Equivalence of Lagrangian and Hamiltonian BRST quantizations
International Nuclear Information System (INIS)
Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.
1992-01-01
Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme
Reducible gauge theories in local superfield Lagrangian BRST quantization
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Gitman, D. M. [Universidade de Sao Paulo (USP), SP (Brazil). Inst. de Fisica; Moshin, P.Yu. [Tomsk State Pedagogical University (Russian Federation); Reshetnyak, A.A. [Inst. of Strength Physics and Materials Science, Tomsk (Russian Federation). Lab. of Non-equilibrium State Theory
2007-12-15
The construction of {theta}-local superfield Lagrangian BRST quantization in non-Abelian hyper gauges for generic gauge theories based on the action principle is examined in the case of reducible local superfield models (LSM) on the basis of embedding a gauge theory into a special {theta}-local superfield model with anti symplectic constraints and a Grassmann-odd time parameter {theta}. We examine the problem of establishing a new correspondence between the odd-Lagrangian and odd-Hamiltonian formulations of a local LSM in the case of degeneracy of the Lagrangian description with respect to derivatives over {theta} of generalized classical superfields A{sup I}({theta}). We also reveal the role of the nilpotent BRST-BFV charge for a formal dynamical system corresponding to the BV-BFV dual description of an LSM. (author)
BRST and anti-BRST symmetries for the spinning particle
International Nuclear Information System (INIS)
Gomis, J.; Paris, J.; Roca, J.; Rafanelli, K.
1990-01-01
We consider the open and closed gauge algebras for the spinning particle resulting from two different sets of gauge generators. Using the Batalin-Vilkovisky lagrangian formalism, the BRST and anti-BRST generators are constructed for both cases. (orig.)
A Chern-Simons gauge-fixed Lagrangian in a 'non-canonical' BRST approach
International Nuclear Information System (INIS)
Constantinescu, R; Ionescu, C
2009-01-01
This paper presents a possible path which starts from the extended BRST Hamiltonian formalism and ends with a covariant Lagrangian action, using the equivalence between the two formalisms. The approach allows a simple account of the form of the master equation and offers a natural identification of some 'non-canonical' operators and variables. These are the main items which solve the major difficulty of the extended BRST Lagrangian formalism, i.e., the gauge-fixing problem. The algorithm we propose applies to a non-Abelian Chern-Simons model coupled with Dirac fields
Auxiliary representations of Lie algebras and the BRST constructions
International Nuclear Information System (INIS)
Burdik, C.; Pashnev, A.I.; Tsulaya, M.M.
2000-01-01
The method of construction of auxiliary representations for a given Lie algebra is discussed in the framework of the BRST approach. The corresponding BRST charge turns out to be nonhermitian. This problem is solved by the introduction of the additional kernel operator in the definition of the scalar product in the Fock space. The existence of the kernel operator is proved for any Lie algebra
BRST and Anti-BRST Symmetries in Perturbative Quantum Gravity
Faizal, Mir
2011-02-01
In perturbative quantum gravity, the sum of the classical Lagrangian density, a gauge fixing term and a ghost term is invariant under two sets of supersymmetric transformations called the BRST and the anti-BRST transformations. In this paper we will analyse the BRST and the anti-BRST symmetries of perturbative quantum gravity in curved spacetime, in linear as well as non-linear gauges. We will show that even though the sum of ghost term and the gauge fixing term can always be expressed as a total BRST or a total anti-BRST variation, we can express it as a combination of both of them only in certain special gauges. We will also analyse the violation of nilpotency of the BRST and the anti-BRST transformations by introduction of a bare mass term, in the massive Curci-Ferrari gauge.
Superfield extended BRST quantization in general coordinates
Geyer, B.; Gitman, D. M.; Lavrov, P. M.; Moshin, P. Yu.
2003-01-01
We propose a superfield formalism of Lagrangian BRST-antiBRST quantization of arbitrary gauge theories in general coordinates with the base manifold of fields and antifields desribed in terms of both bosonic and fermionic variables.
Pedagocial introduction to BRST
International Nuclear Information System (INIS)
Niemi, A.J.
1989-01-01
We review some recent results in the BRST quantization of constrained systems. In particular, we explain how the Parisi-Sourlas extension of BRST supersymmetry emerges and how it implies formal equivalence with reduced phase space quantization. We construct the pertinent generators of Parisi-Sourlas superrotations for both first and second class constraint algebras, and as an explicit example we consider open bosonic strings. (orig.)
BRST gauge fixing and regularization
International Nuclear Information System (INIS)
Damgaard, P.H.; Jonghe, F. de; Sollacher, R.
1995-05-01
In the presence of consistent regulators, the standard procedure of BRST gauge fixing (or moving from one gauge to another) can require non-trivial modifications. These modifications occur at the quantum level, and gauges exist which are only well-defined when quantum mechanical modifications are correctly taken into account. We illustrate how this phenomenon manifests itself in the solvable case of two-dimensional bosonization in the path-integral formalism. As a by-product, we show how to derive smooth bosonization in Batalin-Vilkovisky Lagrangian BRST quantization. (orig.)
On the mixed symmetry irreducible representations of the Poincare group in the BRST approach
International Nuclear Information System (INIS)
Burdik, C.; Pashnev, A.; Tsulaya, M.
2001-01-01
The Lagrangian description of irreducible massless representations of the Poincare group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose the method of the BRST constructions is used adopted to the systems of the second class constraints by the construction of auxiliary representations of the algebras of constraints in terms of Verma modules
BRST field theory of relativistic particles
International Nuclear Information System (INIS)
Holten, J.W. van
1992-01-01
A generalization of BRST field theory is presented, based on wave operators for the fields constructed out of, but different from the BRST operator. The authors discuss their quantization, gauge fixing and the derivation of propagators. It is shown, that the generalized theories are relevant to relativistic particle theories in the Brink-Di Vecchia-Howe-Polyakov (BDHP) formulation, and argue that the same phenomenon holds in string theories. In particular it is shown, that the naive BRST formulation of the BDHP theory leads to trivial quantum field theories with vanishing correlation functions. (author). 22 refs
International Nuclear Information System (INIS)
Kulshreshtha, U.
1998-01-01
A chiral Schwinger model with the Faddeevian regularization a la Mitra is studied in the light-front frame. The front-form theory is found to be gauge-non-invariant. The Hamiltonian formulation of this gauge-non-invariant theory is first investigated and then the Stueckelberg term for this theory is constructed. Finally, the Hamiltonian and BRST formulations of the resulting gauge-invariant theory, obtained by the inclusion of the Stueckelberg term in the action of the above gauge-non-invariant theory, are investigated with some specific gauge choices. (orig.)
BRST cosmology and BRST gauge fixing
International Nuclear Information System (INIS)
Kalau, W.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica; Holten, J.W. van
1991-01-01
Some general aspects of BRST cohomology are discussed. The BRST gauge-fixing procedure based on the harmonic gauges in the ghost-extended quantum mechanical Hilbert space. A general classification of states according to their BRST transformation properties is obtained.On the basis of these results necessary and sufficient conditions are found for the positivity of the physical state space following an earlier analysis of Spiegelglas. The method is applied to a system with a non semi-simple, solvable algebra of first-class constraints, such as appears in the theory of massless higher spins. It is found that both the Dirac and Gupta-Bleuler quantization procedures are contained within the BRST approach. (author). 15 refs
Free Abelian 2-form gauge theory: BRST approach
International Nuclear Information System (INIS)
Malik, R.P.
2008-01-01
We discuss various symmetry properties of the Lagrangian density of a four- (3+1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge theory is endowed with a Curci-Ferrari type condition, which happens to be a key signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the above condition that the nilpotent BRST and anti-BRST symmetries of our present theory are found to be absolutely anticommuting in nature. For the present 2-form theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry properties of the Lagrangian densities and derive the corresponding conserved charges. The algebraic structure, obeyed by the above conserved charges, is deduced and the constraint analysis is performed with the help of physicality criteria, where the conserved and nilpotent (anti-)BRST charges play completely independent roles. These physicality conditions lead to the derivation of the above Curci-Ferrari type restriction, within the framework of the BRST formalism, from the constraint analysis. (orig.)
Dimensional reduction and BRST approach to the description of a Regge trajectory
International Nuclear Information System (INIS)
Pashnev, A.I.; Tsulaya, M.M.
1997-01-01
The local free field theory for Regge trajectory is described in the framework of the BRST-quantization method. The corresponding BRST-charge is constructed with the help of the method of dimensional reduction
Gauged BRST symmetry and the occurence of higher cocycles in quantum field theory
International Nuclear Information System (INIS)
Baulieu, L.; Grossman, B.; Stora, R.
1986-06-01
The BRST symmetry of Yang Mills theories can be gauged via the introduction of an anticommuting single gauge field. There follows the construction of a local BRST operation which allows an algebraic analysis of the BRST current algebra. This construction provides, in particular, a field theory interpretation of most higher cocycles which accompany the usual chiral anomaly
BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space
Öttinger, Hans Christian
2018-04-01
We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.
BRST invariant mixed string vertex for the bosonic string
International Nuclear Information System (INIS)
Clarizia, A.; Pezzella, F.
1987-09-01
We construct a BRST invariant (N+M)-string vertex including both open and closed string states. When we saturate it with N open string and M closed string physical states it reproduces their corresponding scattering amplitude. As a particular case we obtain BRST invariant vertex for the open-closed string transition. (orig.)
International Nuclear Information System (INIS)
Hueffel, H.
1990-01-01
After a brief review of the BRST formalism and of the Parisi-Wu stochastic quantization method we introduce the BRST stochastic quantization scheme. It allows the second quantization of constrained Hamiltonian systems in a manifestly gauge symmetry preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed by a discussion on the interacting field theory associated to the relativistic point particle system. 58 refs. (Author)
The BRST complex as the square root of the Casimir operator
International Nuclear Information System (INIS)
Holten, J.W. van
1990-02-01
The authors investigate the BRST cohomology of compact Lie algebras. An anti-BRST operator different from the one usually defined is introduced to construct a BRST invariant operator W, the zero-modes of which are in one-to-one correspondence with the BRST cohomology. Solutions to the BRST cohomology conditions with different ghost number are shown to exist, all of which can be used to define a physical state space for a constrained quantum system. A connection with sypersymmetric topological quantum theories is observed. (author). 17 refs
Perturbative string theory in BRST invariant formalism
International Nuclear Information System (INIS)
Di Vecchia, P.; Hornfeck, K.; Frau, M.; Lerda, A.
1988-01-01
In this talk we present a constructive and very explicit way of calculating multiloop amplitudes in string theories. The main ingredients are the BRST invariant N String Vertex and the BRST invariant twisted propagator. This approach naturally leads to the Schottky parametrization of moduli space in terms of multipliers and fixed points of the g projective transformations which characterize a Riemann surface of genus g. The complete expression (including measure) of the multiloop corrections to the N String Vertex for the bosonic string is exhibited. (orig.)
Some novel features in 2D non-Abelian theory: BRST approach
Srinivas, N.; Kumar, S.; Kureel, B. K.; Malik, R. P.
2017-08-01
Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss some novel features of a two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci-Ferrari (CF-)type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned.
Ruan, Wei-Dong
2004-01-01
This paper is the sequel to my recent paper [10]. It will provide technical details of our gradient flow construction and related problems, which are essential for our construction of Lagrangian torus fibrations in [10] and subsequent papers [11, 13, 14].
Half-integer ghost states and simple BRST quantization
International Nuclear Information System (INIS)
Marnelius, R.
1987-01-01
Quantum mechanical BRST systems are considered. As is well known an odd number of ghost operators has a representation with respect to the ghost number operator consisting of states with half-integer ghost numbers. Here it is shown that an eigenstate representation of the ghost operators requires a particular mixed Grassmann character of the states. It is also shown that such states always may be avoided provided only one starts from a lagrangian where the fundamental constraints are generated by Lagrange multipliers. In the latter case there also exists an anti-BRST charge. Some relevant properties of the different BRST approaches are displayed. The existence of inequivalent physical representations is demonstrated. (orig.)
Sp(2) BRST invariant quantization of strings: The harmonic gauge
International Nuclear Information System (INIS)
Latorre, J.I.; Massachusetts Inst. of Tech., Cambridge
1988-01-01
We analyze the mixed algebra of local diffeomorphisms and Weyl transformations for bosonic strings. BRST and anti-BRST operators are then constructed keeping a manifest Sp(2) invariance. The harmonic gauge arises as a natural gauge choice. All this work is redone in the presence of a two-dimensional background metric. We manage to write down a simple action, to compute the stress tensor and to work out the critical dimensions. (orig.)
On the dynamics of non-holonomic systems: the construction of a lagrangian and a hamiltonian
International Nuclear Information System (INIS)
Galvao, C.A.P.; Negri, L.J.
