{sub a}, and study the problem of gauge-dependence. The general approach is exemplified by the Freedman–Townsend model of a non-Abelian antisymmetric tensor field.
Finite BRST–antiBRST transformations in Lagrangian formalism
Pavel Yu. Moshin
2014-12-01
Full Text Available We continue the study of finite BRST–antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [1], with a doublet λa, a=1,2, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant λa. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian (proved to be correct in [31] for finite field-dependent BRST–antiBRST transformations with functionally-dependent parameters, λa=saΛ, induced by a finite even-valued functional Λ(ϕ,π,λ and by the generators sa of BRST–antiBRST transformations, acting in the space of fields ϕ, antifields ϕa⁎,ϕ¯ and auxiliary variables πa,λ. On the basis of this Jacobian, we present and solve a compensation equation for Λ, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities, containing the parameters λa, and study the problem of gauge-dependence. The general approach is exemplified by the Freedman–Townsend model of a non-Abelian antisymmetric tensor field.
Behaviour of Lagrangian triangular mixed fluid finite elements
S Gopalakrishnan; G Devi
2000-02-01
The behaviour of mixed fluid finite elements, formulated based on the Lagrangian frame of reference, is investigated to understand the effects of locking due to incompressibility and irrotational constraints. For this purpose, both linear and quadratic mixed triangular fluid elements are formulated. It is found that there exists a close relationship between the penalty finite element approach that uses reduced/selective numerical integration to alleviate locking, and the mixed finite element approach. That is, performing reduced/selective integration in the penalty approach amounts to reducing the order of pressure interpolation in the mixed finite element approach for obtaining similar results. A number of numerical experiments are performed to determine the optimum degree of interpolation of both the mean pressure and the rotational pressure in order that the twin constraints are satisfied exactly. For this purpose, the benchmark solution of the rigid rectangular tank is used. It is found that, irrespective of the degree of mean and the rotational pressure interpolation, the linear triangle mesh, with or without central bubble function (incompatible mode), locks when both the constraints are enforced simultaneously. However, for quadratic triangle, linear interpolation of the mean pressure and constant rotational pressure ensures exact satisfaction of the constraints and the mesh does not lock. Based on the results obtained from the numerical experiments, a number of important conclusions are arrived at.
Chiral Lagrangian from Duality and Monopole Operators in Compactified QCD
Cherman, Aleksey; Unsal, Mithat
2016-01-01
We show that there exists a special compactification of QCD on $\\mathbb{R}^3 \\times S^1$ in which the theory has a domain where continuous chiral symmetry breaking is analytically calculable. We give a microscopic derivation of the chiral lagrangian, the chiral condensate, and the Gell-Mann-Oakes-Renner relation $m_{\\pi}^2 f_{\\pi}^2 = m_q \\langle \\bar{q} q \\rangle$. Abelian duality, monopole operators, and flavor-twisted boundary conditions, or a background flavor holonomy, play the main roles. The flavor twisting leads to the new effect of fractional jumping of fermion zero modes among monopole-instantons. Chiral symmetry breaking is induced by monopole-instanton operators, and the Nambu-Goldstone pions arise by color-flavor transmutation from gapless "dual photons". We also give a microscopic picture of the "constituent quark" masses. Our results are consistent with expectations from chiral perturbation theory at large $S^1$, and yield strong support for adiabatic continuity between the small-$S^1$ and larg...
Hamiltonian analysis for linearly acceleration-dependent Lagrangians
Cruz, Miguel; Gómez-Cortés, Rosario; Molgado, Alberto; Rojas, Efraín
2016-06-01
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 together 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.
Metriplectic Algebra for Dissipative Fluids in Lagrangian Formulation
Massimo Materassi
2015-03-01
Full Text Available The dynamics of dissipative fluids in Eulerian variables may be derived from an algebra of Leibniz brackets of observables, the metriplectic algebra, that extends the Poisson algebra of the frictionless limit of the system via a symmetric semidefinite component, encoding dissipative forces. The metriplectic algebra includes the conserved total Hamiltonian H, generating the non-dissipative part of dynamics, and the entropy S of those microscopic degrees of freedom draining energy irreversibly, which generates dissipation. This S is a Casimir invariant of the Poisson algebra to which the metriplectic algebra reduces in the frictionless limit. The role of S is as paramount as that of H, but this fact may be underestimated in the Eulerian formulation because S is not the only Casimir of the symplectic non-canonical part of the algebra. Instead, when the dynamics of the non-ideal fluid is written through the parcel variables of the Lagrangian formulation, the fact that entropy is symplectically invariant clearly appears to be related to its dependence on the microscopic degrees of freedom of the fluid, that are themselves in involution with the position and momentum of the parcel.
Lagrangian simulation of mixing and reactions in complex geochemical systems
Engdahl, Nicholas B.; Benson, David A.; Bolster, Diogo
2017-04-01
Simulations of detailed geochemical systems have traditionally been restricted to Eulerian reactive transport algorithms. This note introduces a Lagrangian method for modeling multicomponent reaction systems. The approach uses standard random walk-based methods for the particle motion steps but allows the particles to interact with each other by exchanging mass of their various chemical species. The colocation density of each particle pair is used to calculate the mass transfer rate, which creates a local disequilibrium that is then relaxed back toward equilibrium using the reaction engine PhreeqcRM. The mass exchange is the only step where the particles interact and the remaining transport and reaction steps are entirely independent for each particle. Several validation examples are presented, which reproduce well-known analytical solutions. These are followed by two demonstration examples of a competitive decay chain and an acid-mine drainage system. The source code, entitled Complex Reaction on Particles (CRP), and files needed to run these examples are hosted openly on GitHub (https://github.com/nbengdahl/CRP), so as to enable interested readers to readily apply this approach with minimal modifications.
A First-order Augmented Lagrangian Method for Compressed Sensing
Aybat, Necdet Serhat
2010-01-01
In this paper, we propose a first-order augmented Lagrangian algorithm (FAL) that solves the basis pursuit problem min{|x|_1: Ax = b} by inexactly solving a sequence of problems of the form min{lambda(k) |x|_1+ |Ax-b-lambda(k)theta(k)|_2^2}, for an appropriately chosen sequence of multipliers {lambda(k),theta(k)}. Each of these subproblems are solved using Algorithm 3 in [19] by Paul Tseng wherein each update reduces to "shrinkage" [12] or constrained "shrinkage". We show that FAL converges to an optimal solution x* of the basis pursuit problem, i.e. x*=argmin{|x|_1: Ax= b} and that there exist a priori fixed sequence {lambda(k)} such that for all epsilon>0, iterates x(k) computed by FAL are epsilon-feasible, i.e. |Ax(k) - b|_2 <= epsilon, and epsilon-optimal, | |x(k)|_1 - |x*|_1 | <= epsilon, after O(1/epsilon) iterations, where the complexity of each iteration is O(n log(n)). We also report the results of numerical experiments comparing the performance of FAL with SPA [1], NESTA [18], FPC [10, 11], FP...
Fast multipole method applied to Lagrangian simulations of vortical flows
Ricciardi, Túlio R.; Wolf, William R.; Bimbato, Alex M.
2017-10-01
Lagrangian simulations of unsteady vortical flows are accelerated by the multi-level fast multipole method, FMM. The combination of the FMM algorithm with a discrete vortex method, DVM, is discussed for free domain and periodic problems with focus on implementation details to reduce numerical dissipation and avoid spurious solutions in unsteady inviscid flows. An assessment of the FMM-DVM accuracy is presented through a comparison with the direct calculation of the Biot-Savart law for the simulation of the temporal evolution of an aircraft wake in the Trefftz plane. The role of several parameters such as time step restriction, truncation of the FMM series expansion, number of particles in the wake discretization and machine precision is investigated and we show how to avoid spurious instabilities. The FMM-DVM is also applied to compute the evolution of a temporal shear layer with periodic boundary conditions. A novel approach is proposed to achieve accurate solutions in the periodic FMM. This approach avoids a spurious precession of the periodic shear layer and solutions are shown to converge to the direct Biot-Savart calculation using a cotangent function.
Phenomenology of the Higgs effective Lagrangian via FEYNRULES
Alloul, Adam [Groupe de Recherche de Physique des Hautes Énergies (GRPHE), Université de Haute-Alsace, IUT Colmar, 34 rue du Grillenbreit BP 50568, 68008 Colmar Cedex (France); Fuks, Benjamin [Theory Division, Physics Department, CERN, CH-1211 Geneva 23 (Switzerland); Institut Pluridisciplinaire Hubert Curien/Département Recherches Subatomiques,Université de Strasbourg/CNRS-IN2P3, 23 rue du Loess, F-67037 Strasbourg (France); Sanz, Verónica [Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH (United Kingdom)
2014-04-16
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 FEYNRULES 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 FEYNRULES capable to generate model files that can be understood by the MADGRAPH 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.
Phenomenology of the Higgs Effective Lagrangian via FeynRules
Alloul, Adam; Sanz, Verónica
2014-01-01
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 FeynRules 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 FeynRules capable to generate model files that can be understood by the MadGraph 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-...
Cosmological Structure Formation with Augmented Lagrangian Perturbation Theory
Kitaura, Francisco-Shu
2012-01-01
We present a new fast and efficient approach to model structure formation with aug- mented Lagrangian perturbation theory (ALPT). Our method is based on splitting the dis- placement field into a long and a short range component. The long range component is computed by second order LPT (2LPT). This approximation contains a tidal nonlocal and nonlinear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zeldovich approximation). We propose to combine both approximations using for the short range displacement field the SC solution. A Gaussian filter with a smoothing radius r_S is used to separate between both regimes. We use the re...
A perturbation-theoretic approach to Lagrangian flow networks
Fujiwara, Naoya; Kirchen, Kathrin; Donges, Jonathan F.; Donner, Reik V.
2017-03-01
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway, or airline infrastructures over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (as arising if the background flow is perturbed itself). Our results demonstrate that in all three cases, changes to the steady state solution can be analytically expressed in terms of the eigensystem of the unperturbed flow and the perturbation itself. These results are potentially relevant for developing more efficient strategies for coping with contaminations of fluid or gaseous media such as ocean and atmosphere by oil spills, radioactive substances, non-reactive chemicals, or volcanic aerosols.
GPU implementation of the simplex identification via split augmented Lagrangian
Sevilla, Jorge; Nascimento, José M. P.
2015-10-01
Hyperspectral imaging can be used for object detection and for discriminating between different objects based on their spectral characteristics. One of the main problems of hyperspectral data analysis is the presence of mixed pixels, due to the low spatial resolution of such images. This means that several spectrally pure signatures (endmembers) are combined into the same mixed pixel. Linear spectral unmixing follows an unsupervised approach which aims at inferring pure spectral signatures and their material fractions at each pixel of the scene. The huge data volumes acquired by such sensors put stringent requirements on processing and unmixing methods. This paper proposes an efficient implementation of a unsupervised linear unmixing method on GPUs using CUDA. The method finds the smallest simplex by solving a sequence of nonsmooth convex subproblems using variable splitting to obtain a constraint formulation, and then applying an augmented Lagrangian technique. The parallel implementation of SISAL presented in this work exploits the GPU architecture at low level, using shared memory and coalesced accesses to memory. The results herein presented indicate that the GPU implementation can significantly accelerate the method's execution over big datasets while maintaining the methods accuracy.
Reaction enhancement of initially distant scalars by Lagrangian coherent structures
Pratt, Kenneth R., E-mail: kenneth.pratt@colorado.edu; Crimaldi, John P., E-mail: john.crimaldi@colorado.edu [Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, Colorado 80309-0428 (United States); Meiss, James D., E-mail: james.meiss@colorado.edu [Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526 (United States)
2015-03-15
Turbulent fluid flows have long been recognized as a superior means of diluting initial concentrations of scalars due to rapid stirring. Conversely, experiments have shown that the structures responsible for this rapid dilution can also aggregate initially distant reactive scalars and thereby greatly enhance reaction rates. Indeed, chaotic flows not only enhance dilution by shearing and stretching but also organize initially distant scalars along transiently attracting regions in the flow. To show the robustness of this phenomenon, a hierarchical set of three numerical flows is used: the periodic wake downstream of a stationary cylinder, a chaotic double gyre flow, and a chaotic, aperiodic flow consisting of interacting Taylor vortices. We demonstrate that Lagrangian coherent structures (LCS), as identified by ridges in finite time Lyapunov exponents, are directly responsible for this coalescence of reactive scalar filaments. When highly concentrated filaments coalesce, reaction rates can be orders of magnitude greater than would be predicted in a well-mixed system. This is further supported by an idealized, analytical model that was developed to quantify the competing effects of scalar dilution and coalescence. Chaotic flows, known for their ability to efficiently dilute scalars, therefore have the competing effect of organizing initially distant scalars along the LCS at timescales shorter than that required for dilution, resulting in reaction enhancement.
Eulerian-Lagrangian Simulation of an Explosive Dispersal of Particles
Rollin, Bertrand; Ouellet, Frederick; Koneru, Rahul; Annamalai, Subramanian
2016-11-01
Explosive dispersal of solid particles can be observed in a wide variety of contexts, notably in natural phenomenon such as volcanic eruptions or in engineering applications such as detonation of multiphase explosives. As the initial blast wave crosses the surrounding layer of particles, compaction occurs shortly before particles disperse radially outward at high speed. During the dispersion phase, complex multiphase interactions occurs between particles and detonation products of the explosive. Using a Eulerian-Lagrangian approach, namely point particle simulations, we study the case of a bed of particles of cylindrical shape surrounding an explosive chord. Our interest lies in predicting the behavior of particles after detonation. In particular, capturing and describing the mechanisms responsible for late-time formation of stable particle jets is sought. Therefore, detonation of the explosive material is not simulated. Instead an equivalent energy source is used to initiate the simulation. We present a detailed description of our approach to solving this problem, and our most recent progress in the analysis of particles explosive dispersal. This work was supported by the U.S. DoE, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.