1982-01-01
It is shown that once the motion of a non-holonomic system is known it is possible to reduce the system to the holonomic form. A (singular) Lagrangian function and a Hamiltonian which correctly describe the dynamics of the system can be constructed. This procedure is applied to a well known system. (Author) [pt
The BRST complex and the cohomology of compact lie algebras
International Nuclear Information System (INIS)
Holten, J.W. van
1990-02-01
The authors construct the BRST and anti-BRST operator for a compact Lie algebra which is a direct sum of abelian and simple ideals. Two different inner products are defined on the ghost space and the hermiticity propeties of the ghost and BRST operators with respect to these inner products are discussed. A decomposition theorem for ghost states is derived and the cohomology of the BRST complex is shown to reduce to the standard Lie-algebra cohomology. The authors show that the cohomology classes of the Lie algebra are given by all invariant anti-symmetric tensors and explain how thse can be obtained as zero-modes of an invariant operator in the representation space of the ghosts. Explicit examples are given. (author) 24 refs
Extended BRST symmetries in the gauge field theory
International Nuclear Information System (INIS)
Babalean, Aurel; Constantinescu, Radu; Ionescu, Carmen
2001-01-01
The BRST procedure provides one of the most powerful methods for the quantum description of the gauge field theories. As already stated, the unphysical degrees of freedom that appear in this case can be easily canceled by the introduction of the ghost type variables. In the Hamiltonian formalism, the structure of the ghost that must be used mainly depends on two factors: - the type of the theory, that this the relations among the constraints of the theory; - the extension of the symmetry to be implemented. The paper presents the structure of the extended phase space suitable for the BRST canonical quantization of a 1- reducible gauge theory in the frame of a BRST symmetry of order three. The corresponding BRST charges and the extended Hamiltonian are also constructed. (authors)
The BRST formulation of the Gupta-Bleuler quantization method
International Nuclear Information System (INIS)
Hasiewicz, Z.; Lukierski, J.; Holten, J.W. van
1990-03-01
In this paper the authors show, how an algebra of mixed first and second class constraints can be transformed into an algebra of the Gupta-Bleuler type, consisting of holomorphic and antiholomorphic constraints. We perform its quantization by BRST methods. The authors construct a second-level BRST operator ω by introducing a new ghost sector (the second-level ghosts), in addition to the ghosts of the standard BRST operator. We find an inner product in this ghost sector such that the operator ω is hermitean. The physical states, as defined by the non-hermitean holomorphic constraints, are shown to be given in terms of the cohomology of this hermitean BRST charge. (author) 27 refs
Finite field dependent mixed BRST transformation
International Nuclear Information System (INIS)
Upadhyay, Sudhaker; Mandal, Bhabani Prasad
2013-01-01
Joglekar and Mandal have generalized the usual Bechhi-Rouet-Stora-Tyutin (BRST) transformation by allowing infinitesimal BRST parameter finite and field dependent. Such a generalized BRST transformation (so-called FFBRST transformation) is also the symmetry of the effective action but not of the generating functional of the theory. We generalize the mixed BRST (sum of totally anti-commuting BRST and anti-BRST) symmetry transformation in same manner. We show that such a generalized mixed BRST transformation is the symmetry of the effective action as well as of the generating functional. We show our result by considering several explicit examples. (author)
Covariant Quantization with Extended BRST Symmetry
Geyer, B.; Gitman, D. M.; Lavrov, P. M.
1999-01-01
A short rewiev of covariant quantization methods based on BRST-antiBRST symmetry is given. In particular problems of correct definition of Sp(2) symmetric quantization scheme known as triplectic quantization are considered.
BRST operator for superconformal algebras with quadratic nonlinearity
International Nuclear Information System (INIS)
Khviengia, Z.; Sezgin, E.
1993-07-01
We construct the quantum BRST operators for a large class of superconformal and quasi-superconformal algebras with quadratic nonlinearity. The only free parameter in these algebras is the level of the (super) Kac-Moody sector. The nilpotency of the quantum BRST operator imposes a condition on the level. We find this condition for (quasi) superconformal algebras with a Kac-Moody sector based on a simple Lie algebra and for the Z 2 x Z 2 -graded superconformal algebras with a Kac-Moody sector based on the superalgebra osp(N modul 2M) or sl (N + 2 modul N). (author). 22 refs, 3 tabs
String loop effect on the BRST charge
International Nuclear Information System (INIS)
Das, A.; Nishino, H.
1987-07-01
An effective BRST charge Q BRST which incorporates the string one-loop corrections is presented for the closed bosonic string in an arbitrary background. The effective σ-model action which leads to such a Q BRST is obtained and some consequences are discussed. (author). 14 refs, 1 fig
Aspects of a Lagrangian formulation for modular invariant co-set constructions
International Nuclear Information System (INIS)
Rabinovici, E.
1988-01-01
Strings are allowed to propagate on backgrounds that are two dimensional conformal field theories (CFTs). Each such background describes the target space in which the string moves, a universe. The problem of finding all possible allowed backgrounds is thus strongly related to the problem of classifying all possible two dimensional CFTs. The matter sector of the CFT is further restricted to be a representation of the (super) Virasoro algebra with a value (15) 26 for the central charge (c). The exact geography of the conformal space (the space of all possible CFTs) is far from being known. Only bits and pieces of that space are chartered.For c 1 the information is still less organized, although progress has been made. This paper focuses on the c < 1. The authors explicitly construct the possible lagrangian realizations of the c < 1 discrete series in particular and co-set like models in general. A local lagrangian field theoretic description offers several advantages, among them the possibility to directly construct models which are modular invariant and closed under the operator algebra
A BRST charge for non-critical W2,s strings
International Nuclear Information System (INIS)
Palacios, L.
1994-10-01
We present a general argument for the construction of BRST charges of the 'non-critical' W 2,4 , W 2,5 W 2,6 , and W 2,8 strings. This evidences the existence of BRST charges for a kind of soft-type algebras which can be constructed from two copies of quantum W 2,s algebras, (s=3,4,5,6,8). (author). 15 refs
A BRST charge for non-critical $\\W_{2,s}$ strings
Palacios, L.
1994-01-01
We present a general argument for the construction of BRST charges of the `non-critical' $\\W_{2,4}$, $\\W_{2,5}$, $\\W_{2,6}$, and $\\W_{2,8}$ strings. This evidences the existence of BRST charges for a kind of soft-type algebras which can be constructed from two copies of quantum $\\W_{2,s}$ algebras, (s=3,4,5,6,8).
BRST-operator for quantum Lie algebra and differential calculus on quantum groups
International Nuclear Information System (INIS)
Isaev, A.P.; Ogievetskij, O.V.
2001-01-01
For A Hopf algebra one determined structure of differential complex in two dual external Hopf algebras: A external expansion and in A* dual algebra external expansion. The Heisenberg double of these two Hopf algebras governs the differential algebra for the Cartan differential calculus on A algebra. The forst differential complex is the analog of the de Rame complex. The second complex coincide with the standard complex. Differential is realized as (anti)commutator with Q BRST-operator. Paper contains recursion relation that determines unequivocally Q operator. For U q (gl(N)) Lie quantum algebra one constructed BRST- and anti-BRST-operators and formulated the theorem of the Hodge expansion [ru
Lefschetz trace formula and BRST
International Nuclear Information System (INIS)
Schwarz, A.
1989-04-01
Quantum systems with constraints showing how the BRST-transformation and the BFV-method of quantization can be understood directly in this case are studied in this paper. The results concerning the quantization of classical constrained systems can be derived from the results for quantum systems. 7 refs
Nilpotent BRST charge without auxillary B fields in quantum gauge theories
International Nuclear Information System (INIS)
Tsai, E.C.
1991-01-01
This paper introduces a modified BRST transformation for non-Abelian gauge theories. In this transformation, there is no need to introduce auxiliary B fields, yet the generatior Q for the modified transformation is nilpotent and commutes with the Hamiltonian. The Lagrangian is no longer invariant under Q, but the quantum theory which is defined by the Hamiltonian is still symmetric with respect to the transformation generated by Q
Directory of Open Access Journals (Sweden)
Junyoung Ko
2017-10-01
Full Text Available This paper presents the application of the Coupled Eulerian–Lagrangian (CEL technique on the constructability problems of site on very soft soil. The main objective of this study was to investigate the constructability and application of two ground improvement methods, such as the forced replacement method and the deep mixing method. The comparison between the results of CEL analyses and field investigations was performed to verify the CEL modelling. The behavior of very soft soil and constructability with methods can be appropriately investigated using the CEL technique, which would be useful tools for comprehensive reviews in preliminary design.
BRST, generalized Maurer-Cartan equations and CFT
Energy Technology Data Exchange (ETDEWEB)
Zeitlin, Anton M. [Department of Mathematics, Yale University, 442 Dunham Lab, 10 Hillhouse Ave., New Haven, CT 06511 (United States); St. Petersburg Department of Steklov Mathematical Institute, Fontanka, 27, St. Petersburg 191023 (Russian Federation)]. E-mail: zam@math.ipme.ru
2006-12-25
The paper is devoted to the study of BRST charge in perturbed two-dimensional conformal field theory. The main goal is to write the operator equation expressing the conservation law of BRST charge in perturbed theory in terms of purely algebraic operations on the corresponding operator algebra, which are defined via the OPE. The corresponding equations are constructed and their symmetries are studied up to the second order in formal coupling constant. It appears that the obtained equations can be interpreted as generalized Maurer-Cartan ones. We study two concrete examples in detail: the bosonic nonlinear sigma model and perturbed first order theory. In particular, we show that the Einstein equations, which are the conformal invariance conditions for both these perturbed theories, expanded up to the second order, can be rewritten in such generalized Maurer-Cartan form.
Lovelock terms and BRST cohomology
International Nuclear Information System (INIS)
Cnockaert, Sandrine; Henneaux, Marc
2005-01-01
Lovelock terms are polynomial scalar densities in the Riemann curvature tensor that have the remarkable property that their Euler-Lagrange derivatives contain derivatives of the metric of an order not higher than 2 (while generic polynomial scalar densities lead to Euler-Lagrange derivatives with derivatives of the metric of order 4). A characteristic feature of Lovelock terms is that their first nonvanishing term in the expansion g λμ = η λμ + h λμ of the metric around flat space is a total derivative. In this paper, we investigate generalized Lovelock terms defined as polynomial scalar densities in the Riemann curvature tensor and its covariant derivatives (of arbitrarily high but finite order) such that their first nonvanishing term in the expansion of the metric around flat space is a total derivative. This is done by reformulating the problem as a BRST cohomological one and by using cohomological tools. We determine all the generalized Lovelock terms. We find, in fact, that the class of nontrivial generalized Lovelock terms contains only the usual ones. Allowing covariant derivatives of the Riemann tensor does not lead to a new structure. Our work provides a novel algebraic understanding of the Lovelock terms in the context of BRST cohomology
Some Lagrangians for systems without a Lagrangian
International Nuclear Information System (INIS)
Nucci, M C; Leach, P G L
2011-01-01
We demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle.
BFV-BRST analysis of the classical and quantum q-deformations of the sl(2) algebra
International Nuclear Information System (INIS)
Dayi, O.F.
1993-01-01
BFV-BRST charge for q-deformed algebras is not unique. Different constructions of it in the classical as well as in the quantum phase space for the q-deformed algebra sl q (2) are discussed. Moreover, deformation of the phase space without deforming the generators of sl(2) is considered. h -q-deformation of the phase space is shown to yield the Witten's second deformation. To study the BFV-BRST cohomology problem when both the quantum phase space and the group are deformed, a two parameter deformation of sl(2) is proposed, and its BFV-BRST charge is given. (author). 21 refs
BFV-BRST quantization of 2D supergravity
International Nuclear Information System (INIS)
Fujiwara, T.; Igarashi, Y.; Kuriki, R.; Tabei, T.
1995-02-01
Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Fradkin (BF) formalism, the anomaly-canceling super-Liouville fields are introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. The BFV-BRST quantization applies to formulate the theory in the most general class of gauges. A local effective action constructed in the configuration space contains two super-Liouville actions; one is a noncovariant but local functional written only in terms of 2D supergravity fields, and the other contains the super-Liouville fields canceling the super-Weyl anomaly. Auxiliary fields for the Liouville and the gravity super-multiplets are introduced to make the BRST algebra close off-shell. Inclusion of them turns out to be essentially important especially in the super-lightcone gauge-fixing, where the super-curvature equations (δ - 3 g ++ =δ - 2 χ ++ =0) are obtained as a result of BRST invariance of the theory. Our approach reveals the origin of the OSp (1,2) current algebra symmetry in a transparent manner. (author)
Generalization of Faddeev-Popov rules in Yang-Mills theories: N = 3,4 BRST symmetries
Reshetnyak, Alexander
2018-01-01
The Faddeev-Popov rules for a local and Poincaré-covariant Lagrangian quantization of a gauge theory with gauge group are generalized to the case of an invariance of the respective quantum actions, S(N), with respect to N-parametric Abelian SUSY transformations with odd-valued parameters λp, p = 1,…,N and generators sp: spsq + sqsp = 0, for N = 3, 4, implying the substitution of an N-plet of ghost fields, Cp, instead of the parameter, ξ, of infinitesimal gauge transformations: ξ = Cpλ p. The total configuration spaces of fields for a quantum theory of the same classical model coincide in the N = 3 and N = 4 symmetric cases. The superspace of N = 3 SUSY irreducible representation includes, in addition to Yang-Mills fields 𝒜μ, (3 + 1) ghost odd-valued fields Cp, B̂ and 3 even-valued Bpq for p, q = 1, 2, 3. To construct the quantum action, S(3), by adding to the classical action, S0(𝒜), of an N = 3-exact gauge-fixing term (with gauge fermion), a gauge-fixing procedure requires (1 + 3 + 3 + 1) additional fields, Φ¯(3): antighost C¯, 3 even-valued Bp, 3 odd-valued B̂pq and Nakanishi-Lautrup B fields. The action of N = 3 transformations on new fields as N = 3-irreducible representation space is realized. These transformations are the N = 3 BRST symmetry transformations for the vacuum functional, Z3(0) =∫dΦ(3)dΦ¯(3)exp{(ı/ℏ)S(3)}. The space of all fields (Φ(3),Φ¯(3)) proves to be the space of an irreducible representation of the fields Φ(4) for N = 4-parametric SUSY transformations, which contains, in addition to 𝒜μ the (4 + 6 + 4 + 1) ghost-antighost, Cr = (Cp,C¯), even-valued, Brs = -Bsr = (Bpq,Bp4 = Bp), odd-valued B̂r = (B̂,B̂pq) and B fields. The quantum action is constructed by adding to S0(𝒜) an N = 4-exact gauge-fixing term with a gauge boson, F(4). The N = 4 SUSY transformations are by N = 4 BRST transformations for the vacuum functional, Z4(0) =∫dΦ(4)exp{(ı/ℏ)S(4)}. The procedures are valid for
The BRST complex of homological Poisson reduction
Müller-Lennert, Martin
2017-02-01
BRST complexes are differential graded Poisson algebras. They are associated with a coisotropic ideal J of a Poisson algebra P and provide a description of the Poisson algebra (P/J)^J as their cohomology in degree zero. Using the notion of stable equivalence introduced in Felder and Kazhdan (Contemporary Mathematics 610, Perspectives in representation theory, 2014), we prove that any two BRST complexes associated with the same coisotropic ideal are quasi-isomorphic in the case P = R[V] where V is a finite-dimensional symplectic vector space and the bracket on P is induced by the symplectic structure on V. As a corollary, the cohomology of the BRST complexes is canonically associated with the coisotropic ideal J in the symplectic case. We do not require any regularity assumptions on the constraints generating the ideal J. We finally quantize the BRST complex rigorously in the presence of infinitely many ghost variables and discuss the uniqueness of the quantization procedure.
A general solution of the BV-master equation and BRST field theories
International Nuclear Information System (INIS)
Dayi, O.F.
1993-05-01
For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd-dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories, when one replaces the role of the exterior derivative with the BRST charge of first quantization. (author). 17 refs
BRST quantization of Polyakov's two-dimensional gravity
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Itoh, Katsumi
1990-01-01
Two-dimensional gravity coupled to minimal models is quantized in the chiral gauge by the BRST method. By using the Wakimoto construction for the gravity sector, we show how the quartet mechanism of Kugo and Ojima works and solve the physical state condition. As a result the positive semi-definiteness of the physical subspace is shown. The formula of Knizhnik et al. for gravitational scaling dimensions is rederived from the physical state condition. We also observe a relation between the chiral gauge and the conformal gauge. (orig.)
Degenerate gauge conditions, generalized Gribov's ambiguity and BRST symmetry
International Nuclear Information System (INIS)
Fabbrichesi, M.E.
1987-01-01
The BFS-BRST approach to gauge theories is considered. It is argued that the BRST-invariant boundary conditions ordinarily used do not maintain the necessary degeneracy in the gauge fixing. As a by-product of this discussion, the existence of a generalized Gribov-like ambiguity is suggested. This ambiguity is however shown to be just a particular BRST transformation
Subgrid-scale stresses and scalar fluxes constructed by the multi-scale turnover Lagrangian map
AL-Bairmani, Sukaina; Li, Yi; Rosales, Carlos; Xie, Zheng-tong
2017-04-01
The multi-scale turnover Lagrangian map (MTLM) [C. Rosales and C. Meneveau, "Anomalous scaling and intermittency in three-dimensional synthetic turbulence," Phys. Rev. E 78, 016313 (2008)] uses nested multi-scale Lagrangian advection of fluid particles to distort a Gaussian velocity field and, as a result, generate non-Gaussian synthetic velocity fields. Passive scalar fields can be generated with the procedure when the fluid particles carry a scalar property [C. Rosales, "Synthetic three-dimensional turbulent passive scalar fields via the minimal Lagrangian map," Phys. Fluids 23, 075106 (2011)]. The synthetic fields have been shown to possess highly realistic statistics characterizing small scale intermittency, geometrical structures, and vortex dynamics. In this paper, we present a study of the synthetic fields using the filtering approach. This approach, which has not been pursued so far, provides insights on the potential applications of the synthetic fields in large eddy simulations and subgrid-scale (SGS) modelling. The MTLM method is first generalized to model scalar fields produced by an imposed linear mean profile. We then calculate the subgrid-scale stress, SGS scalar flux, SGS scalar variance, as well as related quantities from the synthetic fields. Comparison with direct numerical simulations (DNSs) shows that the synthetic fields reproduce the probability distributions of the SGS energy and scalar dissipation rather well. Related geometrical statistics also display close agreement with DNS results. The synthetic fields slightly under-estimate the mean SGS energy dissipation and slightly over-predict the mean SGS scalar variance dissipation. In general, the synthetic fields tend to slightly under-estimate the probability of large fluctuations for most quantities we have examined. Small scale anisotropy in the scalar field originated from the imposed mean gradient is captured. The sensitivity of the synthetic fields on the input spectra is assessed by
International Nuclear Information System (INIS)
Beyl, L.M.
1979-01-01
It is shown that the Einstein, Weyl, supergravity and superconformal theories are special cases of gauge transformations in SU(4vertical-barN). This group is shown to contain SU(2,2) x SU(N) x U(1) for its commuting or Bose part, and to contain 8N supersymmetry generators for its anticommuting or Fermi part. Using the electromagnetic Lagrangian as a model, a super-Lagrangian is constructed for vector potentials. Invariance is automatic in free space, but, in the presence of matter, restrictions on the supersymmetry transformations are necessary. The Weyl action and the Einstein cosmological field equations are obtained in the appropriate limits. Finally, a super-Lagrangian is constructed from nongeometric principles which includes the Dirac Lagrangian and except for a sum over symmetry indices resembles the electron-electromagnetic Lagrangian
On the BRST invariance of field deformations
International Nuclear Information System (INIS)
Alfaro, J.; Damgaard, P.H.; Latorre, J.I.; Montano, D.
1989-08-01
Topological quantum field theories are distinguished by a BRST symmetry corresponding to local field deformations. We investigate in this letter to what extent an arbitrary quantum field theory may be related to this BRST invariance. We demonstrate that at the expense of having to add extra variables (but without changing the physics) one may always extend to symmetry of an arbitrary action to include local field deformations. New avenues for gauge-fixing are then available. Examples are worked out for Yang-Mills theories. (orig.)
International Nuclear Information System (INIS)
Reshetnyak, A.
2013-01-01
We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the BRST–BFV approach suggested for bosonic fields in our first article [I.L. Buchbinder, A. Reshetnyak, Nucl. Phys. B 862 (2012) 270, (arXiv:1110.5044 [hep-th])]. Starting from a description of fermionic mixed-symmetry higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with a special Poincare module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a system of first-class constraints. To do this, we find, in first time, by means of generalized Verma module the auxiliary representations of the constraint subsuperalgebra, to be isomorphic due to Howe duality to osp(k|2k) superalgebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We suggest a universal procedure of finding unconstrained gauge-invariant Lagrangians with reducible gauge symmetries, describing the dynamics of both massless and massive fermionic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by constraints corresponding to an irreducible Poincare-group representation. As examples of the general approach, we propose a method of Lagrangian construction for fermionic fields subject to an arbitrary Young tableaux having 3 rows, and obtain a gauge-invariant Lagrangian for a new model of a massless rank-3 spin-tensor field of spin (5/2,3/2) with first-stage reducible gauge symmetries and a non-gauge Lagrangian for a massive rank-3 spin-tensor field of spin (5/2,3/2)
BRST cohomology operators on string superforms
International Nuclear Information System (INIS)
Dao Vong Duc; Nguyen Thi Hong.
1988-08-01
BRST cohomology calculus in the space of superstring differential forms is treated in detail. The explicit expressions of cohomology operators are derived for superforms of arbitrary order. Various identities for the structure constants of the associated superalgebras are also given. (author). 16 refs
Constraints, BRST-Cohomology and stochastic quantization
International Nuclear Information System (INIS)
Hueffel, H.
1989-01-01
After presenting a pedagogical introduction to the Becchi-Rouet-Stora-formalism we introduce stochastic quantization in extended configuration space. The appearance of a specific projection operator and its relationship to the BRST-cohomology is pointed out. 20 refs. (Author)
Exact Lagrangian caps and non-uniruled Lagrangian submanifolds
Dimitroglou Rizell, Georgios
2015-04-01
We make the elementary observation that the Lagrangian submanifolds of C n , n≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov-Eliashberg algebra is acyclic.
Physical state condition in quantum general relativity as a consequence of BRST symmetry
International Nuclear Information System (INIS)
Castellana, Michele; Montani, Giovanni
2008-01-01
Quantization of systems with constraints can be carried out with several methods. In the Dirac formulation the classical generators of gauge transformations are required to annihilate physical quantum states to ensure their gauge invariance. Carrying on BRST symmetry it is possible to get a condition on physical states which, different from the Dirac method, requires them to be invariant under the BRST transformation. Employing this method for the action of general relativity expressed in terms of the spin connection and tetrad fields with path integral methods, we construct the generator of the BRST transformation associated with the underlying local Lorentz symmetry of the theory and write a physical state condition following from BRST invariance. This derivation is based on the general results on the dependence of the effective action used in path integrals and consequently of Green's functions on the gauge-fixing functionals used in the DeWitt-Faddeev-Popov method. The condition we gain differs from the one obtained within Ashtekar's canonical formulation, showing how we recover the latter only by a suitable choice of the gauge-fixing functionals. Finally we discuss how it should be possible to obtain all of the requested physical state conditions associated with all the underlying gauge symmetries of the classical theory using our approach
A note on the BFV-BRST operator quantization method
International Nuclear Information System (INIS)
Dayi, O.F.
1988-03-01
The BFV-BRST operator quantization method is applied to massive, abelian (Yang-Mills) theory which has only second class constraints. A nilpotent BFV-BRST-charge is derived and used to define a unitarizing hamiltonian. Unphysical degrees of freedom can be eliminated either in a canonical gauge or in a relativistic one. In the latter gauge this is a general feature (at least locally) of the BFV-BRST quantization of the systems with irreducible constraints. (author). 23 refs
BRST symmetry and de Rham cohomology
Hong, Soon-Tae
2015-01-01
This book provides an advanced introduction to extended theories of quantum field theory and algebraic topology, including Hamiltonian quantization associated with some geometrical constraints, symplectic embedding and Hamilton-Jacobi quantization and Becci-Rouet-Stora-Tyutin (BRST) symmetry, as well as de Rham cohomology. It offers a critical overview of the research in this area and unifies the existing literature, employing a consistent notation. Although the results presented apply in principle to all alternative quantization schemes, special emphasis is placed on the BRST quantization for constrained physical systems and its corresponding de Rham cohomology group structure. These were studied by theoretical physicists from the early 1960s and appeared in attempts to quantize rigorously some physical theories such as solitons and other models subject to geometrical constraints. In particular, phenomenological soliton theories such as Skyrmion and chiral bag models have seen a revival following experiment...
Decontracted double BRST symmetry on the lattice
International Nuclear Information System (INIS)
Smekal, L. von; Ghiotti, M.; Williams, A. G.
2008-01-01
We present the Curci-Ferrari model on the lattice. In the massless case the topological interpretation of this model with its double Becchi-Rouet-Stora-Tyutin (BRST) symmetry relates to the Neuberger 0/0 problem which we extend to include the ghost/antighost symmetric formulation of the nonlinear-covariant Curci-Ferrari gauges on the lattice. The introduction of a Curci-Ferrari mass term, however, serves to regulate the 0/0 indeterminate form of physical observables observed by Neuberger. While such a mass m decontracts the double BRST/anti-BRST algebra, which is well known to result in a loss of unitarity, observables can be meaningfully defined in the limit m→0 via l'Hospital's rule. At finite m, the topological nature of the partition function used as the gauge-fixing device seems lost. We discuss the gauge parameter ξ and mass m dependence of the model and show how both cancel when m≡m(ξ) is appropriately adjusted with ξ.
International Nuclear Information System (INIS)
Hojman, S.
1982-01-01
We present a review of the inverse problem of the Calculus of Variations, emphasizing the ambiguities which appear due to the existence of equivalent Lagrangians for a given classical system. In particular, we analyze the properties of equivalent Lagrangians in the multidimensional case, we study the conditions for the existence of a variational principle for (second as well as first order) equations of motion and their solutions, we consider the inverse problem of the Calculus of Variations for singular systems, we state the ambiguities which emerge in the relationship between symmetries and conserved quantities in the case of equivalent Lagrangians, we discuss the problems which appear in trying to quantize classical systems which have different equivalent Lagrangians, we describe the situation which arises in the study of equivalent Lagrangians in field theory and finally, we present some unsolved problems and discussion topics related to the content of this article. (author)
BRST quantization of superconformal theories on higher genus Riemann surfaces
International Nuclear Information System (INIS)
Leman Kuang
1992-01-01
A complex contour integral method is constructed and applied to the Becchi-Rouet-Stora-Tyutin (BRST) quantization procedure of string theories on higher genus Riemann surfaces with N=0 and 1 Krichever-Novikov (KN) algebras. This method makes calculations very simple. It is shown that the critical spacetime dimension of the string theories on a genus-g Riemann surface equals that of the string theories on a genus-zero Riemann surface, and that the 'Regge intercepts' in the genus-g case are α(g)=1-3/4g-9/8g 2 and 1/2-3/4g-17/16g 2 for bosonic strings and superstrings, respectively. (orig.)
Lagrangian cobordism and tropical curves
Sheridan, Nick; Smith, Ivan
2018-01-01
We study a cylindrical Lagrangian cobordism group for Lagrangian torus fibres in symplectic manifolds which are the total spaces of smooth Lagrangian torus fibrations. We use ideas from family Floer theory and tropical geometry to obtain both obstructions to and constructions of cobordisms; in particular, we give examples of symplectic tori in which the cobordism group has no non-trivial cobordism relations between pairwise distinct fibres, and ones in which the degree zero fibre cobordism gr...
BRST structure of two dimensional conformal field theories
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Rivelles, V.O.
1987-09-01
We present a procedure to obtain the BRST charge for the representations of the Virassoro algebra. For C ≤ 1 the BRST charge has in general terms containing products of more than three ghosts. It is nilpotent for any allowed value of the central charge and conformal weight of the representation. (Author) [pt
International Nuclear Information System (INIS)
Weinberg, S.
1979-01-01
The author presents an argument that phenomenological Lagrangians can be used not only to reproduce the soft pion results of current algebra, but also to justify these results, without any use of operator algebra, and shows how phenomenological Lagrangians can be used to calculate corrections to the leading soft pion results to any desired order in external momenta. The renormalization group is used to elucidate the structure of these corrections. Corrections due to the finite mass of the pion are treated and speculations are made about another possible application of phenomenological Lagrangians. (Auth.)