The life cycle of a coherent Lagrangian Agulhas ring
Wang, Y; Olascoaga, M J
2016-01-01
We document the long-term evolution of an Agulhas ring detected from satellite altimetry using a technique from nonlinear dynamical systems that enables objective (i.e., observer-independent) eddy framing. Such objectively detected eddies have Lagrangian (material) boundaries that remain coherent (unfilamented) over the detection period. The ring preserves a quite compact material entity for a period of about 2 years even after most initial coherence is lost within 5 months after detection. We attribute this to the successive development of short-term coherent material boundaries around the ring. These boundaries provide effective short-term shielding for the ring, which prevents a large fraction of the ring's interior from being mixed with the ambient turbulent flow. We show that such coherence regain events cannot be inferred from Eulerian analysis. This process is terminated by a ring-splitting event which marks the ring demise, near the South American coast. The genesis of the ring is characterized by a r...
Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-09-20
The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered
A Lagrangian framework for deriving triples and quadruples corrections to the CCSD energy
Eriksen, Janus Juul; Kristensen, Kasper; Kjærgaard, Thomas;
2014-01-01
Using the coupled cluster Lagrangian technique, we have determined perturbative corrections to the coupled cluster singles and doubles (CCSD) energy that converge towards the coupled cluster singles, doubles, and triples (CCSDT) and coupled cluster singles, doubles, triples, and quadruples (CCSDT...
A covering second-order Lagrangian for the relativistic top without forces
Matsyuk, Roman
2012-01-01
A parameter-invariant variational problem with a manifestly covariant Lagrangian function of second order is considered, which covers the case of the free relativistic top at constraint manifold of constant acceleration
Intermittent Lagrangian velocities and accelerations in three-dimensional porous medium flow.
Holzner, M; Morales, V L; Willmann, M; Dentz, M
2015-07-01
Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors.
Hieber, Simone E.; Koumoutsakos, Petros
2008-11-01
We present a novel Lagrangian particle method for the simulation of linear and nonlinear elastic models of soft tissue. Linear solids are represented by the Lagrangian formulation of the stress-strain relationship that is extended to nonlinear solids by using the Lagrangian evolution of the deformation gradient described in a moving framework. The present method introduces a level set description, along with the particles, to capture the body deformations and to enforce the boundary conditions. Furthermore, the accuracy of the method in cases of large deformations is ensured by implementing a particle remeshing procedure. The method is validated in several benchmark problems, in two and three dimensions and the results compare well with the results of respective finite elements simulations. In simulations of large solid deformation under plane strain compression, the finite element solver exhibits spurious structures that are not present in the Lagrangian particle simulations. The particle simulations are compared with experimental results in an aspiration test of liver tissue.
Schroeder, Craig
2012-02-01
We present a method for applying semi-implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has semi-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension force, which when treated explicitly leads to a tight time step restriction. By applying surface tension as a semi-implicit Lagrangian force, the resulting method benefits from improved stability and the ability to take larger time steps. The resulting discretization is also able to maintain parasitic currents at low levels. © 2011.
Further Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions
J. Zhang
2010-01-01
Full Text Available We apply the quadratic penalization technique to derive strong Lagrangian duality property for an inequality constrained invex program. Our results extend and improve the corresponding results in the literature.
Altomare, Cristina; Guglielmann, Raffaella; Riboldi, Marco; Bellazzi, Riccardo; Baroni, Guido
2015-01-01
.... Such tracking depends on external fiducial points placement. The main purpose of our work is to propose a new algorithm based on simulated annealing and augmented Lagrangian pattern search (SAPS...
U.S. Geological Survey, Department of the Interior — Satellite-tracked, DGPS-equipped Lagrangian surface-current drifter deployments were conducted over 12 weeks between 14 April and 7 July 2015 at various locations...
Thirty years of research and development of Lagrangian buoys at the Institute of Marine Sciences
Emilio García-Ladona
2016-09-01
Full Text Available Since the mid-1980s, physical oceanographers at the Institute of Marine Sciences have been involved in the use of Lagrangian drifters as a complementary technology for their oceanographic research. As Lagrangian observations became more feasible, these researchers continued developing their own drifters in what was to be the seed of current technological activities at the Physical and Technological Oceanography Department. In this paper we overview the work done during the last 30 years with special focus on Lagrangian developments from the initial activities to the latest developments. In addition to basic oceanography research applications, Lagrangian technological developments include prototypes for measuring surface and subsurface ocean properties, for tracking purposes in search and rescue operations and pollution events, and for monitoring ice motion and thickness in the Arctic. The paper emphasizes original and unpublished technical aspects related to the latest developments.
Inference and classifications of the Lagrangian dark matter sheet in the SDSS
Leclercq, Florent; Lavaux, Guilhem; Wandelt, Benjamin
2016-01-01
Whereas previous studies have demonstrated that the shape of the cosmic web can be described by studying the Lagrangian displacement field, state-of-the-art analyses have been limited to cosmological simulations. This letter reports on the possibility to perform a Lagrangian description of cosmic web environments in real data from large-scale structure surveys. Building upon recent Bayesian large-scale inference of initial conditions, we present an analysis of the Lagrangian dark matter sheet in the nearby universe as probed by the Sloan Digital Sky Survey. In particular, we consider its stretchings and foldings and we dissect cosmic structures into four distinct components (voids, sheets, filaments, and clusters), using the Lagrangian classifiers DIVA and ORIGAMI. As a result, identified structures explicitly carry physical information about their formation history. The present study carries potential for profound implications in the analysis of the cosmological large-scale structure, as it opens the way for...
Stress-energy-momentum tensors in Lagrangian field theory; 1, superpotentials
Giachetta, G
1995-01-01
Differential conservation laws in Lagrangian field theory are usually related to symmetries of a Lagrangian density and are obtained if the Lie derivative of a Lagrangian density by a certain class of vector fields on a fiber bundle vanishes. However, only two field models meet this property in fact. In gauge theory of exact internal symmetries, the Lie derivative by vertical vector fields corresponding to gauge transformations is equal to zero. The corresponding N\\"oether current is reduced to a superpotential that provides invariance of the N\\"oether conservation law under gauge transformations. In the gravitation theory, we meet the phenomenon of "hidden energy". Only the superpotential part of energy-momentum of gravity and matter is observed when the general covariant transformations are exact. Other parts of energy-momentum display themselves if the invariance under general covariance transformations is broken, e.g., by a background world metric. In this case, the Lie derivatives of Lagrangian densities...
Stress-energy-momentum tensors in Lagrangian field theory; 2, gravitational superpotential
Giachetta, G
1995-01-01
Our investigation of differential conservation laws in Lagrangian field theory is based on the first variational formula which provides the canonical decomposition of the Lie derivative of a Lagrangian density by a projectable vector field on a bundle (Part 1: gr-qc/9510061). If a Lagrangian density is invariant under a certain class of bundle isomorphisms, its Lie derivative by the associated vector fields vanishes and the corresponding differential conservation laws take place. If these vector fields depend on derivatives of parameters of bundle transformations, the conserved current reduces to a superpotential. This Part of the work is devoted to gravitational superpotentials. The invariance of a gravitational Lagrangian density under general covariant transformations leads to the stress-energy-momentum conservation law where the energy-momentum flow of gravity reduces to the corresponding generalized Komar superpotential. The associated energy-momentum (pseudo) tensor can be defined and calculated on solu...
Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability
Arnaudon, Marc
2010-01-01
We prove a variational principle for stochastic Lagrangian Navier-Stokes trajectories on manifolds. We study the behaviour of such trajectories concerning stability as well as rotation between particles; the two-dimensional torus case is described in detail.
The forms of three-order Lagrangian equation in relative motion
Ma Shan-Jun; Liu Ming-Ping; Huang Pei-Tian
2005-01-01
In this paper, the general expressions of three-order Lagrangian equations in a motional coordinate system are obtained. In coordinate systems with some specific forms of motion, the expressions corresponding to these equations are also presented.
EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS
DU Xue-wu; ZHANG Lian-sheng; SHANG You-lin; LI Ming-ming
2005-01-01
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions,the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, from the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
Beron-Vera, F J; Haller, G; Farazmand, M; Trinanes, J; Wang, Y
2014-01-01
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 satell...
Rationally convex domains and singular Lagrangian surfaces in $mathbb {C}(2) $ C 2
Nemirovski, Stefan; Siegel, Kyler
2016-01-01
We give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in $\\mathbb{C}^2$. We recall some classical obstructions and prove some deeper ones related to symplectic and contact topology. We explain the close connection to Lagrangian surfaces with isolated singularities and develop techniques for constructing such surfaces. Our proof also gives a complete characterization of Lagrangian surfaces with open Whitney umbrellas, answering a question first posed by Givental in 1986.
Munteanu, Florian
2016-01-01
In this paper, we will present Lagrangian and Hamiltonian k-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will obtain new kinds of conservation laws for k-symplectic Hamiltonian systems and k-symplectic Lagrangian systems.
N.N. Bogolubov (Jr.
2009-01-01
Full Text Available The work is devoted to the study of the Lagrangian and Hamiltonian properties of some relativistic electrodynamics models and is a continuation of our previous investigations. Based on the vacuum field theory approach, the Lagrangian and Hamiltonian reformulation of some classical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed. Within the approach proposed in the work a possibility of the combined description both of electrodynamics and gravity is analyzed.
Nordtvedt, Kenneth
2015-01-01
A method for constructing metric gravity's N-body Lagrangian is developed which uses iterative, liner algebraic euqations which enforce invariance properties of gravity --- exterior effacement, interior effacement, and the time dilation and Lorentz contraction of matter under boosts. The method is demonstrated by obtaining the full 1/c^4 order Lagrangian, and a combination of exterior and interior effacement enforcement permits construction of the full Schwarzschild temporal and spatial metric potentials.
Classical field theories of first order and lagrangian submanifolds of premultisymplectic manifolds
Campos, Cédric M; Marrero, Juan Carlos
2011-01-01
A description of classical field theories of first order in terms of Lagrangian submanifolds of premultisymplectic manifolds is presented. For this purpose, a Tulczyjew's triple associated with a fibration is discussed. The triple is adapted to the extended Hamiltonian formalism. Using this triple, we prove that Euler-Lagrange and Hamilton-De Donder-Weyl equations are the local equations defining Lagrangian submanifolds of a premultisymplectic manifold.
Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere
Tang, Wenbo; Mahalov, Alex
2013-03-01
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, 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.
Identification of Lagrangian coherent structures in the turbulent boundary layer
无
2009-01-01
Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vor- tices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is im- plemented to get the ensemble-averaged inclination angle θ R of typical LCS. θ R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y+=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y+=100. The ensem- ble-averaged convection velocity Uc of typical LCS is finally calculated from temporal-spatial correla- tion analysis of FTLE field. It is found that the wall-normal profile of the convection velocity Uc(y) ac- cords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the down- stream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond.
Identification of Lagrangian coherent structures in the turbulent boundary layer
PAN Chong; WANG JinJun; ZHANG Cao
2009-01-01
Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vor-tices extending deep into the near wall region with an inclination angle θto the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of # accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is im-plemented to get the ensemble-averaged inclination angle θR of typical LCS. θR first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of 8 saturates at Y+=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around Y+=100. The ensem-ble-averaged convection velocity Uc of typical LCS is finally calculated from temporal-spatial correla-tion analysis of FTLE field. It is found that the wall-normal profile of the convection velocity Uc(Y) ac-cords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the down-stream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond.
The Lagrangian particle dispersion model FLEXPART version 10
Pisso, Ignacio; Sollum, Espen; Grythe, Henrik; Kristiansen, Nina; Cassiani, Massimo; Eckhardt, Sabine; Thompson, Rona; Groot Zwaaftnik, Christine; Evangeliou, Nikolaos; Hamburger, Thomas; Sodemann, Harald; Haimberger, Leopold; Henne, Stephan; Brunner, Dominik; Burkhart, John; Fouilloux, Anne; Fang, Xuekun; Phillip, Anne; Seibert, Petra; Stohl, Andreas
2017-04-01
The Lagrangian particle dispersion model FLEXPART was in its first original release in 1998 designed for calculating the long-range and mesoscale dispersion of air pollutants from point sources, such as after an accident in a nuclear power plant. The model has now evolved into a comprehensive tool for atmospheric transport modelling and analysis. Its application fields are extended to a range of atmospheric transport processes for both atmospheric gases and aerosols, e.g. greenhouse gases, short-lived climate forces like black carbon, volcanic ash and gases as well as studies of the water cycle. We present the newest release, FLEXPART version 10. Since the last publication fully describing FLEXPART (version 6.2), the model code has been parallelised in order to allow for the possibility to speed up computation. A new, more detailed gravitational settling parametrisation for aerosols was implemented, and the wet deposition scheme for aerosols has been heavily modified and updated to provide a more accurate representation of this physical process. In addition, an optional new turbulence scheme for the convective boundary layer is available, that considers the skewness in the vertical velocity distribution. Also, temporal variation and temperature dependence of the OH-reaction are included. Finally, user input files are updated to a more convenient and user-friendly namelist format, and the option to produce the output-files in netCDF-format instead of binary format is implemented. We present these new developments and show recent model applications. Moreover, we also introduce some tools for the preparation of the meteorological input data, as well as for the processing of FLEXPART output data.