Lagrangian vector field and Lagrangian formulation of partial differential equations
Directory of Open Access Journals (Sweden)
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.
On the BRST charge over infinite-dimensional algebras
International Nuclear Information System (INIS)
Hlousek, Zvonimir.
1988-01-01
The author studies the BRST charge defined over an infinite algebra of gauged local symmetries. This is of great importance to string theories. The BRST charge of the gauge symmetry must be nilpotent. In string theories this implies the cancellation of conformal anomalies in critical dimension; 26 for bosonic string, 10 for superstring, and 2 for O(2) string. Furthermore, the O(2) symmetry of the O(2) string (a string theory with two, two-dimensional supersymmetries) is realized as a Kac-Moody symmetry. In general, the BRST quantization of the local, gauged KAC-Moody symmetry requires special care due to chiral anomaly. The chiral anomaly breaks the chiral gauge invariance, and the corresponding BRST charge is not nilpotent. To arrive at the nilpotent BRST charge for the gauged Kac-Moody symmetry, one has to modify the theory by adding a one-cocycle over the gauge group. A similar problem and its solution exist in the case of supersymmetric Kac-Moody algebras. The BRST charge of the first quantized string theory is a building block of the covariant string field theory. The BRST invariance of the first quantized theory generalizes to gauge invariance of string field theory. In Witten's open string field theory the BRST charge plays a role of exterior derivation on the space of string field functionals. The Fock space realization of the theory was given by Gross and Jevicki. For the consistency of the theory it is crucial that all the vertex operators are BRST invariant. The ghost part of the vertex comes in few varieties. The author has shown that all the versions of the ghost vertex are equivalent, as long as the total vertex is BRST invariant
Field transformations, collective coordinates and BRST invariance
International Nuclear Information System (INIS)
Alfaro, J.; Damgaard, P.H.
1989-12-01
A very large class of general field transformations can be viewed as a field theory generalization of the method of collective coordinates. The introduction of new variables induces a gauge invariance in the transformed theory, and the freedom left in gauge fixing this new invariance can be used to find equivalent formulations of the same theory. First the Batalin-Fradkin-Vilkovisky formalism is applied to the Hamiltonian formulation of physical systems that can be described in terms of collective coordinates. We then show how this type of collective coordinate scheme can be generalized to field transformations, and discuss the War Identities of the associated BRST invariance. For Yang-Mills theory a connection to topological field theory and the background field method is explained in detail. In general the resulting BRST invariance we find hidden in any quantum field theory can be viewed as a consequence of our freedom in choosing a basis of coordinates φ(χ) in the action S[φ]. (orig.)
Spontaneous breaking of the BRST symmetry in the ABJM theory
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Faizal, Mir; Upadhyay, Sudhaker
2014-01-01
In this paper, we will analyze the ghost condensation in the ABJM theory. We will perform our analysis in N=1 superspace. We show that in the Delbourgo–Jarvis–Baulieu–Thierry–Mieg gauge the spontaneous breaking of BRST symmetry can occur in the ABJM theory. This spontaneous breaking of BRST symmetry is caused by ghost–anti-ghost condensation. We will also show that in the ABJM theory, the ghost–anti-ghost condensates remain present in the modified abelian gauge. Thus, the spontaneous breaking of BRST symmetry in ABJM theory can even occur in the modified abelian gauge
Open BRST algebras, ghost unification and string field theory
Baulieu, Laurent; Bergshoeff, Eric; Sezgin, Ergin
1988-01-01
Geometrical aspects of the BRST quantization of charged antisymmetric tensor fields and string fields are studied within the framework of the Batalin and Vilkovisky method. In both cases, candidate anomalies which obey the Wess-Zumino consistency conditions are given.
On the BRST cohomology in U(1) gauge theory
International Nuclear Information System (INIS)
Malik, R.P.
1998-08-01
We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology in the case of two-dimensional free U(1) gauge theory. In addition to the usual BRST charge, we deduce a conserved and nilpotent dual-BRST charge under which the gauge-fixing term remains invariant. This charge is the analogue of the adjoint (dual) exterior derivative of differential geometry. The BRST extended Casimir operator, corresponding to the Laplacian operator of differential geometry, turns out to generate a symmetry under which the ghost term remains invariant. We take a single photon state in the Hilbert space and demonstrate the notion of gauge invariance, no-(anti)ghost theorem and transversality of photon by exploiting the refinement of cohomology by selecting the physical state as the harmonic state of the Hodge decomposition theorem. (author)
Constraint theory, singular lagrangians and multitemporal dynamics
International Nuclear Information System (INIS)
Lusanna, L.
1988-01-01
Singular Lagrangians and constraint theory permeate theoretical physics, as shown by the relevance of gauge theories, string models and general relativity. Their study used finite---dimensional models as a guide to develop the theory, but their main use was in classical field theory, due to the necessity of understanding their quantization. The covariant quantization of singular Lagrangians led to the BRST approach and to the theory of the effective action. On the other hand their phase---space formulation, culminated with the BFV approach for first class, second class and reducible constraints. It, in turn, gave new insights in the theory of singular Lagrangians and constraints and in their cohomological aspects. However the Hamiltonian approach to field theory is highly nontrivial, is open to criticism due to its problems with locality, geometry and manifest covariance and its canonical quantization has still to be developed, because there is no proof of the renormalizability of the Schroedinger representation of field theory. This paper discusses how, notwithstanding these developments, there is still a big amount of ambiguity at every level of the theory
BRST operator quantization of generally covariant gauge systems
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Ferraro, R.; Sforza, D.M.
1997-01-01
The BRST generator is realized as a Hermitian nilpotent operator for a finite-dimensional gauge system featuring a quadratic super-Hamiltonian and linear supermomentum constraints. As a result, the emerging ordering for the Hamiltonian constraint is not trivial, because the potential must enter the kinetic term in order to obtain a quantization invariant under scaling. Namely, BRST quantization does not lead to the curvature term used in the literature as a means to get that invariance. The inclusion of the potential in the kinetic term, far from being unnatural, is beautifully justified in light of the Jacobi's principle. copyright 1997 The American Physical Society
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 ...
Open BRST algebras, ghost unification and string field theory
International Nuclear Information System (INIS)
Baulieu, L.; Bergshoeff, E.; Sezgin, E.
1988-01-01
Geometrical aspects of the BRST quantization of charged antisymmetric tensor fields and string fields are studied within the framework of the Batalin and Vilkovisky method. In both cases, candidate anomalies which obey the Wess-Zumino consistency conditions are given. (author). 18 refs, 1 fig
BRST quantization, IOSp(D,2vertical stroke2) invariance and the PCT theorem. Pt. 2
International Nuclear Information System (INIS)
Gozzi, E.; Reuter, M.
1989-01-01
In this paper we investigate the IOSp(D,2vertical stroke2) extension of the Poincare group in the BRST quantization of the spinning particle. We construct the corresponding field theory and prove its dimensional reduction a la Parisi-Sourlas. As for the scalar particle, we show that the PCT transformation is induced by a certain element of the SO(D,2) subgroup of the IOSp(D,2vertical stroke2). This gives us the tools for a simple interpretation of the PCT theorem for Dirac fields. We then continue by clarifying the role of the 'modular' transformation (i.e. world-line orientation-reversing diffeomorphism) and indicating how the PCT transformation could be regarded as a modular transformation in a 'SO(D,2)-rotated' frame. In this work we also consider BRST field theories leading to D-dimensional chiral theories. In this case, of the full IOSp(D,2vertical stroke2) symmetry, only the subgroup IO(D-1,1)xOSp(1,1vertical stroke2) survives together with the (isolated) SO(D,2) transformation that implements PCT. (orig.)
Physical states and BRST operators for higher-spin W strings
International Nuclear Information System (INIS)
Liu, Yu-Xiao; Wei, Shao-Wen; Ren, Ji-Rong; Zhang, Li-Jie
2009-01-01
In this paper, we mainly investigate the W 2,s M x W 2,s L system, in which the matter and the Liouville subsystems generate the W 2,s M and W 2,s L algebras, respectively. We first give a brief discussion of the physical states for the corresponding W strings. The lower states are given by freezing the spin-2 and spin-s currents. Then, introducing two pairs of ghost-like fields, we give the realizations of the W 1,2,s algebras. Based on these linear realizations, the BRST operators for the W 2,s algebras are obtained. Finally, we construct new BRST charges of the Liouville system for the W 2,s L strings at the specific values of the central charges c: c=-(22)/(5) for the W 2,3 L algebra, c=-24 for the W 2,4 L algebra and c=-2,-(286)/(3) for the W 2,6 L algebra, at which the corresponding W 2,s L algebras are singular. (orig.)
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.
Comments on the Gauge Fixed BRST Cohomology and the Quantum Noether Method
Barnich, G; Skenderis, K; Barnich, Glenn; Hurth, Tobias; Skenderis, Kostas
2004-01-01
We discuss in detail the relation between the gauge fixed and gauge invariant BRST cohomology. In particular in certain gauges some cohomology classes of the gauge fixed BRST differential do not correspond to gauge invariant observables, and in addition ``accidental'' conserved currents may appear. These correspond 1-1 to observables that become trivial in this gauge. We explicitly show how the gauge fixed BRST cohomology appears in the context of the Quantum Noether Method.
State space in BRST-quantization and Kugo-Ojima quartets
International Nuclear Information System (INIS)
Rybkin, G.N.
1989-01-01
The structure of the state space in the BRST-quantization is considered and the connection between different approaches to the proof of the positive definiteness of the metric on the physical state space is established. The correspondence between different expressions for the BRST-charge, quadratic in fields, is obtained. The relation between different representations of the BRST-algebra is found. 22 refs
Maximal Abelian gauge and a generalized BRST transformation
Directory of Open Access Journals (Sweden)
Shinichi Deguchi
2016-05-01
Full Text Available We apply a generalized Becchi–Rouet–Stora–Tyutin (BRST formulation to establish a connection between the gauge-fixed SU(2 Yang–Mills (YM theories formulated in the Lorenz gauge and in the Maximal Abelian (MA gauge. It is shown that the generating functional corresponding to the Faddeev–Popov (FP effective action in the MA gauge can be obtained from that in the Lorenz gauge by carrying out an appropriate finite and field-dependent BRST (FFBRST transformation. In this procedure, the FP effective action in the MA gauge is found from that in the Lorenz gauge by incorporating the contribution of non-trivial Jacobian due to the FFBRST transformation of the path integral measure. The present FFBRST formulation might be useful to see how Abelian dominance in the MA gauge is realized in the Lorenz gauge.
BRST cohomology of the superstring at arbitrary ghost number
International Nuclear Information System (INIS)
Horowitz, G.T.; Myers, R.C.; Martin, S.P.
1989-01-01
We investigate the cohomology of the BRST operator of the NSR superstring. No restriction is placed on the ghost number of the states. It is shown that every cohomology class can be written as a picture changed version of one of the known cohomology classes at a fixed ghost number. A generalization of this result is also found for the cohomology in the large algebra of a new bosonization of the superconformal ghosts. (orig.)
A geometric view on BRST extension of the phase space
International Nuclear Information System (INIS)
Kyuldjiev, A.
1994-11-01
The role of complex polarizations is emphasized as providing coordinate-free approach to creation and annihilation operators needed for particle interpretation. With their help a proposition is made for explanation of BRST extension of the phase space due to fixing to zero the number of particles corresponding to constraint functions. The procedure treats the case when no group action is assumed and does not require any form of supersymmetry. (author). 19 refs
On operators of the ghost number and conjugation in the BRST quantization formalism
International Nuclear Information System (INIS)
Azizov, T.Ya.; Khoruzhij, S.S.
1989-01-01
Detailed and rigorous study is made of operators of the ghost number Q c and ghost conjugation U c which are operators in Krein spaces arising in the BRST quantization formalism for constrained dynamical systems. A number of conditions are obtained which guarantee that Q c is well-defined and J-symmetric. It is shown that properties of Q c are related to the following geometrical problem: to find conditions under which a pair of lineals in the Krein space can be made neutral by the appropriate choice of J-metrics. The complete solution of this problem is given. Whole series of examples is constructed which demonstrate the connections between properties of Q c and geometry of its spectral subspaces
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
Pereira, A. D.; Sobreiro, R. F.; Sorella, S. P.
2016-10-01
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi: 10.1103/PhysRevD.92.045039 arXiv:1506.06995 [hep-th], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions.
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
International Nuclear Information System (INIS)
Pereira, A.D.; Sobreiro, R.F.; Sorella, S.P.
2016-01-01
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
Energy Technology Data Exchange (ETDEWEB)
Pereira, A.D. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Potsdam (Germany); UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Sobreiro, R.F. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Sorella, S.P. [UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil)
2016-10-15
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
{beta}-{gamma} systems and the deformations of the BRST operator
Energy Technology Data Exchange (ETDEWEB)
Zeitlin, Anton M [Department of Mathematics, Yale University, 442 Dunham Lab, 10 Hillhouse Ave, New Haven, CT 06511 (United States)], E-mail: anton.zeitlin@yale.edu
2009-09-04
We describe the relation between simple logarithmic CFTs associated with closed and open strings, and their 'infinite metric' limits, corresponding to the {beta}-{gamma} systems. This relation is studied on the level of the BRST complex: we show that the consideration of metric as a perturbation leads to a certain deformation of the algebraic operations of the Lian-Zuckerman type on the vertex algebra, associated with the {beta}-{gamma} systems. The Maurer-Cartan equations corresponding to this deformed structure in the quasi-classical approximation lead to the nonlinear field equations. As an explicit example, we demonstrate that using this construction, Yang-Mills equations can be derived. This gives rise to a nontrivial relation between the Courant-Dorfman algebroid and homotopy algebras emerging from the gauge theory. We also discuss a possible algebraic approach to the study of beta-functions in sigma-models.