Mechanisms underlying temperature extremes in Iberia: a Lagrangian perspective
João A. Santos
2015-04-01
Full Text Available The mechanisms underlying the occurrence of temperature extremes in Iberia are analysed considering a Lagrangian perspective of the atmospheric flow, using 6-hourly ERA-Interim reanalysis data for the years 1979–2012. Daily 2-m minimum temperatures below the 1st percentile and 2-m maximum temperatures above the 99th percentile at each grid point over Iberia are selected separately for winter and summer. Four categories of extremes are analysed using 10-d backward trajectories initialized at the extreme temperature grid points close to the surface: winter cold (WCE and warm extremes (WWE, and summer cold (SCE and warm extremes (SWE. Air masses leading to temperature extremes are first transported from the North Atlantic towards Europe for all categories. While there is a clear relation to large-scale circulation patterns in winter, the Iberian thermal low is important in summer. Along the trajectories, air mass characteristics are significantly modified through adiabatic warming (air parcel descent, upper-air radiative cooling and near-surface warming (surface heat fluxes and radiation. High residence times over continental areas, such as over northern-central Europe for WCE and, to a lesser extent, over Iberia for SWE, significantly enhance these air mass modifications. Near-surface diabatic warming is particularly striking for SWE. WCE and SWE are responsible for the most extreme conditions in a given year. For WWE and SCE, strong temperature advection associated with important meridional air mass transports are the main driving mechanisms, accompanied by comparatively minor changes in the air mass properties. These results permit a better understanding of mechanisms leading to temperature extremes in Iberia.
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
Felici, Helene Marie
1992-06-01
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.
B. Rutherford
2012-12-01
Full Text Available The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation.
Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance.
The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.
Lagrangian Displacement Ensembles for Aerosol Data Assimilation (Invited)
da Silva, A.; Colarco, P. R.; Govindaraju, R. C.
2010-12-01
A challenge common to many constituent data assimilation applications is the fact that one observes a much smaller fraction of the phase space that one wishes to estimate. For example, remotely-sensed estimates of the column average concentrations are available, while one is faced with the problem of estimating 3D concentractions for initializing a prognostic model. This problem is exarcebated in the the case of aerosols because the observable Aerosol Optical Depth (AOD) is not only a column integrated quantity, but it also sums over a large number of species (dust, sea-salt, carbonaceous and sulfate aerosols). An aerosol transport model when driven by high-resolution, state-of-the-art analysis of meterorological fields and realistc emissions can produce skillful forecasts even when no aerosol data is assimilated. The main task of aerosol data assimilation is to address the bias arising from innacurate emissions, and the Lagrangian misplacement of plumes induced by errors in the driving meterorological fields. As long as one decouples the meteorological and aerosol assimilation as we do here, the classic baroclinic growth of errors is no longer the main order of business. We will describe and aerosol data assimilation scheme in which the anaysis update step is conducted in observation space, using an adaptive maximum-likelihood scheme for estimating background errors in AOD space. This scheme includes explicit sequential bias estimation as in Dee and da Silva (1998). Unlikely existing aerosol data assimiltion schemes we do not obtain analysis increments of the 3D concentrations by scalling the background profiles. Instead, we explore the Langrangian characteristics of the problem for generating local displacement ensembles. These high-resolution, state-dependent ensembles are then used to parameterize the background errors and generate 3D aerosol increments. The algorithm has computational complexity comparable to the forecasting step by the aerosol transport model
Lagrangian Analysis of Kerguelen's Naturally Iron-fertilised Phytoplankton Bloom
Della Penna, A.; Trull, T. W.; Grenier, M.; Wotherspoon, S.; Johnson, C.; De Monte, S.; d'Ovidio, F.
2015-12-01
The role of iron as a limiting micro-nutrient for primary production in High Nutrient Low Chlorophyll regions has been highlighted by paleoceanography, artificial fertilisation experiments and observed naturally fertilised systems. Examples of natural fertilisation have suggested that (sub-)mesoscale (1-100 km, days-months) horizontal transport modulates and structures the spatial and temporal extent of iron enrichment, phytoplankton production and biogeography. Here we combine different satellite products (altimetry, ocean color, PHYSAT), in-situ sampling, drifting floats and autonomous profilers to analyse the naturally iron-fertilised phytoplankton bloom of the Kerguelen region (Southern Ocean). Considering the Kerguelen Plateau as the main local source of iron, we compute two Lagrangian diagnostics: the "age" - how long before a water parcel has touched the plateau- and the "origin" - the latitude where a water parcel has left the plateau. First, we verify that these altimetry-defined diagnostics' spatial patterns -computed using geostrophic and Ekman corrected velocity fields- are coherent with the ones structuring the trajectories of more than 100 drifters and that trends in surface Chlorophyll (Chl) present an overall agreement with total column content (yet with ~2-3x differences in dynamic ranges likely due to the varying presence of Chl below the mixed layer). Second, assuming a first-order removal, we fit "age" with iron measurements and we estimate removal rates for bloom and abiotic conditions of respectively 0.058 and 0.041 1/d. Then, we relate "age" and "origin" with locations of high Chl concentrations and diatom-dominance. We find out that locations of high Chl concentration correspond to water parcels that have recently left the plateau. Furthermore, general additive models reveal that recently enriched waters are more likely to present a diatom dominance. However, the expected exponential fit varies within the geographic domain suggesting that
Lagrangian Coherent Structures in a Non-Euclidean Global Thermosphere
Wang, N.; Ramirez, U.; Flores, F.; Datta-Barua, S.
2016-12-01
Lagrangian Coherent Structures (LCSs) are manifolds of maximum divergence or convergence in 2D or 3D time-varying flow fields. The study of LCSs has been used to predict material transport in numerous geophysical flows. The most commonly used computational method for finding LCSs is to compute the finite time Lyapunov exponent (FTLE), a scalar field measuring the ratio of stretching after a given interval of time among neighboring particles, relative to their initial separation. LCS ridges are located at the local maxima of the FTLE. The LCS must be objective (frame-invariant for different observers), and the technique for computing the FTLE that determines the LCS typically assumes a Euclidean domain. Previous work showed that LCSs are likely to exist globally at high latitudes using the Euclidean norm. Here we refine that calculation by deriving the FTLE calculation for the Riemannian manifold of a spherical surface, and applying it to the thermospheric layer of the atmosphere globally. The thermosphere is treated as a closed spherical 2D domain on which the fluid flows, assuming negligible vertical flow. The domain is discretized in longitude and latitude, and the Horizontal Wind Model 2014 (HWM14) is used to generate the 2D velocity field at each grid point, each of which is a ground speed in the local east-north-up (ENU) frame. To make the LCS objective, the ground speed in each local ENU frame is converted to angular velocity in the earth-centered earth-fixed (ECEF) coordinates. Using bilinear interpolation and including the rotational velocity of Earth to transform to an inertial frame, we trace the trajectory of each particle to compute the final positions after the integration time. Replacing the Euclidean distance between particles with the great circle distance gives the FTLE scalar field from which the LCSs can be identified. We find and illustrate objective LCSs in the neutral wind flow field at high latitudes by applying this algorithm for the
A larval dispersion study using lagrangian simulation of particles
Laura Rodríguez Díaz
2014-06-01
Full Text Available The continuous displacement of water allows stabilize the temperature and also distributes nutrients and plankton in the ocean and seas permitting the development of organisms and the transfers of larvae from the spawning areas to the habitat where adult fishes can be found. The area of study covers The North Atlantic Ocean so the principal aim of the study is analyze if released particles at the Florida Strait could cross the North Atlantic Ocean and reach the European shelf. To test this, it has simulated Lagrangian trajectories for different numbers of particles or "larvae" with a passive behavior (fixing at a depth of dispersion. It has analyzed the dispersion of those particles by using the data of the components U, V and W from the speed of currents provided by the database SODA which uses an ocean model based on Geophysical Fluid Dynamics Laboratory MOM2 and data profiles from World Ocean Atlas-94 and from Geosat, ERS-1 and TOPEX/Poseidon satellites. Considering the dispersive nature of the ocean, the simulations were performed by releasing many particles (typically of the order of several thousand and it was also necessary to perform an interpolation process in time and space so that the position of the particles could evolve. The simulations have been run with 5,000 particles and it has been considered a biological parameter (planktonic larval duration, PLD that represents the length of larval life. At this study it has been used PLD for a specific starfish larva (Sclerasterias tanneri larvae that can be found at the Gulf of Mexico at different locations. Particles were released in October at the most oceanward location of the Gulf of Mexico close to the Florida Strait where Sclerasterias tanneri larvae can be found. Those particles have been tracked for 660 days (660 days is the PLD of Sclerasterias tanneri larvae recording their position every 15 days. That it has done for a period of more than 100 years (1901-2010. The period (1901
Buchbinder, I.L., E-mail: joseph@tspu.edu.ru [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation); National Research Tomsk State University (Russian Federation); Snegirev, T.V., E-mail: snegirev@tspu.edu.ru [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation); Zinoviev, Yu.M., E-mail: Yurii.Zinoviev@ihep.ru [Institute for High Energy Physics, Protvino, Moscow Region, 142280 (Russian Federation)
2014-11-10
We construct the frame-like gauge-invariant Lagrangian formulation for massive fermionic arbitrary spin fields in three-dimensional AdS space. The Lagrangian and complete set of gauge transformations are obtained. We also develop the formalism of gauge-invariant curvatures for the massive theory under consideration and show how the Lagrangian is formulated in their terms. The massive spin-5/2 field is discussed as an example.
From classical Lagrangians to Hamilton operators in the Standard-Model Extension
Schreck, Marco
2016-01-01
In this article we investigate whether a theory based on a classical Lagrangian for the minimal Standard-Model Extension (SME) can be quantized such that the result is equal to the corresponding low-energy Hamilton operator obtained from the field-theory description. This analysis is carried out for the whole collection of minimal Lagrangians found in the literature. The upshot is that first quantization can be performed consistently. The unexpected observation is made that at first order in Lorentz violation and at second order in the velocity the Lagrangians are related to the Hamilton functions by a simple transformation. Under mild assumptions, it is shown that this holds universally. This result is used successfully to obtain classical Lagrangians for two complicated sectors of the minimal SME that have not been considered in the literature so far. Therefore, it will not be an obstacle anymore to derive such Lagrangians even for involved sets of coefficients - at least to the level of approximation state...
On necessary and sufficient conditions of the BV quantization of a generic Lagrangian field system
Bashkirov, D; Mangiarotti, L; Sardanashvily, G
2005-01-01
We address the problem of extending an original field Lagrangian to ghosts and antifields in order to satisfy the master equation in the framework of the BV quantization of Lagrangian field systems. This extension essentially depends on the degeneracy of an original Lagrangian. A generic Lagrangian system of even and odd fields on an arbitrary smooth manifold is examined in the algebraic terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys the Noether identities which need not be independent, but satisfy the first-stage Noether identities, and so on. We state the necessary and sufficient condition of the existence of the exact antifield Koszul-tate complex with the boundary operator whose nilpotency property provides all the Noether and higher-stage Noether identities of an original Lagrangian system. The Noether inverse second theorem that we prove associates to this Koszul-Tate complex the sequence graded in ghosts whose ascent operator provides the gauge and higher-stage g...
From classical Lagrangians to Hamilton operators in the standard model extension
Schreck, M.
2016-07-01
In this article we investigate whether a theory based on a classical Lagrangian for the minimal Standard Model Extension (SME) can be quantized such that the result is equal to the corresponding low-energy Hamilton operator obtained from the field-theory description. This analysis is carried out for the whole collection of minimal Lagrangians found in the literature. The upshot is that the first quantization can be performed consistently. The unexpected observation is made that at first order in Lorentz violation and at second order in the velocity, the Lagrangians are related to the Hamilton functions by a simple transformation. Under mild assumptions, it is shown that this holds universally. That result is used successfully to obtain classical Lagrangians for two complicated sectors of the minimal SME that have not been considered in the literature so far. Therefore, it will not be an obstacle anymore to derive such Lagrangians even for involved sets of coefficients—at least to the level of approximation stated above.
A LES-based Eulerian-Lagrangian approach to predict the dynamics of bubble plumes
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.
Space-Time Transformation in Flux-form Semi-Lagrangian Schemes
Peter C. Chu Chenwu Fan
2010-01-01
Full Text Available With a finite volume approach, a flux-form semi-Lagrangian (TFSL scheme with space-time transformation was developed to provide stable and accurate algorithm in solving the advection-diffusion equation. Different from the existing flux-form semi-Lagrangian schemes, the temporal integration of the flux from the present to the next time step is transformed into a spatial integration of the flux at the side of a grid cell (space for the present time step using the characteristic-line concept. The TFSL scheme not only keeps the good features of the semi-Lagrangian schemes (no Courant number limitation, but also has higher accuracy (of a second order in both time and space. The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation. Computational stability and high accuracy makes this scheme useful in ocean modeling, computational fluid dynamics, and numerical weather prediction.
A Lagrangian variational formulation for nonequilibrium thermodynamics. Part II: Continuum systems
Gay-Balmaz, François; Yoshimura, Hiroaki
2017-01-01
Part I of this paper introduced a Lagrangian variational formulation for nonequilibrium thermodynamics of discrete systems. This variational formulation extends Hamilton's principle to allow the inclusion of irreversible processes in the dynamics. The irreversibility is encoded into a nonlinear nonholonomic constraint given by the expression of entropy production associated to all the irreversible processes involved. In Part II, we develop this formulation for the case of continuum systems by extending the setting of Part I to infinite dimensional nonholonomic Lagrangian systems. The variational formulation is naturally expressed in the material representation, while its spatial version is obtained via a nonholonomic Lagrangian reduction by symmetry. The theory is illustrated with the examples of a viscous heat conducting fluid and its multicomponent extension including chemical reactions and mass transfer.
Computing the Lagrangians of the Standard Model II. The Ghost Term
Selesnick, S. A.
2016-08-01
We follow up an earlier attempt to compute the Yang-Mills Lagrangian density from first principles. In that work, the Lagrangian density emerged replete with a Feynman-'t Hooft gauge fixing term. In this note we find that similar methods may be applied to produce the concomitant ghost term. Our methods are elementary and entirely and straightforwardly algebraic. Insofar as one of our first principles in the earlier computation was the Schwinger Action Principle, which is a differential version of the Feynman path integral, our computation here may be viewed as a differential version of the Faddeev-Popov functional integral approach to generating the ghost Lagrangian. As such, it avoids all measure theoretic difficulties and ambiguities, though at the price of generality.