International Nuclear Information System (INIS)
Jaskolski, Z.
1991-05-01
The geometrical approach to the functional integral over Faddeev-Popov ghost fields is developed and applied to construct the BRST extension of the off-shell closed string amplitudes in the constant curvature gauge. In this gauge the overlap path integral for off-shell amplitudes is evaluated. It leads to the nonlocal sewing procedure generating all off-shell amplitudes from the cubic interaction vertex. The general scheme of the reconstruction of a covariant closed string field theory from the off-shell amplitudes is discussed within the path integral framework. (author). 30 refs
Description of the higher massless irreducible integer spins in the BRST approach
International Nuclear Information System (INIS)
Pashnev, A.; Tsulaya, M.
1998-01-01
The BRST approach is applied to the description of irreducible massless higher spins representations of the Poincare group in arbitrary dimensions. The total system of constraints in such theory includes both the first and the second class constraints. The corresponding nilpotent BRST charge contains terms up to the seventh degree in ghosts
Generalised BRST symmetry and gaugeon formalism for perturbative quantum gravity: Novel observation
International Nuclear Information System (INIS)
Upadhyay, Sudhaker
2014-01-01
In this paper the novel features of Yokoyama gaugeon formalism are stressed out for the theory of perturbative quantum gravity in the Einstein curved spacetime. The quantum gauge transformations for the theory of perturbative gravity are demonstrated in the framework of gaugeon formalism. These quantum gauge transformations lead to renormalised gauge parameter. Further, we analyse the BRST symmetric gaugeon formalism which embeds more acceptable Kugo–Ojima subsidiary condition. Further, the BRST symmetry is made finite and field-dependent. Remarkably, the Jacobian of path integral under finite and field-dependent BRST symmetry amounts to the exact gaugeon action in the effective theory of perturbative quantum gravity. -- Highlights: •We analyse the perturbative gravity in gaugeon formalism. •The generalisation of BRST transformation is also studied in this context. •Within the generalised BRST framework we found the exact gaugeon modes in the theory
Problems of vector Lagrangians in field theories
International Nuclear Information System (INIS)
Krivsky, I.Yu.; Simulik, V.M.
1997-01-01
A vector Lagrange approach to the Dirac spinor field and the relationship between the vector Lagrangians for the spinor and electromagnetic fields are considered. A vector Lagrange approach for the system of interacting electromagnetic B=(B μ υ)=(E-bar,H-bar) and spinor Ψ fields is constructed. New Lagrangians (scalar and vector) for electromagnetic field in terms of field strengths are found. The foundations of two new QED models are formulated
New inner products for physical states in BRST quantization
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Marnelius, R.; Oegren, M.
1991-01-01
In a BRST quantization involving operators with continuous eigenvalues the naive inner products of physical states are usually undefined. In order to include such cases we propose new inner products defined by , where ρ is an odd gauge-fixing operator. In this definition, which requires the use of dynamical Lagrange multipliers, the factor exp i[ρ,Q] is naturally provided by the choice of dynamics. Several examples are worked out. In particular it is shown that the worldline supersymmetric model for a massless spin-1/2 particle leads to fermions whose chiral projections have opposite norms. (orig.)
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Kaminski, J.Z.
1981-01-01
A renormalization group equation for the effective Lagrangian of QED is obtained. Starting from this equation, perturbation theory for the renormalization group equation (PTRGE) is developed. The results are in full agreement with the standard perturbation theory. Conjecturing that the asymptotic effective coupling constant is finite, the effective Lagrangian for a strong magnetic field is obtained, which is proportional to the Maxwellian Lagrangian. For the asymptotically free theories the situation is diametrically opposed to QED. In these cases the effective Lagrangian of the Yang-Mills system tends to infinity for very strong external Yang-Mills fields. (Auth.)
The BRST quantization and the no-ghost theorem for AdS3
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Asano, Masako; Natsuume, Makoto
2003-01-01
In our previous papers, we prove the no-ghost theorem without light-cone directions. We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS 3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OCQ equivalence for AdS 3 . The key in both approaches lies in the certain structure of the matter Hilbert space as a product of two Verma modules. We also present the no-ghost theorem in the most general form. (author)
BRST Formalism in Self-Dual Chern-Simons Theory with Matter Fields
Dai, Jialiang; Fan, Engui
2018-04-01
We apply BRST method to the self-dual Chern-Simons gauge theory with matter fields and the generators of symmetries of the system from an elegant Lie algebra structure under the operation of Poisson bracket. We discuss four different cases: abelian, nonabelian, relativistic, and nonrelativistic situations and extend the system to the whole phase space including ghost fields. In addition, we obtain the BRST charge of the field system and check its nilpotence of the BRST transformation which plays an important role such as in topological quantum field theory and string theory.
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories
Buican, Matthew; Laczko, Zoltan
2018-02-01
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.
Buican, Matthew; Laczko, Zoltan
2018-02-23
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
Effective lagrangian for strong interactions
International Nuclear Information System (INIS)
Jain, P.
1988-01-01
We attempt to construct a realistic phenomenological Lagrangian in order to describe strong interactions. This is in general a very complicated problem and we shall explore its various aspects. We first include the vector mesons by writing down the most general chiral invariant terms proportional to the Levi-Civita symbol ε μναβ . These terms involve three unknown coefficients, which are calculated by using the experimental results of strong interaction processes. We then calculate the static nucleon properties by finding the solitonic excitations of this model. The results turn out to be, as is also the case for most other vector-pseudoscalar Lagrangians, better than the Skyrme model but are still somewhat different from the experiments. Another aspect that we shall study is the incorporation of scale anomaly of QCD into the Skyrme model. We thus introduce a scalar glueball in our Lagrangian. Here we find an interesting result that the effective glue field dynamically forms a bag for the soliton. Depending on the values of the parameters, we get either a deep bag or a shallow bag. However by including the scalar meson, we find that to get realistic scalar sector we must have the shallow bag. Finally we show some intriguing connections between the chiral quark model, in which the nucleon is described as a solitonic excitation, and the ordinary potential binding quark model
Lagrangian descriptors in dissipative systems.
Junginger, Andrej; Hernandez, Rigoberto
2016-11-09
The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory-that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of Lagrangian descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the Lagrangian descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the Lagrangian descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.
Slavnov-Taylor1.0: A Mathematica package for computation in BRST formalism
Picariello, Marco; Picariello, Marco; Torrente-Lujan, Emilio
2004-01-01
Slavnov-Taylor1.0 is a Mathematica package which allows us to perform automatic simbolic computation in BRST formalism. This article serves as a self-contained guide to prospective users, and indicates the conventions and approximations used.
Existence, uniqueness and cohomology of the classical BRST charge with ghosts of ghosts
International Nuclear Information System (INIS)
Fisch, J.; Stasheff, J.
1989-01-01
A complete canonical formulation of the BRST theory of systems with redundant gauge symmetries is presented. These systems include p-form gauge fields, the superparticle, and the superstring. We first define the Koszul-Tate differential and explicitly show how the introduction of the momenta conjugate to the ghosts of ghosts makes it acyclic. The global existence of the BRST generator is then demonstrated, and the BRST charge is proved to be unique up to canonical transformations in the extended phase space, which includes the ghosts. Finally, the BRST cohomology in classical mechanics is investigated and shown to be equal to the cohomology of the exterior derivative along the gauge orbits, as in the irreducible case. This is done by re-expressing the exterior algebra along the gauge orbits as a free differential algebra containing generators of higher degree, which are identified with the ghosts of ghosts. The quantum cohomology is not dealt with. (orig.)
"Lagrangian" for a Non-Lagrangian Field Theory with N=2 Supersymmetry.
Gadde, Abhijit; Razamat, Shlomo S; Willett, Brian
2015-10-23
We suggest that at least some of the strongly coupled N=2 quantum field theories in 4D can have a nonconformal N=1 Lagrangian description flowing to them at low energies. In particular, we construct such a description for the N=2 rank one superconformal field theory with E(6) flavor symmetry, for which a Lagrangian description was previously unavailable. We utilize this description to compute several supersymmetric partition functions.
Lagrangian formalism for constrained systems. 2. Gauge symmetries
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Pyatov, P.N.
1990-01-01
Using the Lagrangian formalism for constrained systems all gauge symmetries peculiar for a given Lagrangian system and in establishing the relation between them and the constraints are constructed. Besides, the question about the possible dependence of gauge transformations on accelerations and other higher order time derivatives of coordinates is clarified. 14 refs
Lagrangian approach in spin-oscillations problem
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P.V. Pyshkin
2014-12-01
Full Text Available Lagrangian of electronic liquid in magneto-inhomogeneous micro-conductor has been constructed. A corresponding Euler-Lagrange equation has been solved. It was shown that the described system has eigenmodes of spin polarization and total electric current oscillations. The suggested approach permits to study the spin dynamics in an open-circuit which contains capacitance and/or inductivity.
Lagrangian and Hamiltonian dynamics
Mann, Peter
2018-01-01
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...
Lagrangian Curves on Spectral Curves of Monopoles
International Nuclear Information System (INIS)
Guilfoyle, Brendan; Khalid, Madeeha; Ramon Mari, Jose J.
2010-01-01
We study Lagrangian points on smooth holomorphic curves in TP 1 equipped with a natural neutral Kaehler structure, and prove that they must form real curves. By virtue of the identification of TP 1 with the space LE 3 of oriented affine lines in Euclidean 3-space, these Lagrangian curves give rise to ruled surfaces in E 3 , which we prove have zero Gauss curvature. Each ruled surface is shown to be the tangent lines to a curve in E 3 , called the edge of regression of the ruled surface. We give an alternative characterization of these curves as the points in E 3 where the number of oriented lines in the complex curve Σ that pass through the point is less than the degree of Σ. We then apply these results to the spectral curves of certain monopoles and construct the ruled surfaces and edges of regression generated by the Lagrangian curves.
Integration over families of Lagrangian submanifolds in BV formalism
Mikhailov, Andrei
2018-03-01
Gauge fixing is interpreted in BV formalism as a choice of Lagrangian submanifold in an odd symplectic manifold (the BV phase space). A natural construction defines an integration procedure on families of Lagrangian submanifolds. In string perturbation theory, the moduli space integrals of higher genus amplitudes can be interpreted in this way. We discuss the role of gauge symmetries in this construction. We derive the conditions which should be imposed on gauge symmetries for the consistency of our integration procedure. We explain how these conditions behave under the deformations of the worldsheet theory. In particular, we show that integrated vertex operator is actually an inhomogeneous differential form on the space of Lagrangian submanifolds.
Topological conformal algebra and BRST algebra in non-critical string theories
International Nuclear Information System (INIS)
Fujikawa, Kazuo; Suzuki, Hiroshi.
1991-03-01
The operator algebra in non-critical string theories is studied by treating the cosmological term as a perturbation. The algebra of covariantly regularized BRST and related currents contains a twisted N = 2 superconformal algebra only at d = -2 in bosonic strings, and a twisted N = 3 superconformal algebra only at d = ±∞ in spinning strings. The bosonic string at d = -2 is examined by replacing the string coordinate by a fermionic matter with c = -2. The resulting bc-βγ system accommodates various forms of BRST cohomology, and the ghost number assignment and BRST cohomology are different in the c = -2 string theory and two-dimensional topological gravity. (author)
Renormalization and effective lagrangians
International Nuclear Information System (INIS)
Polchinski, J.
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 lambda PHI 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. (orig.)
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…
Geometry of Lagrangian first-order classical field theories
International Nuclear Information System (INIS)
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N.
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 Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the 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. (orig.)
Geometry of Lagrangian first-order classical field theories
Energy Technology Data Exchange (ETDEWEB)
Echeverria-Enriquez, A. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Munoz-Lecanda, M.C. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Roman-Roy, N. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica
1996-10-01
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 Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the 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. (orig.)
Lagrangian procedures for higher order field equations
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.
1986-01-01
We present in a pedagogical way a Lagrangian procedure for the treatment of higher order field equations. We build the energy-momentum tensor and the conserved density current. In particular we discuss the case in which the derivatives appear only in the invariant D'Alembertian operator. We discuss some examples. We quantize the fields and construct the corresponding Hamiltonian which is shown not to be positive definite. We give the rules for the causal propagators. (Author) [pt
Renormalizability of a quark-gluon model with soft BRST breaking in the infrared region
Baulieu, L; Gomez, A J; Lemes, V E R; Sobreiro, R F; Sorella, S P
2010-01-01
We prove the renormalizability of a quark-gluon model with a soft breaking of the BRST symmetry, which accounts for the modification of the large distance behavior of the quark and gluon correlation functions. The proof is valid to all orders of perturbation theory, by making use of softly broken Ward identities.
International Nuclear Information System (INIS)
Jarvis, P.D.; Thompson, G.
1987-04-01
We establish the equivalence between the extended BRST invariances, and the conventional Slavnov-Taylor transformations together with a new ''dual'' analogue. However, the latter (a non-local gauge transformation, generating an A-dependent translation of the gauge-fixing surface) is not an invariance of the Faddeev-Popov determinant, contrary to the published claim. (author)
Lagrangian multiforms and multidimensional consistency
Energy Technology Data Exchange (ETDEWEB)
Lobb, Sarah; Nijhoff, Frank [Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT (United Kingdom)
2009-10-30
We show that well-chosen Lagrangians for a class of two-dimensional integrable lattice equations obey a closure relation when embedded in a higher dimensional lattice. On the basis of this property we formulate a Lagrangian description for such systems in terms of Lagrangian multiforms. We discuss the connection of this formalism with the notion of multidimensional consistency, and the role of the lattice from the point of view of the relevant variational principle.
BRST with background field method of the (4,0) supersymmetric σ-model in two dimensions
International Nuclear Information System (INIS)
Lhallabi, T.