BRST-BFV Lagrangian Formulations for Higher Spin Fields subject to two-column Young Tableaux
Reshetnyak, Alexander A
2014-01-01
The details of Lagrangian description of irreducible integer higher-spin representations of the Poincare group with an Young tableaux $Y[\\hat{s}_1,\\hat{s}_2]$ having $2$ columns are considered for Bose particles propagated on an arbitrary dimensional Minkowski space-time. The procedure is based, first, on using of an auxiliary Fock space generated by Fermi oscillators (antisymmetric basis), second, on construction of the Verma module and finding auxiliary oscillator realization for $sl(2)\\oplus sl(2)$ algebra which encodes the second-class operator constraints subsystem in the HS symmetry superalgebra. Application of an BRST-BFV receipt permits to reproduce gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive mixed-antisymmetric bosonic fields of any spin with appropriate number of gauge and Stueckelberg fields. The general prescription possesses by the possibility to derive constrained Lagrangians with only BRST-invariant extended algebraic con...
Lagrangian study of transport and mixing in a mesoscale eddy street
Prants, S V; Ponomarev, V I; Uleysky, M Yu; 10.1016/j.ocemod.2011.02.008
2012-01-01
We use dynamical systems approach and Lagrangian tools to study surface transport and mixing of water masses in a selected coastal region of the Japan Sea with moving mesoscale eddies associated with the Primorskoye Current. Lagrangian trajectories are computed for a large number of particles in an interpolated velocity field generated by a numerical regional multi-layer eddy-resolving circulation model. We compute finite-time Lyapunov exponents for a comparatively long period of time by the method developed and plot the Lyapunov synoptic map quantifying surface transport and mixing in that region. This map uncovers the striking flow structures along the coast with a mesoscale eddy street and repelling material lines. We propose new Lagrangian diagnostic tools --- the time of exit of particles off a selected box, the number of changes of the sign of zonal and meridional velocities --- to study transport and mixing by a pair of strongly interacting eddies often visible at sea-surface temperature satellite imag...
Computing the Lagrangians of the Standard Model II. The Ghost Term
Selesnick, S. A.
2016-11-01
We follow up an earlier attempt to compute the Yang-Mills Lagrangian density from first principles. In that work, the Lagrangian density emerged replete with a Feynman-'t Hooft gauge fixing term. In this note we find that similar methods may be applied to produce the concomitant ghost term. Our methods are elementary and entirely and straightforwardly algebraic. Insofar as one of our first principles in the earlier computation was the Schwinger Action Principle, which is a differential version of the Feynman path integral, our computation here may be viewed as a differential version of the Faddeev-Popov functional integral approach to generating the ghost Lagrangian. As such, it avoids all measure theoretic difficulties and ambiguities, though at the price of generality.
Machicoane, Nathanaël
2015-01-01
We investigate the response of large inertial particle to turbulent fluctuations in a inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding partical dynamics and may permit stochastic process modelization using two-time models (for instance Saw-ford's). As particles are tracked over long times in the quasi totality of a closed flow, the mean flow influences their behaviour and also biases the velocity time statistics, in particular the velocity correlation functions. By using a method that allows for the computation of turbulent velocity trajectories, we can obtain unbiased Lagrangian integral time. This is particularly usef...
A covariant nonlocal Lagrangian for the description of the scalar kaonic sector
Soltysiak, Milena
2016-01-01
Mesons are extended objects, hence their interaction can be described by utilizing form factors. At the Lagrangian level, one can use nonlocal interaction terms. Here we describe two possible nonlocal Lagrangians leading to a 3D form factor: the first one is simple but does not fulfill covariance (if one insists on a 3D cutoff), the second extension is more involved but guarantees covariance. Such form factors are useful when calculating mesonic loops. As an important example, we discuss the scalar kaonic sector, $I(J^{P})=\\frac{1}{2}(0^{+})$. The Lagrangian contains a single scalar kaon (the well-establish state $K_{0}^{\\ast}(1430)$), but through loops $K_{0}^{\\ast}(800)$ emerges as a dynamically generated companion pole (which disappears in the large-$N_{c}$ limit).
Mielke, Alexander
1991-01-01
The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists,...
The general form of the coupled Horndeski Lagrangian that allows cosmological scaling solutions
Gomes, Adalto R
2015-01-01
We consider the general scalar field Horndeski Lagrangian coupled to 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 matter to field density and the equation of state remain constant. Scaling solutions of this kind may help solving the coincidence problem 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.
Pratt, J; Mueller, W -C; Chapman, S C; Watkins, N W
2014-01-01
Local regions of anomalous particle dispersion, and intermittent events that occur in turbulent flows can greatly influence the global statistical description of the flow. These local behaviors can be identified and analyzed by comparing the growth of neighboring convex hulls of Lagrangian tracer particles. Although in our simulations of homogeneous turbulence the convex hulls generally grow in size, after the Lagrangian particles that define the convex hulls begin to disperse, our analysis reveals short periods when the convex hulls of the Lagrangian particles shrink, evidence that particles are not dispersing simply. Shrinkage can be associated with anisotropic flows, since it occurs most frequently in the presence of a mean magnetic field or thermal convection. We compare dispersion between a wide range of statistically homogeneous and stationary turbulent flows ranging from homogeneous isotropic Navier-Stokes turbulence over different configurations of magnetohydrodynamic turbulence and Boussinesq convect...
A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO
Heisenberg, Lavinia; Bartelmann, Matthias
2010-01-01
Subject of this paper is a careful and detailed analysis of the PINOCCHIO algorithm for studying the relative velocity statistics of merging haloes in Lagrangian perturbation theory. Given a cosmological background model, a power spectrum of fluctuations as well as a Gaussian linear density contrast field $\\delta_{\\rm l}$ is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position $\\bmath{q}$ and each smoothing radius $R$, the collapse time, the velocities and ellipsoidal truncation are computed using Lagrangian Perturbation Theory. The collapsed medium is then fragmented into isolated objects by an algorithm designed to mimic the accretion and merger events of hierarchical collapse. Directly after the fragmentation process the mass function, merger histories of haloes and the statistics of the relative velocities at merging are evaluated. We reimplemented the algorithm in C++ and optimised the construction of halo merging histories. Comparin...
Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics.
Glavatskiy, K S
2015-05-28
We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an "integral of evolution" which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.
Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space
Buchbinder, I L; Lavrov, P M
2006-01-01
We develop the BRST approach to Lagrangian construction for the massive integer higher spin fields in an arbitrary dimensional AdS space. The theory is formulated in terms of auxiliary Fock space. Closed nonlinear symmetry algebra of higher spin bosonic theory in AdS space is found and method of deriving the BRST operator for such an algebra is proposed. General procedure of Lagrangian construction describing the dynamics of bosonic field with any spin is given on the base of the BRST operator. No off-shell constraints on the fields and the gauge parameters are used from the very beginning. As an example of general procedure, we derive the Lagrangians for massive bosonic fields with spin 0, 1 and 2 containing total set of auxiliary fields and gauge symmetries.
Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space
Buchbinder, I.L. [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634041 (Russian Federation)]. E-mail: joseph@tspu.edu.ru; Krykhtin, V.A. [Laboratory of Mathematical Physics, Tomsk Polytechnic University, Tomsk 634034 (Russian Federation)]. E-mail: krykhtin@mph.phtd.tpu.edu.ru; Lavrov, P.M. [Department of Mathematical Analysis, Tomsk State Pedagogical University, Tomsk 634041 (Russian Federation)]. E-mail: lavrov@tspu.edu.ru
2007-02-05
In this work we develop the BRST approach to Lagrangian construction for the massive integer higher spin fields in an arbitrary dimensional AdS space. The theory is formulated in terms of auxiliary Fock space. Closed nonlinear symmetry algebra of higher spin bosonic theory in AdS space is found and a method of deriving the BRST operator for such an algebra is proposed. A general procedure of Lagrangian construction, describing the dynamics of a bosonic field with any spin is given on the base of the BRST operator. No off-shell constraints on the fields and the gauge parameters are used from the very beginning. As an example of general procedure, we derive the Lagrangians for massive bosonic fields with spin 0, 1 and 2, containing the total set of auxiliary fields and gauge symmetries.
On the notion of gauge symmetries of generic Lagrangian field theory
Giachetta, G; Sardanashvily, G
2008-01-01
Treating gauge theories in a general setting, one meets the following problems: (i) any Lagrangian possesses gauge symmetries which therefore should be separated into the trivial and non-trivial ones, (ii) there is no intrinsic definition of higher-stage gauge symmetries, (iii) gauge and higher-stage gauge symmetries need not form an algebra. We define gauge symmetries as those associated to the Noether identities. Generic Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Under certain conditions, its non-trivial Noether and higher-stage Noether identities are well defined by constructing the antifield Koszul--Tate complex. The inverse second Noether theorem associates to this complex the cochain sequence of ghosts whose ascent operator provides all non-trivial gauge and higher-stage gauge symmetries of Lagrangian theory. This ascent operator, called the gauge operator, is not nilpotent, unless gauge symmetries are abelian. We replace a condition that gauge symmetries for...
Response to: "Limitations of the Method of Lagrangian Descriptors" [arXiv:1510.04838
Balibrea-Iniesta, F; García-Garrido, V J; Lopesino, C; Mancho, A M; Mendoza, C; Wiggins, S
2016-01-01
This Response is concerned with the recent Comment of Ruiz-Herrera, "Limitations of the Method of Lagrangian Descriptors" [arXiv:1510.04838], criticising the method of Lagrangian Descriptors. In spite of the significant body of literature asserting the contrary, Ruiz-Herrera claims that the method fails to reveal the presence of stable and unstable manifolds of hyperbolic trajectories in incompressible systems and in almost all linear systems. He supports this claim by considering the method of Lagrangian descriptors applied to three specific examples. However in this response we show that Ruiz-Herrera does not understand the proper application and interpretation of the method and, when correctly applied, the method beautifully and unambiguously detects the stable and unstable manifolds of the hyperbolic trajectories in his examples.
Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows
Innocenti, A; Chibbaro, S
2016-01-01
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves for a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided b...
Finite-time Partitions for Lagrangian Structure Identification in Gulf Stream Eddy Transport
Fabregat, Alexandre; Poje, Andrew C
2016-01-01
We develop a methodology to identify finite-time Lagrangian structures from data and models using an extension of the Koopman operator-theoretic methods developed for velocity fields with simple (periodic, quasi-periodic) time-dependence. To achieve this, the notion of the Finite Time Ergodic (FiTER) partition is developed and rigorously justified. In combination with a clustering-based approach, the methodology enables identification of the temporal evolution of Lagrangian structures in a classic, benchmark, oceanographic transport problem, namely the cross-stream flux induced by the interaction of a meso- scale Gulf Stream Ring eddy with the main jet. We focus on a single mixing event driven by the interaction between an energetic cold core ring (a cyclone), the strong jet, and a number of smaller scale cyclones and anticyclones. The new methodology enab les reconstruction of Lagrangian structures in three dimensions and analysis of their time-evolution.
Effective Lagrangian in nonlinear electrodynamics and its properties of causality and unitarity
Shabad, Anatoly E.; Usov, Vladimir V.
2011-05-01
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 at 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.
Effective Lagrangian in nonlinear electrodynamics and its properties of causality and unitarity
Shabad, Anatoly E
2011-01-01
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 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 at 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 magnetiz...
Monitoring the Amazon plume northwestward transport along Lagrangian pathways
Fournier, Severine; Gaultier, Lucile; Vandemark, Douglas; Lee, Tong; Gierach, Michelle
2016-04-01
area. The objective of this study is to investigate the interannual variability in Amazon-Orinoco freshwater transport from the rivers' mouth northwestward over 2010-2014. We use a Lagrangian advection method to track the particles and follow their biophysical properties along their trajectory using measurements from Aquarius, SMOS, and Aqua MODIS. The pathways of the Amazon-Orinoco plume waters can therefore be analyzed and quantified, enabling an investigation of the biophysical processes associated with the Amazon River and Orinoco River freshwaters as they are advected from the river mouth to the open ocean. From one year to another, the amount of Amazon-Orinoco particles reaching the northwestern part of the plume is variable causing different physical and biogeochemical influences in the area. In 2011, a larger amount of particles reaches that area, the mechanisms responsible for this unusual northwestward transport of the shallow plume waters are under investigation, such as river discharge, advection, NBC rings. On the contrary, in 2014, fewer particles reach this northwestern area taking a more coastal pathway. This suggests a higher influence of the Orinoco River that year.
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.
George Livadiotis
2014-07-01
Full Text Available The paper studies the “Lagrangian temperature” defined through the entropy maximization in the canonical ensemble, which is the negative inverse Lagrangian multiplier corresponding to the constraint of internal energy. The Lagrangian temperature is derived for systems out of thermal equilibrium described by kappa distributions such as space plasmas. The physical meaning of temperature is manifested by the equivalency of two different definitions, that is, through Maxwell’s kinetic theory and Clausius’ thermodynamics. The equivalency of the two definitions is true either for systems at thermal equilibrium described by Maxwell distributions or for systems out of thermal equilibrium described by kappa distributions, and gives the meaning of the actual temperature, that is, the real or measured temperature. However, the third definition, that of the Lagrangian temperature, coincides with the primary two definitions only at thermal equilibrium, and thus, in the general case of systems out of thermal equilibrium, it does not represent the actual temperature, but it is rather a function of this. The paper derives and examines the exact expression and physical meaning of the Lagrangian temperature, showing that it has essentially different content to what is commonly thought. This is achieved by: (i maximizing the entropy in the continuous description of energy within the general framework of non-extensive statistical mechanics, (ii using the concept of the “N-particle” kappa distribution, which is governed by a special kappa index that is invariant of the degrees of freedom and the number of particles, and (iii determining the appropriate scales of length and speed involved in the phase-space microstates. Finally, the paper demonstrates the behavior of the Lagrangian against the actual temperature in various datasets of space plasmas.
Besse, Nicolas; Frisch, Uriel
2017-01-01
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.
Gravitational Lagrangians, Mach’s Principle, and the Equivalence Principle in an Expanding Universe
Hanno Essén
2014-01-01
Full Text Available 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 Lagrangian particle/panel method for the barotropic vorticity equations on a rotating sphere
Bosler, Peter; Krasny, Robert [Department of Mathematics, University of Michigan, Ann Arbor, MI 48109 (United States); Wang, Lei [Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201 (United States); Christiane Jablonowski, E-mail: krasny@umich.edu [Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, MI 48109 (United States)
2014-06-01
We present a Lagrangian particle/panel method for geophysical fluid flow described by the barotropic vorticity equations on a rotating sphere. The particles carry vorticity and the panels are used in discretizing the Biot–Savart integral for the velocity. Adaptive panel refinement and a new Lagrangian remeshing scheme are applied to reduce the computational cost and maintain accuracy as the flow evolves. Computed examples include a Rossby–Haurwitz wave, a Gaussian vortex, and a perturbed zonal jet. To validate the method, a comparison is made with results obtained using the Lin–Rood finite–volume scheme. (papers)
An Eulerian-Lagrangian open source solver for bubbly flow in vertical pipes
Pena-Monferrer, C.; Munoz-Cobo, J. L.; Monros-Andreu, G.; Martinez-Cuenca, R.; Chiva, S.
2014-07-01
Air-water two-phase flow is present in natural and industrial processes of different nature as nuclear reactors. An accurate local prediction of the boiling flow could support safety and operation analyses of nuclear reactors. An Eulerian-Lagrangian approach is investigated in this contribution as it can be used as a virtual facility to investigate the two-phase flow phenomena. A solver based on the PISO algorithm coupled with the Lagrangian equation of motion have been implemented for computing incompressible bubbly flows. (Author)
WANG Zhi-Min; WANG Qing
2001-01-01
Bosonic part of SU(2)L U(1)Y effective chiral Lagrangian for electroweak symmetry breaking is derived from an underlying technicolor theory with no approximation. The underlying theory is assumed to be the most general gauge theory without fundamental scalars. A condensate is required to exist in the theory which breaks SU(2)L U(1)Y dynamically to U(1)em and the anomaly of the theory caused by gauge interaction must be cancelled. The formulation offers general definitions in terms of underlying theory for the low energy constants in effective chiral Lagrangian.``
Lagrangian viscoelastic flow computations using the Rivlin-Sawyers constitutive model
Rasmussen, Henrik Koblitz
2000-01-01
A new finifte element technique for the numerical simulation of 3D time-dependent flow of viscoelastic fluid is presented. The technique is based on a Lagrangian kinematics description of the fluid flow. It represent a further development of the 3D Lagrangian integral method (3D-LIM) from an upper...... convected Maxwell fluid to a fluid described by an integral constitutive equation of the Rivlin-Sawyers type. This includes the K-BKZ model. The convergence of the method is demonstrated on the axisymmetric problem of the inflation of a polymeric membrane only restricted by a clamping ring....
COMPARISON OF THE EULERIAN AND LAGRANGIAN TIDAL RESIDUALS IN THE BOHAI SEA
魏皓; 赵亮; 冯士笮
2001-01-01
Tidal residual is very important to the transport of water particles, nutrients, plank-ton, etc. in the coastal sea. Eulerian scheme and Lagrangian scheme are two different ways to get the time averaged residual. Solution of the Bohai Sea's hydrodynamic system using a semi-implicit layer aver-aged numerical model yielded different direction Eulerian and Lagrangian tidal residuals. The latter were stronger than the former in most sea areas. Their different directions produced different ciretdation pattern in some areas. Compared with the Eulerian residual, the Lagranglan residual seemed to be more in accord with the observation.
The description for the spin polarizabilities of hadrons based on the covariant Lagrangian
Belousova, S A
2000-01-01
On the basis of the correspondence principle between the relativistic moving medium electrodynamics and relativistic quantum field theory the covariant Lagrangian of the electromagnetic field interaction with the polarized spin particles have been obtained. This Lagrangian satisfies the main relativistic quantum field theory requirements and contains four independent covariant spin structures, which have particular physical meaning. It is shown that the spin polarizabilities give the contribution to the amplitude for Compton scattering on the spin-1/2 hadron in the ${\\cal O}(\\omega^3)$.
Schreck, M
2015-01-01
This article is devoted to finding classical point-particle equivalents for the fermion sector of the nonminimal Standard-Model Extension (SME). For a series of nonminimal operators, such Lagrangians are derived at first order in Lorentz violation using the algebraic concept of Gr\\"obner bases. Subsequently, the Lagrangians serve as a basis for reanalyzing the results of certain kinematic tests of Special Relativity that were carried out in the last century. Thereby, a number of new constraints on coefficients of the nonminimal SME is obtained. In the last part of the paper we point out connections to Finsler geometry.
Schreck, M.
2016-05-01
This article is devoted to finding classical point-particle equivalents for the fermion sector of the nonminimal standard model extension (SME). For a series of nonminimal operators, such Lagrangians are derived at first order in Lorentz violation using the algebraic concept of Gröbner bases. Subsequently, the Lagrangians serve as a basis for reanalyzing the results of certain kinematic tests of special relativity that were carried out in the past century. Thereby, a number of new constraints on coefficients of the nonminimal SME is obtained. In the last part of the paper we point out connections to Finsler geometry.
Hunter, Richard
2010-01-01
It is known that all weakly conformal Hamiltonian stationary Lagrangian immersions of tori in the complex projective plane may be constructed by methods from integrable systems theory. This article describes the precise details of a construction which leads to a form of classification. The immersion is encoded as spectral data in a similar manner to the case of minimal Lagrangian tori in the complex projective plane, but the details require a careful treatment of both the "dressing construction" and the spectral data to deal with a loop of flat connexions which is quadratic in the loop parameter.
The Effective Lagrangian for the Seesaw Model of Neutrino Mass and Leptogenesis
Broncano, A; Jenkins, E
2003-01-01
The effective Lagrangian for the seesaw model is derived including effects due to CP violation. Besides the usual dimension-5 operator responsible for light neutrino masses, a dimension-6 operator is obtained. For three or less heavy neutrino generations, the inclusion of both operators is necessary and sufficient for all independent physical parameters of the high-energy seesaw Lagrangian to appear in the low-energy effective theory, including the CP-odd phases relevant for leptogenesis. The dimension-6 operator implies exotic low-energy couplings for light neutrinos, providing a link between the high-energy physics and low-energy observables.
The effective Lagrangian for the seesaw model of neutrino mass and leptogenesis
Broncano, A.; Gavela, M.B.; Jenkins, E
2003-01-23
The effective Lagrangian for the seesaw model is derived including effects due to CP-violation. Besides the usual dimension-5 operator responsible for light neutrino masses, a dimension-6 operator is obtained. For three or less heavy neutrino generations, the inclusion of both operators is necessary and sufficient for all independent physical parameters of the high-energy seesaw Lagrangian to appear in the low-energy effective theory, including the CP-odd phases relevant for leptogenesis. The dimension-6 operator implies exotic low-energy couplings for light neutrinos, providing a link between the high-energy physics and low-energy observables.
USAMA Umer; XIE Lijing; WANG Xibin
2006-01-01
A two-dimensional finite element (FE) model for the high speed turning operations when orthogonally machining AISI H13 tool steel at 49HRC using poly crystalline cubic boron nitride(PCBN) is described. An arbitrary Lagrangian Eulerian (ALE) method has been adopted which does not need any chip separation criteria as opposed to the traditional Lagrangian approach. Through FE simulations temperature and stresses distributions are presented that could be helpful in predicting tool life and improving process parameters. The results show that high temperatures are generated along the tool rake face as compared to the shear zone temperatures due to high thermal conductivity of PCBN tools.
S. V. Prants
2017-06-01
Full Text Available A Lagrangian methodology is developed to simulate, track, document and analyze the origin and history of water masses in ocean mesoscale features. It aims to distinguish whether water masses inside the mesoscale eddies originated from the main currents in the Kuroshio–Oyashio confluence zone. By computing trajectories for a large number of synthetic Lagrangian particles advected by the AVISO velocity field after the Fukushima accident, we identify and track the mesoscale eddies which were sampled in the cruises in 2011 and 2012 and estimate their risk of being contaminated by Fukushima-derived radionuclides. The simulated results are compared with in situ measurements, showing a good qualitative correspondence.
Lagrangian Submanifolds Foliated by (n-1)-spheres in R2n
Henri ANCIAUX; Ildefonso CASTRO; Pascal ROMON
2006-01-01
We study Lagrangian submanifolds foliated by (n-1)-spheres in R2n for n≥3. We give a general parametrization for such submanifolds, and refine that description when the submanifold is special Lagrangian, self-similar, Hamiltonian stationary or has mean curvature vector of constant length. In all these cases, the submanifold is centered, i.e. invariant under the action of SO(n). It suffices then to solve a simple ODE in two variables to describe the geometry of the solutions.
Rashid, M.
2011-01-01
Considering the Lagrangian density of the electromagnetic field, a 4 × 4 transformation matrix is found which can be used to include two of the symmetrized Maxwell’s equations as one of the Euler-Lagrange equations of the complete Lagrangian density. The 4 × 4 transformation matrix introduces newly
Estimation of the Lagrangian structure function constant ¤C¤_{0} from surface-layer wind data
Anfossi, D.; Degrazia, G.; Ferrero, E.
2000-01-01
Eulerian turbulence observations, made in the surface layer under unstable conditions (z/L > 0), by a sonic anemometer were used to estimate the Lagrangian structure function constant C(0). Two methods were considered. The first one makes use of a relationship, widely used in the Lagrangian stoch...
Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering
Rampf, Cornelius [Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen, Physikzentrum RWTH-Melaten, D-52056 Aachen (Germany); Buchert, Thomas, E-mail: rampf@physik.rwth-aachen.de, E-mail: buchert@obs.univ-lyon1.fr [Université de Lyon, Observatoire de Lyon, Centre de Recherche Astrophysique de Lyon, CNRS UMR 5574: Université Lyon 1 and École Normale Supérieure de Lyon, 9 avenue Charles André, F-69230 Saint-Genis-Laval (France)
2012-06-01
We investigate the Lagrangian perturbation theory of a homogeneous and isotropic universe in the non-relativistic limit, and derive the solutions up to the fourth order. These solutions are needed for example for the next-to-leading order correction of the (resummed) Lagrangian matter bispectrum, which we study in an accompanying paper. We focus on flat cosmologies with a vanishing cosmological constant, and provide an in-depth description of two complementary approaches used in the current literature. Both approaches are solved with two different sets of initial conditions — both appropriate for modelling the large-scale structure. Afterwards we consider only the fastest growing mode solution, which is not affected by either of these choices of initial conditions. Under the reasonable approximation that the linear density contrast is evaluated at the initial Lagrangian position of the fluid particle, we obtain the nth-order displacement field in the so-called initial position limit: the nth order displacement field consists of 3(n-1) integrals over n linear density contrasts, and obeys self-similarity. Then, we find exact relations between the series in Lagrangian and Eulerian perturbation theory, leading to identical predictions for the density contrast and the peculiar-velocity divergence up to the fourth order.
Applications of Lagrangian blending functions for grid generation around airplane geometries
Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.; Smith, Robert E.
1990-01-01
A simple procedure has been developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation has been employed for the grid distributions.
Application of Lagrangian blending functions for grid generation around airplane geometries
Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.
1990-01-01
A simple procedure was developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation was employed for the grid distributions.
On the generalized Helmholtz conditions for Lagrangian systems with dissipative forces
Crampin, M; Sarlet, W
2010-01-01
In two recent papers necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not independent and prove a stronger result accordingly.
Bifurcations of the Lagrangian orbits from the classical to the curved 3-body problem
Diacu, Florin
2016-11-01
We consider the 3-body problem of celestial mechanics in Euclidean, elliptic, and hyperbolic spaces and study how the Lagrangian (equilateral) relative equilibria bifurcate when the Gaussian curvature varies. We thus prove the existence of new classes of orbits. In particular, we find some families of isosceles triangles, which occur in elliptic space.
eHDECAY: an Implementation of the Higgs Effective Lagrangian into HDECAY
Contino, Roberto; Grojean, Christophe; Muhlleitner, Margarete; Spira, Michael
2014-01-01
We present eHDECAY, a modified version of the program HDECAY which includes the full list of leading bosonic operators of the Higgs effective Lagrangian with a linear or non-linear realization of the electroweak symmetry and implements two benchmark composite Higgs models.
A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}
Golovko, Roman
2011-01-01
We study the relation of an embedded Lagrangian cobordism between two closed orientable Legendrian submanifolds of R^{2n+1}. More precisely, we invesigate the behavior of the Thurston-Bennequin number and linearized Legendrian contact homology under this relation. The result about the Thurston-Bennequin number can be considered as a generalization of the result of Chantraine which holds when n=1.
Eulerian–Lagrangian RANS Model Simulations of the NIST Turbulent Methanol Spray Flame
Zhu, Shanglong; Roekaerts, Dirk; Pozarlik, Artur; Meer, van der Theo
2015-01-01
A methanol spray flame in a combustion chamber of the NIST was simulated using an Eulerian–Lagrangian RANS model. Experimental data and previous numerical investigations by other researchers on this flame were analyzed to develop methods for more comprehensive model validation. The inlet boundary co
On the Hamiltonian and Lagrangian formulation of classical dynamics for particles with spin
Ruijgrok, Th.W.; Vlist, H. van der
1980-01-01
The classical mechanics of nonrelativistic particles is generalized by also considering the spin components as canonical variables. Poisson-brackets and canonical transformations are discussed. The Lagrangian equations of motion are given and it is shown how rotational invariance leads to well known
Lagrangian models of the particles with spin the first seventy years
Frydryszak, A M
1996-01-01
We briefly review models of relativistic particles with spin. Departing from the oldest attempts to describe the spin within the lagrangian framework we pass through various non supersymmetric models. Then the component and superfield formulations of the spinning particle and superparticle models are reviewed. Our focus is mainly on the classical side of the problem, but some quantization questions are mentioned as well.