1988-08-01
A manifestly covariant background field formalism for (4,0) supersymmetric non-linear σ-model in two dimensions is presented. The BRST argument is used in order to obtain Faddeev-Popov ghost terms. (author). 13 refs
An ambitwistor Yang-Mills Lagrangian
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Mason, L.J.; Skinner, D.
2006-01-01
We introduce a Chern-Simons Lagrangian for Yang-Mills theory as formulated on ambitwistor space via the Ward, Isenberg, Yasskin, Green, Witten construction. The Lagrangian requires the selection of a codimension-2 Cauchy-Riemann submanifold which is naturally picked out by the choice of space-time reality structure and we focus on the choice of Euclidean signature. The action is shown to give rise to a space-time action that is equivalent to the standard one, but has just cubic vertices. We identify the ambitwistor propagators and vertices and work out their corresponding expressions on space-time and momentum space. It is proposed that this formulation of Yang-Mills theory underlies the recursion relations of Britto, Cachazo, Feng and Witten and provides the generating principle for twistor diagrams for gauge theory
BRST quantization of 2d-Yang Mills theory with anomalies
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Kalau, Wolfgang
1992-01-01
The BRST-quantization of anomalous 2d-Yang Mills (YM) theory is discussed. Since an oscillator basis for the YM-Fock-space is used the anomaly appears already for a pure YM-system and the constraints form a Kac-Moody algebra with negative central charge. The coupling of chiral fermions is also discussed and it is found that the BRST-cohomology for systems with chiral fermions in a sufficiently large representation of the gauge group is completely equivalent to the cohomology of the finite dimensional gauge group. For pure YM theory or YM theory coupled to chiral fermions in small representations there exists an infinite number of inequivalent cohomology classes. This is discussed in some detail for the example of SU(2). (author). 15 refs
d $\\leq$ 1 U d $\\geq$ 25 and W constraints from BRST invariance in the C $\
Gato-Rivera, Beatriz
1992-01-01
The BRST invariance condition in a highest-weight representation of the topological ($\\equiv$ twisted $N=2$) algebra captures the `invariant' content of two-dimensional gravity coupled to matter. The standard DDK formulation is recovered by splitting the topological generators into $c=-26$ reparametrization ghosts+matter +`Liouville', while a similar splitting involving $c=-2$ ghosts gives rise to the matter dressed in exactly the way required in order that the theory be equivalent to Virasoro constraints on the KP hierarchy. The two dressings of matter with the `Liouville' differ also by their `ghost numbers', which is similar to the existence of representatives of BRST cohomologies with different ghost numbers. The topological central charge $\\ctop\
Lynn, Bryan W.; Starkman, Glenn D.
2017-09-01
The weak-scale U (1 )Y Abelian Higgs model (AHM) is the simplest spontaneous symmetry breaking (SSB) gauge theory: a scalar ϕ =1/√{2 }(H +i π )≡1/√{2 }H ˜ei π ˜/⟨H ⟩ and a vector Aμ. The extended AHM (E-AHM) adds certain heavy (MΦ2,Mψ2˜MHeavy2≫⟨H ⟩2˜mWeak2 ) spin S =0 scalars Φ and S =1/2 fermions ψ . In Lorenz gauge, ∂μAμ=0 , the SSB AHM (and E-AHM) has a global U (1 )Y conserved physical current, but no conserved charge. As shown by T. W. B. Kibble, the Goldstone theorem applies, so π ˜ is a massless derivatively coupled Nambu-Goldstone boson (NGB). Proof of all-loop-orders renormalizability and unitarity for the SSB case is tricky because the Becchi-Rouet-Stora-Tyutin (BRST)-invariant Lagrangian is not U (1 )Y symmetric. Nevertheless, Slavnov-Taylor identities guarantee that on-shell T-matrix elements of physical states Aμ,ϕ , Φ , ψ (but not ghosts ω , η ¯ ) are independent of anomaly-free local U (1 )Y gauge transformations. We observe here that they are therefore also independent of the usual anomaly-free U (1 )Y global/rigid transformations. It follows that the associated global current, which is classically conserved only up to gauge-fixing terms, is exactly conserved for amplitudes of physical states in the AHM and E-AHM. We identify corresponding "undeformed" [i.e. with full global U (1 )Y symmetry] Ward-Takahashi identities (WTI). The proof of renormalizability and unitarity, which relies on BRST invariance, is undisturbed. In Lorenz gauge, two towers of "1-soft-pion" SSB global WTI govern the ϕ -sector, and represent a new global U (1 )Y⊗BRST symmetry not of the Lagrangian but of the physics. The first gives relations among off-shell Green's functions, yielding powerful constraints on the all-loop-orders ϕ -sector SSB E-AHM low-energy effective Lagrangian and an additional global shift symmetry for the NGB: π ˜→π ˜+⟨H ⟩θ . A second tower, governing on-shell T-matrix elements, replaces the old Adler
International Nuclear Information System (INIS)
Capri, Marcio; Justo, Igor; Guimaraes, Marcelo; Sorella, Silvio; Dudal, David; Palhares, Leticia
2013-01-01
Full text: In recent years much attention has been devoted to the study of the issue of the Gribov copies and of its relevance for confinement in Yang-Mills theories. The existence of the Gribov copies is a general feature of the gauge-fixing quantization procedure, being related to the impossibility of finding a local gauge condition which picks up only one gauge configuration for each gauge orbit. As it has been shown by Gribov and Zwanziger, a partial solution of the Gribov problem in the Landau gauge can be achieved by restricting the domain of integration in the functional Euclidean integral to the first Gribov horizon. Among the various open aspects of the Gribov-Zwanziger framework, the issue of the BRST symmetry is a source of continuous investigations. In a recent work, we have been able to obtain an equivalent formulation of the Gribov-Zwanziger action which displays an exact BRST symmetry which turns out to be spontaneously broken by the restriction of the domain of integration to the Gribov horizon. In particular, the BRST operator retains the important property of being nilpotent. Moreover, it has also been shown that the Goldstone mode associated to the spontaneous breaking of the BRST symmetry is completely decoupled. The aim of the present work is that of fills up a gap not addressed in the previous work, namely, the renormalizability to all orders of the spontaneous symmetry breaking formulation of the Gribov-Zwanziger theory. As we shall see, the action obtained enjoys a large set of Ward identities which enables to prove that it is, in fact, multiplicatively renormalizable to all orders. (author)
Lagrangian formulation of classical BMT-theory
International Nuclear Information System (INIS)
Pupasov-Maksimov, Andrey; Deriglazov, Alexei; Guzman, Walberto
2013-01-01
Full text: The most popular classical theory of electron has been formulated by Bargmann, Michel and Telegdi (BMT) in 1959. The BMT equations give classical relativistic description of a charged particle with spin and anomalous magnetic momentum moving in homogeneous electro-magnetic field. This allows to study spin dynamics of polarized beams in uniform fields. In particular, first experimental measurements of muon anomalous magnetic momentum were done using changing of helicity predicted by BMT equations. Surprisingly enough, a systematic formulation and the analysis of the BMT theory are absent in literature. In the present work we particularly fill this gap by deducing Lagrangian formulation (variational problem) for BMT equations. Various equivalent forms of Lagrangian will be discussed in details. An advantage of the obtained classical model is that the Lagrangian action describes a relativistic spinning particle without Grassmann variables, for both free and interacting cases. This implies also the possibility of canonical quantization. In the interacting case, an arbitrary electromagnetic background may be considered, which generalizes the BMT theory formulated to the case of homogeneous fields. The classical model has two local symmetries, which gives an interesting example of constrained classical dynamics. It is surprising, that the case of vanishing anomalous part of the magnetic momentum is naturally highlighted in our construction. (author)
Lagrangian averaging with geodesic mean.
Oliver, Marcel
2017-11-01
This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler- α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.
International Nuclear Information System (INIS)
Malik, R. P.; Srinivas, N.; Bhanja, T.
2016-01-01
We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator and its Hermitian conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor and modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of the dual unitary operators and corresponding (anti-)dual-BRST symmetries are completely novel results in our present investigation.
Field-dependent BRST–antiBRST transformations in Yang–Mills and Gribov–Zwanziger theories
Directory of Open Access Journals (Sweden)
Pavel Yu. Moshin
2014-11-01
Full Text Available We introduce the notion of finite BRST–antiBRST transformations, both global and field-dependent, with a doublet λa, a=1,2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in Yang–Mills theories. It turns out that the finite transformations are quadratic in their parameters. At the same time, exactly as in the case of finite field-dependent BRST transformations for the Yang–Mills vacuum functional, special field-dependent BRST–antiBRST transformations, with sa-potential parameters λa=saΛ induced by a finite even-valued functional Λ and by the anticommuting generators sa of BRST–antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST–antiBRST transformations. We present the form of transformation parameters that generates a change of the gauge in the path integral and evaluate it explicitly for connecting two arbitrary Rξ-like gauges. For arbitrary differentiable gauges, the finite field-dependent BRST–antiBRST transformations are used to generalize the Gribov horizon functional h, given in the Landau gauge, and being an additive extension of the Yang–Mills action by the Gribov horizon functional in the Gribov–Zwanziger model. This generalization is achieved in a manner consistent with the study of gauge independence. We also discuss an extension of finite BRST–antiBRST transformations to the case of general gauge theories and present an ansatz for such transformations.
Weyl's Lagrangian in teleparallel form
International Nuclear Information System (INIS)
Burnett, James; Vassiliev, Dmitri
2009-01-01
The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable - the coframe (an orthonormal tetrad of covector fields). We show that when written in terms of this dynamical variable, the Weyl Lagrangian becomes remarkably simple: it is the wedge product of axial torsion of the teleparallel connection with a teleparallel lightlike element of the coframe. We also examine the issues of U(1)-invariance and conformal invariance. Examination of the latter motivates us to introduce a positive scalar field (equivalent to a density) as an additional dynamical variable; this makes conformal invariance self-evident.
Lagrangian postprocessing of computational hemodynamics.
Shadden, Shawn C; Arzani, Amirhossein
2015-01-01
Recent advances in imaging, modeling, and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries, and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows.
Quadratic Lagrangians and Legendre transformation
International Nuclear Information System (INIS)
Magnano, G.
1988-01-01
In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor
Energy Technology Data Exchange (ETDEWEB)
Batalin, Igor A. [P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Pedagogical University, Tomsk (Russian Federation); Bering, Klaus [Masaryk University, Faculty of Science, Brno (Czech Republic); Lavrov, Peter M. [Tomsk State Pedagogical University, Tomsk (Russian Federation); National Research Tomsk State University, Tomsk (Russian Federation)
2016-03-15
Finite BRST-BV transformations are studied systematically within the W-X formulation of the standard and the Sp(2)-extended field-antifield formalism. The finite BRST-BV transformations are introduced by formulating a new version of the Lie equations. The corresponding finite change of the gauge-fixing master action X and the corresponding Ward identity are derived. (orig.)
Superconformal Lagrangian without the need to introduce constraints
International Nuclear Information System (INIS)
Pilot, C.H.
1986-01-01
A field Lagrangian invariant under all the symmetries of the superconformal group has been constructed without the need to introduce constraints on the curvatures. We have thus generalized the action of Townsend, van Nieuwenhuizen, and Kaku. We maintain that any and all constraints on the curvatures should result as a consequence of spontaneous symmetry breaking and not be a priori enforced. 14 refs
Translating solitons to symplectic and Lagrangian mean curvature flows
International Nuclear Information System (INIS)
Han Xiaoli; Li Jiayu
2007-05-01
In this paper, we construct finite blow-up examples for symplectic mean curvature flows and we study symplectic translating solitons. We prove that there is no translating solitons with vertical bar α vertical bar ≤ α 0 to the symplectic mean curvature flow or to the almost calibrated Lagrangian mean curvature flow for some α 0 . (author)
Perturbative QCD lagrangian at large distances and stochastic dimensionality reduction
International Nuclear Information System (INIS)
Shintani, M.
1986-10-01
We construct a Lagrangian for perturbative QCD at large distances within the covariant operator formalism which explains the color confinement of quarks and gluons while maintaining unitarity of the S-matrix. It is also shown that when interactions are switched off, the mechanism of stochastic dimensionality reduction is operative in the system due to exact super-Lorentz symmetries. (orig.)
International Nuclear Information System (INIS)
Chair, N.; Dobrev, V.K.; Kanno, H.
1992-01-01
We consider BRST quantized 2D gravity coupled to conformal matter with arbitrary central change c M = c(p,q) M = 1 chiral ground ring. We show that the ring structure generated by the (relative BRST cohomology) discrete states in the (matter x Liouville x ghosts) Fock module may be obtained by this rotation. We give also explicit formulae for the discrete states. For some of them we use new formulae for c<1 Fock modules singular vectors which we present in terms of Schur polynomials generalizing the c = 1 expressions of Goldstone, while the rest of the discrete states we obtain by finding the proper SO(2,C) rotation. Our formulae give the extra physical states (arising from the relative BRST cohomology) on the boundaries of the p x q rectangles of the conformal lattice and thus all such states in (1,q) or (p,1) models. (author). 24 refs
The anomalous chiral Lagrangian of order p6
International Nuclear Information System (INIS)
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 5 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. (orig.)
International Nuclear Information System (INIS)
Theodorakis, S.
1988-01-01
This paper presents a phenomenological Lagrangian that fully describes the dynamics of any homogeneous phase of superfluid 3 He, unitary or not, omitting relaxation. This Lagrangian is built by using the concept of a local SO(3) x SO(3) x U(1) symmetry. The spin and angular momentum play the role of gauge fields. We derive the Leggett equations for spin and orbital dynamics from the equations of motion, for both the A and the B phase. This Lagrangian not only enables us to describe both the spin and orbital dynamics of superfluid 3 He in a unified fashion, but can also be used for finding the dynamics in any experimental situation. Furthermore, it can describe the dynamics of the magnitude, as well as of the orientation of the order parameter, and thus it can be used to describe the dynamics of the A-B phase transition
Extended hamiltonian formalism and Lorentz-violating lagrangians
Directory of Open Access Journals (Sweden)
Don Colladay
2017-09-01
Full Text Available A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler–Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.