Dodin, I Y; Fraiman, G M
2003-01-01
The Lagrangian and Hamiltonian functions describing average motion of a relativistic particle under the action of intensive high-frequency electromagnetic radiation are obtained. In weak, low-frequency background fields, such a particle on average drifts with an effective, relativistically invariant mass, which depends on the intensity of the electromagnetic field.
Singular Lagrangian, Hamiltonization and Jacobi last multiplier for certain biological systems
Guha, Partha; Ghose Choudhury, Anindya
2013-07-01
We study the construction of singular Lagrangians using Jacobi's last multiplier (JLM). We also demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonian of the Host-Parasite model and a Lotka-Volterra mutualistic system, both of which are well known first-order systems of differential equations arising in biology.
Lagrangian duality applied to the vehicle routing problem with time windows
Kallehauge, Brian; Larsen, Jesper; Madsen, Oli B.G.
2006-01-01
This paper considers the vehicle routing problem with time windows, where the service of each customer must start within a specified time interval. We consider the Lagrangian relaxation of the constraint set requiring that each customer must be served by exactly one vehicle yielding a constrained...
Matching in the method of controlled Lagrangians and IDA-passivity based control
Blankenstein, Guido; Ortega, Romeo; Schaft, van der Arjan J.; Astolfi, A.
2006-01-01
This paper reviews the method of controlled Lagrangians and the interconnection and damping assignment passivity based control (IDA-PBC)method. Both methods have been presented recently in the literature as means to stabilize a desired equilibrium point of an Euler-Lagrange system, respectively Hami
Resonance Chiral Lagrangian Currents and Experimental Data for $\\tau^-\\to\\pi^{-}\\pi^{-}\\pi^{+}\
Nugent, I M; Roig, P; Shekhovtsova, O; Was, Z
2013-01-01
In this paper we document the modifications introduced to the previous version of the Resonance Chiral Lagrangian current ({\\it Phys.Rev.} {\\bf D86} (2012) 113008) of the $\\tau^\\pm \\to \\pi^\\pm \\pi^\\pm \\pi^\\mp \
Comment on ``A reduction of order two for infinite-order Lagrangians''
Damour, Thibault; Schäfer, Gerhard
1988-02-01
It is pointed out that the reduced two-particle Hamiltonian for the Wheeler-Feynman electrodynamics up to order c-4 was incorrectly calculated in the paper of Jaén, Llosa, and Molina. The correct expression is given, and shown to be equivalent (when e1/m1=e2/m2) to the Golubenkov-Smorodinskii Lagrangian.
An improved Lagrangian relaxation and dual ascent approach to facility location problems
Jörnsten, Kurt; Klose, Andreas
2016-01-01
method for optimizing both the semi-Lagrangian dual function as well as its simplified form for the case of a generic discrete facility location problem and apply the method to the uncapacitated facility location problem. Our computational results show that the method generally only requires a very few...
Equivalence of two independent calculations of the higher order guiding center Lagrangian
Parra, F. I. [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom and Culham Centre for Fusion Energy, Abingdon OX14 3DB (United Kingdom); Calvo, I. [Laboratorio Nacional de Fusión, CIEMAT, 28040 Madrid (Spain); Burby, J. W.; Squire, J. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Qin, H. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)
2014-10-15
The difference between the guiding center phase-space Lagrangians derived in J. W. Burby et al. [Phys. Plasmas 20, 072105 (2013)] and F. I. Parra and I. Calvo [Plasma Phys. Controlled Fusion 53, 045001 (2011)] is due to a different definition of the guiding center coordinates. In this brief communication, the difference between the guiding center coordinates is calculated explicitly.
The effective chiral Lagrangian from dimension-six parity and time-reversal violation
de Vries, J.; Mereghetti, E.; Timmermans, R.G.E.; van Kolck, U.
2013-01-01
We classify the parity- and time-reversal-violating operators involving quark and gluon fields that have effective dimension six: the quark electric dipole moment, the quark and gluon chromo-electric dipole moments, and four four-quark operators. We construct the effective chiral Lagrangian with had
When Lagrangian stochastic models for turbulent dispersion are applied to complex flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behavior in the numerical solution. This paper discusses numerical considerations when solving the Langevin-based particle velo...
Osp(1,2)-covariant Lagrangian quantization of general gauge theories
Geyer, B.; Lavrov, P.M. [Universitat Leipzig, Naturwissenschaftlich-Theoretisches Zentrum, Leipzig (Germany); Muelsch, D. [Wissenschaftszentrum Leipzig e.V., Leipzig (Germany)
1998-10-01
An osp(1, 2)-covariant Lagrangian quantization of general gauge theories is introduced which also applies to massive fields. It generalizes the Batalin-Vilkovisky and the Sp(2)-covariant field-antifield approach and guarantees symplectic invariance of the quantized action. Massive gauge theories with closed algebra are considered as an example. (author)
Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems
Campoamor-Stursberg, Rutwig, E-mail: rutwig@ucm.es [Faculted de Ciencias Matematicas Universidad Complutense, Instituto de Matemática Interdisciplinar and Departamento Geometría y Topología (Spain)
2017-03-15
Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.
Progress in mixed Eulerian-Lagrangian finite element simulation of forming processes
Huetink, Han; Vreede, P.T.; van der Lugt, J.
1990-01-01
A review is given of a mixed Eulerian-Lagrangian finite element method for simulation of forming processes. This method permits incremental adaptation of nodal point locations independently from the actual material displacements. Hence numerical difficulties due to large element distortions, as may
Adaptive multiresolution semi-Lagrangian discontinuous Galerkin methods for the Vlasov equations
Besse, N.; Deriaz, E.; Madaule, É.
2017-03-01
We develop adaptive numerical schemes for the Vlasov equation by combining discontinuous Galerkin discretisation, multiresolution analysis and semi-Lagrangian time integration. We implement a tree based structure in order to achieve adaptivity. Both multi-wavelets and discontinuous Galerkin rely on a local polynomial basis. The schemes are tested and validated using Vlasov-Poisson equations for plasma physics and astrophysics.
SO(n)-Invariant Special Lagrangian Submanifolds of Cn+1 with Fixed Loci
无
2006-01-01
Let SO(n) act in the standard way on Cn and extend this action in the usual way toCn+1=C((+))Cn.It is shown that a nonsingular special Lagrangian submanifold L (∩) Cn+1 that is invariant under this SO(n)-action intersects the fixed C (∩) Cn+1 in a nonsingular real-analytic arc A (which may be empty). If n ＞ 2, then A has no compact component.Conversely, an embedded, noncompact nonsingular real-analytic arc A (∩) C lies in an embedded nonsingular special Lagrangian submanifold that is SO(n)-invariant. The same existence result holds for compact A if n = 2. If A is connected, there exist n distinct nonsingular SO(n)-invariant special Lagrangian extensions of A such that any embedded nonsingular SO(n)-invariant special Lagrangian extension of A agrees with one of these n extensions in some open neighborhood of A.The method employed is an analysis of a singular nonlinear PDE and ultimately calls on the work of Gérard and Tahara to prove the existence of the extension.
2014-04-01
drifter position over some time scale (Hernandez et al. 1995; Ishikawa et al. 1996), or by assimilating the La- grangian data directly by evolving a series...Kuznetsov, and C. K. R. T. Jones, 2002: Lagrangian data assimilation for point vortex systems. J. Turbul., 3, 053, doi:10.1088/1468-5248/3/1/053. Ishikawa , Y
Geometric characterization for the least Lagrangian action of n-body problems
张世清; 周青
2001-01-01
For n-body problems with quasihomogeneous potentials in Rk (2［n/2］≤k) we prove that the minimum of the Lagrangian action integral defined on the zero mean loop space is exactly the circles with center at the origin and the configuration of the n-bodies is always a regular n-1 simplex with fixed side length.
A Primal-Dual Augmented Lagrangian Method for Optimal Control of ...
A Primal-Dual Augmented Lagrangian Method for Optimal Control of ... Log in or Register to get access to full text downloads. ... In this paper we are concerned with time-varying optimal control problems whose cost is quadratic and whose ...
k Spectrum of Finite Lifetime Passive Scalars in Lagrangian Chaotic Fluid Flows
Nam, Keeyeol; Antonsen, Thomas M., Jr.; Guzdar, Parvez N.; Ott, Edward
1999-10-01
The power law exponent for the wave number power spectrum of a passive scalar field in Lagrangian chaotic flows is found to differ from the classical value of -1 (Batchelor's law) when the passive particles have a finite lifetime for exponential decay. A theory based on the chaotic dynamics of the passive scalar is developed and compared to numerical simulation results.
Effective Lagrangian of C PN -1 models in the large N limit
Rossi, Paolo
2016-08-01
The effective low energy Lagrangian of C PN -1 models in d <4 dimensions can be constructed in the large N limit by solving the saddle point equations in the presence of a constant field strength. The two-dimensional case is explicitly worked out, and possible applications are briefly discussed.
梁立孚
1999-01-01
By using the involutory transformations, the classical variational principle——Hamiltonian principle of two kinds of variables in general mechanics is advanced and by using undetermined Lagrangian multiplier method, the generalized variational principles and generalized variational principles with subsidiary conditions are established. The stationary conditions of various kinds of variational principles are derived and the relational problems discussed.
Attili, Antonio
2013-09-01
A Lagrangian particle scheme is applied to the solution of soot dynamics in turbulent nonpremixed flames. Soot particulate is described using a method of moments and the resulting set of continuum advection-reaction equations is solved using the Lagrangian particle scheme. The key property of the approach is the independence between advection, described by the movement of Lagrangian notional particles along pathlines, and internal aerosol processes, evolving on each notional particle via source terms. Consequently, the method overcomes the issues in Eulerian grid-based schemes for the advection of moments: errors in the advective fluxes pollute the moments compromising their realizability and the stiffness of source terms weakens the stability of the method. The proposed scheme exhibits superior properties with respect to conventional Eulerian schemes in terms of stability, accuracy, and grid convergence. Taking into account the quality of the solution, the Lagrangian approach can be computationally more economical than commonly used Eulerian schemes as it allows the resolution requirements dictated by the different physical phenomena to be independently optimized. Finally, the scheme posseses excellent scalability on massively parallel computers. © 2013 Elsevier Ltd.
Pressure-field extraction from Lagrangian flow measurements: first experiences with 4D-PTV data
Neeteson, N. J.; Bhattacharya, S.; Rival, D. E.; Michaelis, D.; Schanz, D.; Schröder, A.
2016-06-01
As a follow-up to a previous proof-of-principle study, a novel Lagrangian pressure-extraction technique is analytically evaluated, and experimentally validated using dense 4D-PTV data. The technique is analytically evaluated using the semi-three-dimensional Taylor-Green vortex, and it is found that the Lagrangian technique out-performs the standard Eulerian technique when Dirichlet boundary conditions are enforced. However, the Lagrangian technique produces worse estimates of the pressure field when Neumann boundary conditions are enforced on boundaries with strong pressure gradients. The technique is experimentally validated using flow data obtained for the case of a free-falling, index-matched sphere at Re=2100. The experimental data were collected using a four-camera particle tracking velocimetry measurement system, and processed using 4D-PTV. The pressure field is then extracted using both the Eulerian and Lagrangian techniques, and the resulting pressure fields are compared. Qualitatively, the pressure fields agree; however, quantitative differences are found with respect to the magnitude of the pressure minima on the side of the sphere. Finally, the pressure-drag coefficient is estimated using each technique, and the two techniques are found to be in very close agreement. A comparison to a reference value from literature confirms that the drag coefficient estimates are reasonable, demonstrating the validity of the technique.
Marom, Gil; Bluestein, Danny
2016-01-01
This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using Lagrangian methods with Eulerian computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and ti...
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Rieben, R N; White, D A; Wallin, B K; Solberg, J M
2006-06-12
We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.
Lagrangian flows within reflecting internal waves at a horizontal free-slip surface
Zhou, Qi, E-mail: q.zhou@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA (United Kingdom); Diamessis, Peter J. [School of Civil and Environmental Engineering, Cornell University, Ithaca, New York 14853 (United States)
2015-12-15
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 drift 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.
A High-order Eulerian-Lagrangian Finite Element Method for Coupled Electro-mechanical Systems
Brandstetter, Gerd
The main focus of this work is on the development of a high-order Eulerian-Lagrangian finite element method for the simulation of electro-mechanical systems. The coupled problem is solved by a staggered scheme, where the mechanical motion is discretized by standard Lagrangian finite elements, and the electrical field is solved on a fixed Eulerian grid with embedded boundary conditions. Traditional Lagrangian-Lagrangian or arbitrary Lagrangian-Eulerian (ALE) methods encounter deficiencies, for example, when dealing with mesh distortion due to large deformations, or topology changes due to contacting bodies. The presented Eulerian-Lagrangian approach addresses these issues in a natural way. Within this context we develop a high-order immersed boundary discontinuous-Galerkin (IB-DG) method, which is shown to be necessary for (i) the accurate representation of the electrical gradient along nonlinear boundary features such as singular corners, and (ii) to achieve full convergence during the iterative global solution. We develop an implicit scheme based on the mid-point rule, as well as an explicit scheme based on the centered-difference method, with the incorporation of energy conserving, frictionless contact algorithms for an elastic-to-rigid-surface contact. The performance of the proposed method is assessed for several benchmark tests: the electro-static force vector around a singular corner, the quasi-static pull-in of an electro-mechanically actuated switch, the excitation of a carbon nanotube at resonance, and the cyclic impact simulation of a micro-electro-mechanical resonant-switch. We report improved accuracy for the high-order method as compared to low-order methods, and linear convergence in the iterative solution of the staggered scheme. Additionally, we investigate a Newton-Krylov shooting scheme in order to directly find cyclic steady states of electro-mechanical devices excited at resonance-- as opposed to a naive time-stepping from zero initial
Satoh, Masaki; Damtp
1999-10-01
The meridional distribution of potential vorticity (PV) in the troposphere is examined in terms of the Lagrangian transport by using an idealistic general circulation model. A zonally uniform forcing and uniform boundary conditions are applied to the model to particularly examine the PV structure in the mid-latitudes and the subtropics. Trajectories of air parcels released from each grid point of the model and Lagrangian changes in PV are calculated for a period of 60days. Values of PV of each parcel are changing along the Lagrangian motions due to the diabatic effect, the frictional effect and the mixing effect which has smaller scales than those resolvable in the model. Both diabatic and frictional effects are dominant in the lower layers, and the mixing effect is larger in the other regions. It is found that the zonal mean PV changes have different characteristics between the "Underworld" in which isentropes intersect the ground and the "Middleworld" in which isentropes are above the ground and intersect the tropopause. In the Underworld, the zonal mean PV changes are determined by the equatorial flow in the lower layers. In particular, the PV changes are negative in the lower layers of the low- and the mid-latitudes. (The sign of PV tendency is for the northern hemisphere. The southern hemispheric tendency is opposite as in the followings.) This negative tendency is due to the diabatic effect near the surface. In the Middleworld, there remain positive and negative tendency regions, which are resulted from the isentropic mixing. In general, if a parcel moves poleward in the mid-latitudes, the value of PV increases, whereas the value of PV decreases if a parcel moves equatorward. The sign of the Lagrangian mean change in PV corresponds to whether the Lagrangian mean motions cross the PV contours equatorward or poleward in the meridional plane. In particular, the contour of no change in PV has a similar shape to that of meridional distribution of PV in the mid
Rybnikov, A. K.
2017-01-01
The paper is devoted to the investigation, using the method of Cartan-Laptev, of the differential-geometric structure associated with a Lagrangian L, depending on a function z of the variables t, x 1,..., x n and its partial derivatives. Lagrangians of this kind are considered in theoretical physics (in field theory). Here t is interpreted as time, and x 1,..., x n as spatial variables. The state of the field is characterized by a function z( t, x 1,..., x n ) (a field function) satisfying the Euler equation, which corresponds to the variational problem for the action integral. In the present paper, the variables z( t, x 1,..., x n are regarded as adapted local coordinates of a bundle of general type M with n-dimensional fibers and 1-dimensional base (here the variable t is simultaneously a local coordinate on the base). If we agree to call t time, and a typical fiber an n-dimensional space, then M can be called the spatiotemporal bundle manifold. We consider the variables t, x 1,..., x n , z (i.e., the variables t, x 1,..., x n with the added variable z) as adapted local coordinates in the bundle H over the fibered base M. The Lagrangian L, which is a coefficient in the differential form of the variational action integral in the integrand, is a relative invariant given on the manifold J 1 H (the manifold of 1-jets of the bundle H). In the present paper, we construct a tensor with components Λ00, Λ0 i , Λ ij (Λ ij = Λ ji ) which is generated by the fundamental object of the structure associated with the Lagrangian. This tensor is an invariant (with respect to admissible transformations the variables t, x 1,..., x n , z) analog of the energy-momentum tensor of the classical theory of physical fields. We construct an invariant I, a vector G i , and a bivalent tensor G jk generated by the Lagrangian. We also construct a relative invariant of E (in the paper, we call it the Euler relative invariant) such that the equation E = 0 is an invariant form of the Euler
Liao, Yi
2012-01-01
We calculate the multi-photon decay widths of the Higgs boson from an effective Lagrangian for a system of electromagnetic and Higgs fields. We utilize a low-energy theorem to connect the above Lagrangian to the Heisenberg-Euler effective Lagrangian induced by charged particles that gain mass from interactions with the Higgs boson. In the standard model only the W^\\pm gauge bosons and the top quark are relevant, and we compute their contributions to the effective couplings and the multi-photon decay widths of the Higgs boson.
The Eulerian- and Lagrangian-mean flows induced by stationary, dissipating planetary waves
Takahashi, M.; Uryu, M.
1981-01-01
The Eulerian- and the Lagrangian-mean flows induced by stationary, dissipating planetary waves are discussed by employing a simple channel model on a beta-plane. It is assumed that the wave is excited by the bottom undulation and dissipated by Newtonian cooling with relaxation time alpha and by Rayleigh friction with (lambda)(alpha), lambda being constant. Three cases where lambda is equal to one are discussed: (1) the basic zonal wind U sub 0 and the dissipation rate alpha are both constant; (2) U sub 0 varies with height while alpha is constant; and (3) U sub 0 and alpha both vary with height. In case (1), the Eulerian- and the Lagrangian-mean fields are shown to depend on the difference between the dissipation scale-height and the density scale-height. In case (2) and case (3), it is shown that the results for case (1) are modified under slightly more realistic situations.
Marom, Gil; Bluestein, Danny
2016-01-01
This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using Lagrangian methods with Eulerian computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and time averaging. This study demonstrated that the implementation assumptions can significantly affect the resulting stress accumulation, i.e., the blood damage model predictions. Careful considerations should be taken in the use of Lagrangian models. Ultimately, the appropriate assumptions should be considered based the physics of the specific case and sensitivity analysis, similar to the ones presented here, should be employed.
Hyun, Chang Ho; Lee, Hee-Jung
2016-01-01
We investigate the parity-violating pion-nucleon-nucleon coupling constant $h^1_{\\pi NN}$, based on the chiral quark-soliton model. We employ an effective weak Hamiltonian that takes into account the next-to-leading order corrections from QCD to the weak interactions at the quark level. Using the gradient expansion, we derive the leading-order effective weak chiral Lagrangian with the low-energy constants determined. The effective weak chiral Lagrangian is incorporated in the chiral quark-soliton model to calculate the parity-violating $\\pi NN$ constant $h^1_{\\pi NN}$. We obtain a value of about $10^{-7}$ at the leading order. The corrections from the next-to-leading order reduce the leading order result by about 20~\\%.
Podglajen, Aurélien; Hertzog, Albert; Plougonven, Riwal; Legras, Bernard
2016-04-01
Wave-induced Lagrangian fluctuations of temperature and vertical velocity in the lower stratosphere are quantified using measurements from superpressure balloons (SPBs). Observations recorded every minute along SPB flights allow the whole gravity wave spectrum to be described and provide unprecedented information on both the intrinsic frequency spectrum and the probability distribution function of wave fluctuations. The data set has been collected during two campaigns coordinated by the French Space Agency in 2010, involving 19 balloons over Antarctica and 3 in the deep tropics. In both regions, the vertical velocity distributions depart significantly from a Gaussian behavior. Knowledge on such wave fluctuations is essential for modeling microphysical processes along Lagrangian trajectories. We propose a new simple parameterization that reproduces both the non-Gaussian distribution of vertical velocities (or heating/cooling rates) and their observed intrinsic frequency spectrum.
Variational assimilation of Lagrangian trajectories in the Mediterranean ocean Forecasting System
J. A. U. Nilsson
2011-12-01
Full Text Available A novel method for three-dimensional variational assimilation of Lagrangian data with a primitive-equation ocean model is proposed. The assimilation scheme was implemented in the Mediterranean ocean Forecasting System and evaluated for a 4-month period. Four experiments were designed to assess the impact of trajectory assimilation on the model output, i.e. the sea-surface height, velocity, temperature and salinity fields. It was found from the drifter and Argo trajectory assimilation experiment that the forecast skill of surface-drifter trajectories improved by 15 %, that of intermediate-depth float trajectories by 20 %, and moreover, the forecasted sea-surface height fields improved locally by 5 % compared to satellite data, while the quality of the temperature and salinity fields remained at previous levels. In conclusion, the addition of Lagrangian trajectory assimilation proved to reduce the uncertainties in the model fields, thus yielding a higher accuracy of the ocean forecasts.
Solution to the quadratic assignment problem using semi-Lagrangian relaxation
Huizhen Zhang; Cesar Beltran-Royo; Bo Wang; Liang Ma; Ziying Zhang
2016-01-01
The semi-Lagrangian relaxation (SLR), a new exact method for combinatorial optimization problems with equality con-straints, is applied to the quadratic assignment problem (QAP). A dual ascent algorithm with finite convergence is developed for solving the semi-Lagrangian dual problem associated to the QAP. We perform computational experiments on 30 moderately difficult QAP instances by using the mixed integer programming solvers, Cplex, and SLR+Cplex, respectively. The numerical results not only further il ustrate that the SLR and the developed dual ascent algorithm can be used to solve the QAP reasonably, but also dis-close an interesting fact: comparing with solving the unreduced problem, the reduced oracle problem cannot be always effectively solved by using Cplex in terms of the CPU time.
Simultaneous assessment of Lagrangian strain and temperature fields by improved IR-DIC strategy
Wang, X. G.; Liu, C. H.; Jiang, C.
2017-07-01
This paper focuses on the development of a novel digital image correlation strategy based on infrared imaging (IR-DIC) for realizing simultaneous assessment of Lagrangian strain and temperature fields. A major difficulty in the IR-DIC is the evolution of the thermal field during deformation that is unexpected in the image correlation. Two solutions are proposed to tackle this difficulty. The first solution is to utilize a high-pass filter to eliminate the variation part of the thermal signal, and the second solution is to employ an advanced metric, the mutual information, as the correlation criterion. Both methods are verified through a tensile test performed on a notched specimen. The estimated displacement and strain fields demonstrate well the desirable performance of the proposed methods. Thanks to the kinematic field assessment, the obtained thermal fields can be described in the Lagrangian coordinate system, thus the temperature evolution of the material points during deformation can be followed effectively.
In-medium effective chiral lagrangians and the pion mass in nuclear matter
Wirzba, A; Wirzba, Andreas; Thorsson, Vesteinn
1995-01-01
We argue that the effective pion mass in nuclear matter obtained from chiral effective lagrangians is unique and does not depend on off-mass-shell extensions of the pion fields as e.g. the PCAC choice. The effective pion mass in isospin symmetric nuclear matter is predicted to increase slightly with increasing nuclear density, whereas the effective time-like pion decay constant and the magnitude of the density-dependent quark condensate decrease appreciably. The in-medium Gell-Mann-Oakes-Renner relation as well as other in-medium identities are studied in addition. Finally, several constraints on effective lagrangians for the description of the pion propagation in isospin symmetric, isotropic and homogenous nuclear matter are discussed. (Talk presented at the workshop ``Hirschegg '95: Hadrons in Nuclear Matter'', Hirschegg, Kleinwalsertal, Austria, January 16-21, 1995)
The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows
Lufkin, Eric A.; Hawley, John F.
1993-01-01
We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.
A new Lagrangian method for three-dimensional steady supersonic flows
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.
Lagrangian velocity statistics of directed launch strategies in a Gulf of Mexico model
M. Toner
2004-01-01
Full Text Available The spatial dependence of Lagrangian displacement and velocity statistics is studied in the context of a data assimilating numerical model of the Gulf Mexico. In the active eddy region of the Western Gulf, a combination of Eulerian and Lagrangian measures are used to locate strongly hyperbolic regions of the flow. The statistics of the velocity field sampled by sets of drifters launched specifically in these hyperbolic regions are compared to those produced by randomly chosen launch sites. The results show that particle trajectories initialized in hyperbolic regions preferentially sample a broader range of Eulerian velocities than do members of ensembles of randomly launched drifters. The velocity density functions produced by the directed launches compare well with Eulerian velocity pdfs. Implications for the development of launch strategies to improve Eulerian velocity field reconstruction from drifter data are discussed.
Gauge-invariant Lagrangians for mixed-antisymmetric higher spin fields
Reshetnyak, A. A.
2017-03-01
Lagrangian descriptions of integer HS representations of the Poincare group subject to a Young tableaux Y[ {\\hat s}_1,{\\hat s}_2 ] with two columns are constructed within a metric-like formulation in a d-dimensional flat space-time on a basis of the BRST approach. A Lorentz-invariant resolution of the BRST complex within BRST formulations produces a gauge-invariant Lagrangian in terms of the initial tensor field Φ _[ μ ]_{\\hat s}_1,[ μ ]_{\\hat s}_2 subject to Y[ {\\hat s}_1,{\\hat s}_2 ] with an additional tower of gauge parameters realizing the ( {\\hat s}_1 - 1 )-th stage reducible theory with a specific dependence on the value ( {\\hat s}_1 - {\\hat s}_2 ) = 0,1, \\ldots {\\hat s_1}. Minimal BRST-BV action is suggested, providing objects appropriate to construct interacting models with mixed-antisymmetric fields in a general framework.
Semi-implicit semi-Lagrangian modelling of the atmosphere: a Met Office perspective
Benacchio Tommaso
2016-09-01
Full Text Available The semi-Lagrangian numerical method, in conjunction with semi-implicit time integration, provides numerical weather prediction models with numerical stability for large time steps, accurate modes of interest, and good representation of hydrostatic and geostrophic balance. Drawing on the legacy of dynamical cores at the Met Office, the use of the semi-implicit semi-Lagrangian method in an operational numerical weather prediction context is surveyed, together with details of the solution approach and associated issues and challenges. The numerical properties and performance of the current operational version of the Met Office’s numerical model are then investigated in a simplified setting along with the impact of different modelling choices.
Drifter dispersion in the Adriatic Sea: Lagrangian data and chaotic model
G. Lacorata
Full Text Available We analyze characteristics of drifter trajectories from the Adriatic Sea with recently introduced nonlinear dynamics techniques. We discuss how in quasi-enclosed basins, relative dispersion as a function of time, a standard analysis tool in this context, may give a distorted picture of the dynamics. We further show that useful information may be obtained by using two related non-asymptotic indicators, the Finite-Scale Lyapunov Exponent (FSLE and the Lagrangian Structure Function (LSF, which both describe intrinsic physical properties at a given scale. We introduce a simple chaotic model for drifter motion in this system, and show by comparison with the model that Lagrangian dispersion is mainly driven by advection at sub-basin scales until saturation sets in.