Extended hamiltonian formalism and Lorentz-violating lagrangians
Colladay, Don
2017-09-01
A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.
Physical States and BRST Operators for Higher-spin $W$ Strings
Liu, Yu-Xiao; Wei, Shao-Wen; Zhang, Li-Jie; Ren, Ji-Rong
2008-01-01
In this paper, we mainly investigate the $W_{2,s}^{M}\\otimes W_{2,s}^{L}$ system, in which the matter and the Liouville subsystems generate $W_{2,s}^{M}$ and $W_{2,s}^L$ algebras respectively. We first give a brief discussion of the physical states for corresponding $W$ stings. The lower states are given by freezing the spin-2 and spin-$s$ currents. Then, introducing two pairs of ghost-like fields, we give the realizations of $W_{1,2,s}$ algebras. Based on these linear realizations, BRST oper...
Effective Lagrangians for SUSY QCD with properties seen in perturbation theory
International Nuclear Information System (INIS)
Sharatchandra, H.S.
1984-06-01
We construct effective Lagrangians for supersymmetric QCD which properly incorporate the relevant Ward identities and possess features encountered in perturbation theory. This shows that the unusual scenarios, proposed for SUSY QCD, are not necessary. (author)
Remarks on gauge variables and singular Lagrangians
International Nuclear Information System (INIS)
Chela-Flores, J.; Janica-de-la-Torre, R.; Kalnay, A.J.; Rodriguez-Gomez, J.; Rodriguez-Nunez, J.; Tascon, R.
1977-01-01
The relevance is discussed of gauge theory, based on a singular Lagrangian density, to the foundations of field theory. The idea that gauge transformations could change the physics of systems where the Lagrangian is singular is examined. (author)
Lagrangian multi-particle statistics
DEFF Research Database (Denmark)
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...
Sigma decomposition: the CP-odd Lagrangian
Energy Technology Data Exchange (ETDEWEB)
Hierro, I.M. [Dipartimento di Fisica “G. Galilei”, Università di Padova and INFN, Sezione di Padova,Via Marzolo 8, I-35131 Padua (Italy); Merlo, L. [Instituto de Física Teórica, IFT-UAM/CSIC, Universidad Autónoma de Madrid,Cantoblanco, 28049, Madrid (Spain); Rigolin, S. [Dipartimento di Fisica “G. Galilei”, Università di Padova and INFN, Sezione di Padova,Via Marzolo 8, I-35131 Padua (Italy)
2016-04-04
In Alonso et al., http://dx.doi.org/10.1007/JHEP12(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.
Lagrangian descriptors of driven chemical reaction manifolds.
Craven, Galen T; Junginger, Andrej; Hernandez, Rigoberto
2017-08-01
The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.
Local BRST cohomology in the antifield formalism. Pt. 2. Application to Yang-Mills theory
International Nuclear Information System (INIS)
Barnich, G.; Henneaux, M.
1995-01-01
Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential s modulo the exterior spacetime derivative d for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditions sa+db=0 depending non-trivially on the antifields are exhibited. For a semi-simple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition sa+db=0 besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature or Chern-Simons terms. (orig.)
Local BRST cohomology in the antifield formalism. Pt. 2. Application to Yang-Mills theory
International Nuclear Information System (INIS)
Barnich, G.; Henneaux, M.; Brandt, F.
1994-01-01
Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential s modulo the exterior spacetime derivative d for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (= sources for the BRST variations) and their derivatives. New solutions to the consistency conditions sa+db = 0 depending non trivially on the antifields are exhibited. For a semi-simple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition sa+db 0 besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature, or Chern-Simons terms. (orig.)
Lagrangian Studies of Lateral Mixing
2017-09-19
Final Technical 3. DATES COVERED (From - To) 01/01/2009 – 12/31/2015 4. TITLE AND SUBTITLE Lagrangian Studies of Lateral Mixing 5a. CONTRACT NUMBER...public release; distribution is unlimited. 13. SUPPLEMENTARY NOTES 14. ABSTRACT The Lateral Mixing Experiment (LATMIX) focused on mixing and...anomalies. LATMIX2 targeted the wintertime Gulf Stream, where deep mixed layers, strong lateral density gradients (Gulf Stream north wall) and the
Chiral Lagrangians and the SSC
International Nuclear Information System (INIS)
Dawson, S.
1991-09-01
In the event that the SSC does not observe any resonances such as a Higgs boson or a techni-rho meson, we would like to know if the SSC can still discover something about the nature of the electroweak symmetry breaking. We will use chiral Lagrangian techniques to address this question and analyze their utility for studying events containing W and Z gauge bosons at the SSC. 20 refs., 4 figs
Perturbative QCD Lagrangian at large distances and stochastic dimensionality reduction. Pt. 2
International Nuclear Information System (INIS)
Shintani, M.
1986-11-01
Using the method of stochastic dimensional reduction, we derive a four-dimensional quantum effective Lagrangian for the classical Yang-Mills system coupled to the Gaussian white noise. It is found that the Lagrangian coincides with the perturbative QCD at large distances constructed in our previous paper. That formalism is based on the local covariant operator formalism which maintains the unitarity of the S-matrix. Furthermore, we show the non-perturbative equivalence between super-Lorentz invariant sectors of the effective Lagrangian and two dimensional QCD coupled to the adjoint pseudo-scalars. This implies that stochastic dimensionality reduction by two is approximately operative in QCD at large distances. (orig.)
Uncovering the Geometry of Barrierless Reactions Using Lagrangian Descriptors.
Junginger, Andrej; Hernandez, Rigoberto
2016-03-03
Transition-state theories describing barrierless chemical reactions, or more general activated problems, are often hampered by the lack of a saddle around which the dividing surface can be constructed. For example, the time-dependent transition-state trajectory uncovering the nonrecrossing dividing surface in thermal reactions in the framework of the Langevin equation has relied on perturbative approaches in the vicinity of the saddle. We recently obtained an alternative approach using Lagrangian descriptors to construct time-dependent and recrossing-free dividing surfaces. This is a nonperturbative approach making no reference to a putative saddle. Here we show how the Lagrangian descriptor can be used to obtain the transition-state geometry of a dissipated and thermalized reaction across barrierless potentials. We illustrate the method in the case of a 1D Brownian motion for both barrierless and step potentials; however, the method is not restricted and can be directly applied to different kinds of potentials and higher dimensional systems.
BRST cohomology of N = 2 super-Yang-Mills theory in four dimensions
International Nuclear Information System (INIS)
Tanzini, A.; Ventura, O.S.; Vilar, L.C.Q.; Sorella, S.P.
2000-01-01
The BRST cohomology of the N = 2 supersymmetric Yang-Mills theory in four dimensions is discussed by making use of the twisted version of the N = 2 algebra. By the introduction of a set of suitable constant ghosts associated with the generators of N = 2, the quantization of the model can be done by taking into account both gauge invariance and supersymmetry. In particular, we show how the twisted N = 2 algebra can be used to obtain in a straightforward way the relevant cohomology classes. Moreover, we shall be able to establish a very useful relationship between the local gauge-invariant polynomial tr φ 2 and the complete N = 2 Yang-Mills action. This important relation can be considered as the first step towards a fully algebraic proof of the one-loop exactness of the N = 2 β-function.
The rotational aspects of the nuclear spectrum within the BRST formalism
International Nuclear Information System (INIS)
Bes, D.R.; Luca, R. de
1991-01-01
The treatment of collective variables within the BRST formalism is applied to the problem of the coupling between the particles and the rotational degrees of freedom. In zero order the system is described as in the usual version of the unified model, i.e., as the superposition of rotational and intrinsic motions with the usual Coriolis interaction emerging as a leading order coupling term. The higher-order corrections to the collective parameters, as well as the rotational dependence of relevant physical operators, are discussed both for even and odd systems. Several significant differences with the unified model and with the particle-rotor model are emphasized. The Elliott SU(3) model is used as an illustrative example. (orig.)
Symplectic invariants of some families of Lagrangian T3-fibrations
International Nuclear Information System (INIS)
Castano Bernard, R.
2003-12-01
We construct families of Lagrangian 3-torus fibrations resembling the topology of some of the singularities in Topological Mirror Symmetry. We perform a detailed analysis of the affine structure on the base of these fibrations near their discriminant loci. This permits us to classify the aforementioned families up to fibre preserving symplectomorphism. The kind of degenerations we investigate give rise to a large number of symplectic invariants. (author)
Local BRST cohomology in the antifield formalism. Pt. 1. General theorems
Energy Technology Data Exchange (ETDEWEB)
Barnich, G [Universite Libre de Bruxelles (Belgium). Faculte des Sciences; Henneaux, M [Universite Libre de Bruxelles (Belgium). Faculte des Sciences; Brandt, F [Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H
1994-12-31
We establish general theorems on the cohomology H{sup *}(svertical stroke d) of the BRST differential modulo the spacetime exterior derivative, acting in the algebra of local p-forms depending on the fields and the antifields (= sources for the BRST variations). It is shown that H{sup -k}(svertical stroke d) is isomorphic H{sub k}({delta}vertical stroke d) in negative ghost degree -k (k > 0), where {delta} is the Koszul-Tate differential associated with the stationary surface. The cohomological group H{sub 1}({delta}vertical stroke d) in form degree n is proved to be isomorphic to the space of constants of the motion, thereby providing a cohomological reformulation of Noether theorem. More generally, the group H{sub k}({delta}vertical stroke d) in form degree n is isomorphic to the space of n - k forms that are closed when the equations of motion hold. The groups H{sub k}({delta}vertical stroke d) (k > 2) are shown to vanish for standard irreducible gauge theories. The group H{sub 2}({delta}vertical stroke d) is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groups H{sup k}(svertical stroke d) under the introduction of non minimal variables and of auxiliary fields is also demonstrated. In a companion paper, the general formalism is applied to the calculation of H{sup k}(svertical stroke d) in Yang-Mills theory, which is carried out in detail for an arbitrary compact gauge group. (orig.).
The Wess-Zumino lagrangian and colored techni-pseudo-Goldstone bosons
International Nuclear Information System (INIS)
McKay, D.W.; Young Binglin; Iowa State Univ. of Science and Technology, Ames
1986-01-01
The construction of the Wess-Zumino type effective action is discussed for color octet techni-pion and techni-eta fields interacting with the light gauge bosons - gluon, photon, Wsup(+-) and Z. The explicit effective lagrangian for the one-pseudoscalar meson sector is displayed. GAMMA(eta->GWW), GAMMA(eta->GGγ) and GAMMA(eta->GGZ) are compared to GAMMA(eta->GZ) to illustrate the predictive content of the lagrangian. (orig.)
S-equivalents lagrangians in generalized mechanics
International Nuclear Information System (INIS)
Negri, L.J.; Silva, Edna G. da.
1985-01-01
The problem of s-equivalent lagrangians is considered in the realm of generalized mechanics. Some results corresponding to the ordinary (non-generalized) mechanics are extended to the generalized case. A theorem for the reduction of the higher order lagrangian description to the usual order is found to be useful for the analysis of generalized mechanical systems and leads to a new class of equivalence between lagrangian functions. Some new perspectives are pointed out. (Author) [pt
Alternative kinetic energy metrics for Lagrangian systems
Sarlet, W.; Prince, G.
2010-11-01
We examine Lagrangian systems on \\ {R}^n with standard kinetic energy terms for the possibility of additional, alternative Lagrangians with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such Lagrangians. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous Lagrangians for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom.
Low-energy phenomenological chiral Lagrangians
International Nuclear Information System (INIS)
Cavopol, A.V.
1987-01-01
We develop a phenomenological Lagrangian that satisfies the requirements of the so called alternative schemes designed to model low energy meson phenomenology. Linear and nonlinear σ type Lagrangians and symmetry breaking schemes are used to describe pions that exhibit masses proportional to the square of the symmetry breaking term's coefficient, ε. (m π 2 ∼ 0(ε 2 )). The invariance of the theory under coordinate dependent transformations is achieved by introducing gauge fields for both linear and nonlinear Lagrangians. Finally, analogies between the minimal symmetry breaking terms in Quantum Electrodynamics and in our phenomenological lagrangians are used to generate a discussion of the quark-pion mass dependence indicated by the model
Structure of pheomenological lagrangians for broken supersymmetry
International Nuclear Information System (INIS)
Uematsu, T.; Zachos, C.K.
1982-01-01
We consider the explicit connection between linear representations of supersymetry and the non-linear realizations associated with the generic effective lagrangians of the Volkov-Akulov type. We specify and illustrate a systematic approach for deriving the appropriate phenomenological lagrangian by transforming a pedagogical linear model, in which supersymmetry is broken at the tree level, into its corresponding non-linear lagrangian, in close analogy to the linear sigma model of pion dynamics. We discuss the significance and some properties of such phenomenological lagrangians. (orig.)
Cohomology for Lagrangian systems and Noetherian symmetries
International Nuclear Information System (INIS)
Popp, O.T.
1989-06-01
Using the theory of sheaves we find some exact sequences describing the locally Lagrangian systems. Using cohomology theory of groups with coefficients in sheaves we obtain some exact sequences describing the Noetherian symmetries. It is shown how the results can be used to find all locally Lagrangian dynamics Noetherian invariant with respect to a given group of kinematical symmetries.(author)
Lagrangian ocean analysis : Fundamentals and practices
van Sebille, Erik; Deleersnijder, E.L.C.; Heemink, A.W.; Griffies, Stepehn M.; Abernathey, Ryan; Adams, Thomas P.; Berloff, Pavel; Biastoch, Arne; Blanke, Bruno; Chassignet, Eric P.; Authors, More
2018-01-01
Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several
Effective lagrangian description on discrete gauge symmetries
International Nuclear Information System (INIS)
Banks, T.