Key words. Oceanography: General (marginal and semi-closed seas – Oceanography: Physical (turbulence, diffusion, and mixing processes; upper ocean processes
Lagrangian velocity auto-correlations in statistically-steady rotating turbulence
Del Castello, Lorenzo
2013-01-01
Lagrangian statistics of passive tracers in rotating turbulence is investigated by Particle Tracking Velocimetry. A confined and steadily-forced turbulent flow is subjected to five different rotation rates. The PDFs of the velocity components clearly reveal the anisotropy induced by background rotation. Although the statistical properties of the horizontal turbulent flow field are approximately isotropic, in agreement with previously reported results by van Bokhoven and coworkers [Phys. Fluids 21, 096601 (2009)], the velocity component parallel to the (vertical) rotation axis gets strongly reduced (compared to the horizontal ones) while the rotation is increased. The auto-correlation coefficients of all three components are progressively enhanced for increasing rotation rates, although the vertical one shows a tendency to decrease for slow rotation rates. The decorrelation is approximately exponential. Lagrangian data compare favourably with previously reported Eulerian data for horizontal velocity components...
On a Lagrangian Reduction and a Deformation of Completely Integrable Systems
Arnaudon, Alexis
2016-10-01
We develop a theory of Lagrangian reduction on loop groups for completely integrable systems after having exchanged the role of the space and time variables in the multi-time interpretation of integrable hierarchies. We then insert the Sobolev norm H^1 in the Lagrangian and derive a deformation of the corresponding hierarchies. The integrability of the deformed equations is altered, and a notion of weak integrability is introduced. We implement this scheme in the AKNS and SO(3) hierarchies and obtain known and new equations. Among them, we found two important equations, the Camassa-Holm equation, viewed as a deformation of the KdV equation, and a deformation of the NLS equation.
Conformally related metrics and Lagrangians and their physical interpretation in cosmology
Tsamparlis, Michael; Basilakos, Spyros; Capozziello, Salvatore
2013-01-01
Conformally related metrics and Lagrangians are considered in the context of scalar-tensor gravity cosmology. After the discussion of the problem, we pose a lemma in which we show that the field equations of two conformally related Lagrangians are also conformally related if and only if the corresponding Hamiltonian vanishes. Then we prove that to every non-minimally coupled scalar field, we may associate a unique minimally coupled scalar field in a conformally related space with an appropriate potential. The latter result implies that the field equations of a non-minimally coupled scalar field are the same at the conformal level with the field equations of the minimally coupled scalar field. This fact is relevant in order to select physical variables among conformally equivalent systems. Finally, we find that the above propositions can be extended to a general Riemannian space of n-dimensions.
GYSELA, a full-f global gyrokinetic Semi-Lagrangian code for ITG turbulence simulations
Grandgirard, V.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Crouseilles, N.; Latu, G.; Sonnendrücker, E.; Besse, N.; Bertrand, P.
2006-11-01
This work addresses non-linear global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence with the GYSELA code. The particularity of GYSELA code is to use a fixed grid with a Semi-Lagrangian (SL) scheme and this for the entire distribution function. The 4D non-linear drift-kinetic version of the code already showns the interest of such a SL method which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been upgrated to run 5D simulations of toroidal ITG turbulence. Linear benchmarks and non-linear first results prove that semi-lagrangian codes can be a credible alternative for gyrokinetic simulations.
Lagrangian neoclassical transport theory applied to the region near the magnetic axis
Satake, Shinsuke [The Graduate Univ. for Advanced Studies, Dept. of Fusion Science, Toki, Gifu (Japan); Okamoto, Masao; Sugama, Hideo [National Inst. for Fusion Science, Toki, Gifu (Japan)
2002-06-01
Neoclassical transport theory around the magnetic axis of a tokamak is studied, in which relatively wide ''potato'' orbits play an important role in transport. Lagrangian formulation of transport theory, which has been investigated to reflect finiteness of guiding-center orbit widths to transport equations, is developed in order to analyze neoclassical transport near the axis for a low-collisionality plasma. The treatment of self-collision term in Lagrangian formulation is revised to retain momentum conservation property of it. With directly reflecting the orbital properties of all the types of orbits in calculation, the ion thermal conductivity around the axis is found to decrease than from that predicted by conventional neoclassical theory. This result supports recent numerical simulations which show the reduction of thermal conductivity near the magnetic axis. (author)
Spectral - Lagrangian methods for Collisional Models of Non - Equilibrium Statistical States
Gamba, Irene M
2007-01-01
We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann Transport Equation for Variable Hard Potential (VHP) collision kernels with conservative or non-conservative binary interactions.The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computing is reduced to a separate integral over the unit sphere $S^2$. In addition, the conservation of moments is enforced by Lagrangian constraints. The resulting scheme is very versatile and adjusts in a very simple manner, to several cases that involve energy dissipation due to local micro-reversibility (inelastic interactions) or elastic model of slowing down process. Our simulations are benchmarked with the available exact self-similar solutions, exact moment equations and analytical estimates for homogeneous Boltzmann equation for both elastic and inelastic VHP interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the num...
A Lagrangian particle method with remeshing for tracer transport on the sphere
Bosler, Peter A.; Kent, James; Krasny, Robert; Jablonowski, Christiane
2017-07-01
A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracer integral, and preservation of nonlinear correlation in a pair of tracers. We compare results obtained using LPM and the Lin-Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.
Lagrangian quantum field theory in momentum picture. IV. Commutation relations for free fields
Iliev, Bozhidar Z
2007-01-01
Possible (algebraic) commutation relations in the Lagrangian quantum theory of free (scalar, spinor and vector) fields are considered from mathematical view-point. As sources of these relations are employed the Heisenberg equations/relations for the dynamical variables and a specific condition for uniqueness of the operators of the dynamical variables (with respect to some class of Lagrangians). The paracommutation relations or some their generalizations are pointed as the most general ones that entail the validity of all Heisenberg equations. The simultaneous fulfillment of the Heisenberg equations and the uniqueness requirement turn to be impossible. This problem is solved via a redefinition of the dynamical variables, similar to the normal ordering procedure and containing it as a special case. That implies corresponding changes in the admissible commutation relations. The introduction of the concept of the vacuum makes narrow the class of the possible commutation relations; in particular, the mentioned re...
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Solution of the Euler Equations
Anderson, R W; Elliott, N S; Pember, R B
2003-02-14
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. The novel components of the methods are driven by the need to reconcile traditional AMR techniques with the staggered variables and moving, deforming meshes associated with Lagrange based ALE schemes. We develop interlevel solution transfer operators and interlevel boundary conditions first in the case of purely Lagrangian hydrodynamics, and then extend these ideas into an ALE method by developing adaptive extensions of elliptic mesh relaxation techniques. Conservation properties of the method are analyzed, and a series of test problem calculations are presented which demonstrate the utility and efficiency of the method.
Baoshan Zhu; Kyoji Kamemoto
2005-01-01
In this study, an advanced Lagrangian vortexboundary element method is applied to simulate the unsteady impeller-diffuser interactions in a diffuser pump not only for design but also for off-design considerations. In velocity calculations based on the Biot-Savart law we do not have to grid large portions of the flow field and the calculation points are concentrated in the regions where vorticity is present.Lagrangian representation of the evolving vorticity field is well suited to moving boundaries. An integral pressure equation shows that the pressure distribution can be estimated directly from the instantaneous velocity and vorticity field.The numerical results are compared with the experimental data and the comparisons show that the method used in this study can provide us insight into the complicated unsteady impeller-diffuser interaction phenomena in a diffuser pump.
BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields
Moshin, P Yu
2007-01-01
We construct a Lagrangian description for irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a formulation for fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraints subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that only the constraints corresponding to an ...
Eulerian and modified Lagrangian approaches to multi-dimensional condensation and coagulation
Li, Xiang-Yu; Haugen, N E L; Svensson, G
2016-01-01
Turbulence is believed to play a crucial role in cloud droplet growth. It makes the collision process of inertial particles strongly nonlinear, which motivates the study of two rather different numerical schemes. Here, an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and coagulation. 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. Discrepancies between different schemes are most strongly exposed when condensation and coagulation are studied separately, while their combined effects tend to result in smaller discrepancies. In the Eulerian approach, the late growth of the mean particle radius slows down for finer mass bins, especially for collisions caused by different particle sizes. In the Lagrangian approach it is nearly independent of grid resolution at early times and weak...
Yasutake, Nobutoshi; Yamada, Shoichi
2016-01-01
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.
Nonlinear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling
Guan, X. [Pacific Gas and Electric, San Francisco, CA (United States); Luh, P.B.; Zhang, L. [Univ. of Connecticut, Storrs, CT (United States). Dept. of Electrical and Systems Engineering
1995-05-01
When the Lagrangian relaxation technique is used to solve hydrothermal scheduling problems, many subproblems have linear stage-wise cost functions. A well recognized difficulty is that the solutions to these subproblems may oscillate between maximum and minimum generations with slight changes of the multipliers. Furthermore, the subproblem solutions may become singular, i.e., they are un-determined when the linear coefficients become zero. This may result in large differences between subproblem solutions and the optimal primal schedule. In this paper, a nonlinear approximation method is presented which utilizes nonlinear functions, quadratic in this case, to approximate relevant linear cost functions. The analysis shows that the difficulty associated with solution oscillation is reduced, and singularity is avoided. Extensive testing based on Northeast Utilities data indicates that the method consistently generates better schedules than the standard Lagrangian relaxation method.
Contractions of AdS brane algebra and superGalileon Lagrangians
Kamimura, Kiyoshi
2013-01-01
We examine AdS Galileon Lagrangians using the method of non-linear realization. By contractions 1) flat curvature limit and 2) non-relativistic brane algebra limit and 3) (1)+(2) limits we obtain DBI, Newton-Hoock and Galilean Galileons respectively. We make clear how these Lagrangians appear as invariant 4-forms and/or pseudo-invariant Wess-Zumino terms using Maurer-Cartan equations on the coset $G/SO(3,1)$. We show the equations of motion are written in terms of the MC forms only and explain why the inverse Higgs condition is obtained as the equation of motion for all cases. The supersymmetric extension is also examined using SU(2,2|1)/(SO(3,1)x U(1)) supercoset and five WZ forms are constructed. They are reduced to the corresponding five Galileon WZ forms in the bosonic limit and are candidates of for supersymmetric Galileon.
Euler-Heisenberg Lagrangian to all orders in the magnetic field and the Chiral Magnetic Effect
Mages, Simon Wolfgang; Schäfer, Andreas
2010-01-01
In high energy heavy ion collisions as well as in astrophysical objects like magnetars extreme magnetic field strengths are reached. Thus, there exists a need to calculate divers QED processes to all orders in the magnetic field. We calculate the vacuum polarization graph in second order of the electric field and all orders of the magnetic field resulting in a generalization of the Euler-Heisenberg Lagrangian. We perform the calculation in the effective Lagrangian approach of J. Schwinger as well as using modified Feynman rules. We find that both approaches give the same results provided that the different finite renormalization terms are taken into account. Our results imply that any quantitative explanation of the recently proposed Chiral Magnetic Effect has to take 'Strong QED' effects into account, because these corrections are huge.
Stratocumulus over SouthEast Pacific: Idealized 2D simulations with the Lagrangian Cloud Model
Andrejczuk, M; Blyth, A
2012-01-01
In this paper a LES model with Lagrangian representation of microphysics is used to simulate stratucumulus clouds in idealized 2D set-up based on the VOCALS observations. The general features of the cloud simulated by the model, such as cloud water mixing ratio and cloud droplet number profile agree well with the observations. The model can capture observed relation between aerosol distribution and concentration measured below the cloud and cloud droplet number. Averaged over the whole cloud droplet spectrum from the numerical model and observed droplet spectrum are similar, with the observations showing a higher concentration of droplets bigger than 25 {\\mu}m. Much bigger differences are present when comparing modelled and observed droplet spectrum on specific model level. Despite the fact that microphysics is formulated in a Lagrangian framework the standard deviation of the cloud droplet distribution is larger than 1 {\\mu}m. There is no significant narrowing of the cloud droplet distribution in the up-draf...
A cell-centered lagrangian scheme in two-dimensional cylindrical geometry
SHEN ZhiJun; YUAN GuangWei; YUE JingYan; LIU XueZhe
2008-01-01
A new Lagrangian cell-centered scheme for two-dimensional compressible flows in planar geometry is proposed by Malre et al. The main new feature of the algorithm is that the vertex velocities and the numerical fluxes through the cell interfaces are all evaluated in a coherent manner contrary to standard approaches. In this paper the method introduced by Malre et al. is extended for the equations of Lagrangian gas dynamics in cylindrical symmetry. Two different schemes are proposed, whose difference is that one uses volume weighting and the other area weighting in the discretization of the momentum equation. In the both schemes the conservation of total energy is ensured, and the nodal solver is adopted which has the same formulation as that in Cartesian coordinates. The volume weighting scheme preserves the momentum conservation and the area-weighting scheme preserves spherical symmetry. The numerical examples demonstrate our theoretical considerations and the robustness of the new method.
On the gauge symmetries of Maxwell-like higher-spin Lagrangians
Francia, D; Sharapov, A A
2013-01-01
In their simplest form, metric-like Lagrangians for higher-spin massless fields display constrained gauge symmetries, unless auxiliary fields are introduced or locality is foregone. Specifically, in its standard incarnation, gauge invariance of Maxwell-like Lagrangians relies on parameters with vanishing divergence. We propose an alternative form of the corresponding local symmetry involving unconstrained parameters of mixed-symmetry type, described by rectangular two-row Young diagrams and entering high-derivative gauge transformations. The resulting gauge algebra appears to be reducible and we display the full pattern of gauge-for-gauge parameters, testing its correctness via the corresponding counting of degrees of freedom. Incidentally, this shows that massless higher spins admit a local unconstrained formulation with no need for auxiliary fields.