1989-01-01
We exhibit a simple low-energy lagrangian which describes a system with a discrete remnant of a spontaneously broken continuous gauge symmetry. The lagrangian gives a simple description of the effects ascribed to such systems by Krauss and Wilczek: black holes carry discrete hair and interact with cosmic strings, and wormholes cannot lead to violation of discrete gauge symmetries. (orig.)
Lagrangian submanifolds and dynamics on Lie algebroids
International Nuclear Information System (INIS)
Leon, Manuel de; Marrero, Juan C; MartInez, Eduardo
2005-01-01
In some previous papers, a geometric description of Lagrangian mechanics on Lie algebroids has been developed. In this topical review, we give a Hamiltonian description of mechanics on Lie algebroids. In addition, we introduce the notion of a Lagrangian submanifold of a symplectic Lie algebroid and we prove that the Lagrangian (Hamiltonian) dynamics on Lie algebroids may be described in terms of Lagrangian submanifolds of symplectic Lie algebroids. The Lagrangian (Hamiltonian) formalism on Lie algebroids permits us to deal with Lagrangian (Hamiltonian) functions not defined necessarily on tangent (cotangent) bundles. Thus, we may apply our results to the projection of Lagrangian (Hamiltonian) functions which are invariant under the action of a symmetry Lie group. As a consequence, we obtain that Lagrange-Poincare (Hamilton-Poincare) equations are the Euler-Lagrange (Hamilton) equations associated with the corresponding Atiyah algebroid. Moreover, we prove that Lagrange-Poincare (Hamilton-Poincare) equations are the local equations defining certain Lagrangian submanifolds of symplectic Atiyah algebroids. (topical review)
Lagrangian ocean analysis : Fundamentals and practices
van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan; Adams, Thomas P.; Berloff, Pavel; Biastoch, Arne; Blanke, Bruno; Chassignet, Eric P.; Cheng, Yu; Cotter, Colin J.; Deleersnijder, Eric; Döös, Kristofer; Drake, Henri F.; Drijfhout, Sybren; Gary, Stefan F.; Heemink, Arnold W.; Kjellsson, Joakim; Koszalka, Inga Monika; Lange, Michael; Lique, Camille; MacGilchrist, Graeme A.; Marsh, Robert; Mayorga Adame, C. Gabriela; McAdam, Ronan; Nencioli, Francesco; Paris, Claire B.; Piggott, Matthew D.; Polton, Jeff A.; Rühs, Siren; Shah, Syed H.A.M.; Thomas, Matthew D.; Wang, Jinbo; Wolfram, Phillip J.; Zanna, Laure; Zika, Jan D.
2018-01-01
Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades,
Form of the manifestly covariant Lagrangian
Johns, Oliver Davis
1985-10-01
The preferred form for the manifestly covariant Lagrangian function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' Lagrangian and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant Lagrangian theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' Lagrangian, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives Lagrangian theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' Lagrangian is a completely adequate basis for covariant Lagrangian theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the Lagrangian and other four-vector equations.
A Lagrangian-dependent metric space
International Nuclear Information System (INIS)
El-Tahir, A.
1989-08-01
A generalized Lagrangian-dependent metric of the static isotropic spacetime is derived. Its behaviour should be governed by imposing physical constraints allowing to avert the pathological features of gravity at the strong field domain. This would restrict the choice of the Lagrangian form. (author). 10 refs
Lagrangian velocity correlations in homogeneous isotropic turbulence
International Nuclear Information System (INIS)
Gotoh, T.; Rogallo, R.S.; Herring, J.R.; Kraichnan, R.H.
1993-01-01
The Lagrangian velocity autocorrelation and the time correlations for individual wave-number bands are computed by direct numerical simulation (DNS) using the passive vector method (PVM), and the accuracy of the method is studied. It is found that the PVM is accurate when K max /k d ≥2 where K max is the maximum wave number carried in the simulation and k d is the Kolmogorov wave number. The Eulerian and Lagrangian time correlations for various wave-number bands are compared. At moderate to high wave number the Eulerian time correlation decays faster than the Lagrangian, and the effect of sweep on the former is observed. The time scale of the Eulerian correlation is found to be (kU 0 ) -1 while that of the Lagrangian is [∫ 0 k p 2 E(p)dp] -1/2 . The Lagrangian velocity autocorrelation in a frozen turbulent field is computed using the DIA, ALHDIA, and LRA theories and is compared with DNS measurements. The Markovianized Lagrangian renormalized approximation (MLRA) is compared with the DNS, and good agreement is found for one-time quantities in decaying turbulence at low Reynolds numbers and for the Lagrangian velocity autocorrelation in stationary turbulence at moderate Reynolds number. The effect of non-Gaussianity on the Lagrangian correlation predicted by the theories is also discussed
On the canonical treatment of Lagrangian constraints
International Nuclear Information System (INIS)
Barbashov, B.M.
2001-01-01
The canonical treatment of dynamic systems with manifest Lagrangian constraints proposed by Berezin is applied to concrete examples: a special Lagrangian linear in velocities, relativistic particles in proper time gauge, a relativistic string in orthonormal gauge, and the Maxwell field in the Lorentz gauge
Lagrangian properties of particles in turbulence
Toschi, F.; Bodenschatz, E.
2009-01-01
The Lagrangian description of turbulence is characterized by a unique conceptual simplicity and by an immediate connection with the physics of dispersion and mixing. In this article, we report some motivations behind the Lagrangian description of turbulence and focus on the statistical properties of
On the canonical treatment of Lagrangian constraints
International Nuclear Information System (INIS)
Barbashov, B.M.
2001-01-01
The canonical treatment of dynamic systems with manifest Lagrangian constraints proposed by Berezin is applied to concrete examples: a specific Lagrangian linear in velocities, relativistic particles in proper time gauge, a relativistic string in orthonormal gauge, and the Maxwell field in the Lorentz gauge
Unambiguous formalism for higher order Lagrangian field theories
International Nuclear Information System (INIS)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn; Vankerschaver, Joris
2009-01-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Lagrangian formulation and symmetrical description of liquid dynamics.
Trachenko, K
2017-12-01
Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.
The shallow water equations in Lagrangian coordinates
International Nuclear Information System (INIS)
Mead, J.L.
2004-01-01
Recent advances in the collection of Lagrangian data from the ocean and results about the well-posedness of the primitive equations have led to a renewed interest in solving flow equations in Lagrangian coordinates. We do not take the view that solving in Lagrangian coordinates equates to solving on a moving grid that can become twisted or distorted. Rather, the grid in Lagrangian coordinates represents the initial position of particles, and it does not change with time. We apply numerical methods traditionally used to solve differential equations in Eulerian coordinates, to solve the shallow water equations in Lagrangian coordinates. The difficulty with solving in Lagrangian coordinates is that the transformation from Eulerian coordinates results in solving a highly nonlinear partial differential equation. The non-linearity is mainly due to the Jacobian of the coordinate transformation, which is a precise record of how the particles are rotated and stretched. The inverse Jacobian must be calculated, thus Lagrangian coordinates cannot be used in instances where the Jacobian vanishes. For linear (spatial) flows we give an explicit formula for the Jacobian and describe the two situations where the Lagrangian shallow water equations cannot be used because either the Jacobian vanishes or the shallow water assumption is violated. We also prove that linear (in space) steady state solutions of the Lagrangian shallow water equations have Jacobian equal to one. In the situations where the shallow water equations can be solved in Lagrangian coordinates, accurate numerical solutions are found with finite differences, the Chebyshev pseudospectral method, and the fourth order Runge-Kutta method. The numerical results shown here emphasize the need for high order temporal approximations for long time integrations
Consistences for introducing more vector potentials in the same group, by BRST algorithm
International Nuclear Information System (INIS)
Doria, R.; Carvalho, F.A.R. de
1989-01-01
The BRS formalism for quantum formulation of gauge theory is analysed applying to extended models. The quantum effective Lagrangian of gauge is established, invariant under s and s→ for a system with vector potentials belong to one Abelian group of gauge. The BRS charge associated to the system is calculated. (M.C.K.)
Effective Lagrangians in elementary particle physics
International Nuclear Information System (INIS)
Trahern, C.G.
1982-01-01
Non-linear effective Lagrangians are constructed to represent the low energy phenomenology of elementary particles. As approximate descriptions of the dynamics of hadrons, these models simulate the expected (but unproven) behavior of more complex theories such as quantum Chromo-dynamics [QCD]. A general formalism for non-linear models was developed in the late 1960's by Coleman, Wess and Zumino. This dissertation utilizes and extends their work by incorporating some of the advances that have been made in the understanding of quantum field theories in the last decade. In particular the significance of spatial boundary conditions for interpreting the ground state behavior of the non-linear models is investigated. In addition the existence of a dual theory for the non-linear model is discussed. For experimental purposes duality refers to the possibility that in different enrgy regimes there may be wholly distinct kinds of excitations in the physical spectrum. Corresponding to these phenomenological distinctions are mutually exclusive mathematical descriptions. A familiar example is the duality of electric and magnetic charge in electro-dynamics. If magnetic charges do exist, they are expected to be extremely massive states that are unobservable up to very high energies. The analysis of such states within electrodynamics shows that one cannot describe both electric and magnetic charges without admitting the presence of singularities in the electric potential. A completely analogous form of duality is found and discussed for the non-linear models
Deconstructing field-induced ketene isomerization through Lagrangian descriptors.
Craven, Galen T; Hernandez, Rigoberto
2016-02-07
The time-dependent geometrical separatrices governing state transitions in field-induced ketene isomerization are constructed using the method of Lagrangian descriptors. We obtain the stable and unstable manifolds of time-varying transition states as dynamic phase space objects governing configurational changes when the ketene molecule is subjected to an oscillating electric field. The dynamics of the isomerization reaction are modeled through classical trajectory studies on the Gezelter-Miller potential energy surface and an approximate dipole moment model which is coupled to a time-dependent electric field. We obtain a representation of the reaction geometry, over varying field strengths and oscillation frequencies, by partitioning an initial phase space into basins labeled according to which product state is reached at a given time. The borders between these basins are in agreement with those obtained using Lagrangian descriptors, even in regimes exhibiting chaotic dynamics. Major outcomes of this work are: validation and extension of a transition state theory framework built from Lagrangian descriptors, elaboration of the applicability for this theory to periodically- and aperiodically-driven molecular systems, and prediction of regimes in which isomerization of ketene and its derivatives may be controlled using an external field.
Coherent Lagrangian swirls among submesoscale motions.
Beron-Vera, F J; Hadjighasem, A; Xia, Q; Olascoaga, M J; Haller, G
2018-03-05
The emergence of coherent Lagrangian swirls (CLSs) among submesoscale motions in the ocean is illustrated. This is done by applying recent nonlinear dynamics tools for Lagrangian coherence detection on a surface flow realization produced by a data-assimilative submesoscale-permitting ocean general circulation model simulation of the Gulf of Mexico. Both mesoscale and submesoscale CLSs are extracted. These extractions prove the relevance of coherent Lagrangian eddies detected in satellite-altimetry-based geostrophic flow data for the arguably more realistic ageostrophic multiscale flow.
A functional LMO invariant for Lagrangian cobordisms
DEFF Research Database (Denmark)
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...... of Jacobi diagrams. We prove some properties of this functorial LMO invariant, including its universality among rational finite-type invariants of Lagrangian cobordisms. Finally, we apply the LMO functor to the study of homology cylinders from the point of view of their finite-type invariants....
Extension of the chiral perturbation theory meson Lagrangian to order p6
International Nuclear Information System (INIS)
Fearing, H.W.; Scherer, S.
1996-01-01
We have constructed the most general chirally invariant Lagrangian scrL 6 for the meson sector at order p 6 . The result provides an extension of the standard Gasser-Leutwyler Lagrangian scrL 4 to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the construction was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The claim to have obtained the most general Lagrangian relies on this systematic construction and on the elimination of redundant quantities using relations of which we are aware, rather than on a general formal proof of either completeness or independence. The open-quote open-quote equation-of-motion close-quote close-quote terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating p 6 contributions to simple processes. copyright 1995 The American Physical Society
Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS3 space
International Nuclear Information System (INIS)
Buchbinder, I.L.; Snegirev, T.V.; Zinoviev, Yu.M.
2012-01-01
We develop the frame-like formulation of massive bosonic higher spin fields in the case of three-dimensional (A)dS space with the arbitrary cosmological constant. The formulation is based on gauge invariant description by involving the Stueckelberg auxiliary fields. The explicit form of the Lagrangians and the gauge transformation laws are found. The theory can be written in terms of gauge invariant objects similar to the massless theories, thus allowing us to hope to use the same methods for investigation of interactions. In the massive spin 3 field example we are able to rewrite the Lagrangian using the new the so-called separated variables, so that the study of Lagrangian formulation reduces to finding the Lagrangian containing only half of the fields. The same construction takes places for arbitrary integer spin field as well. Further working in terms of separated variables, we build Lagrangian for arbitrary integer spin and write it in terms of gauge invariant objects. Also, we demonstrate how to restore the full set of variables, thus receiving Lagrangian for the massive fields of arbitrary spin in the terms of initial fields.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding.
Krause, Katharina; Klopper, Wim
2016-01-28
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding
International Nuclear Information System (INIS)
Krause, Katharina; Klopper, Wim
2016-01-01
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
Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds
Lehn, Christian
2011-01-01
We generalize Voisin's theorem on deformations of pairs of a symplectic manifold and a Lagrangian submanifold to the case of Lagrangian normal crossing subvarieties. Partial results are obtained for arbitrary Lagrangian subvarieties. We apply our results to the study of singular fibers of Lagrangian fibrations.
Option volatility and the acceleration Lagrangian
Baaquie, Belal E.; Cao, Yang
2014-01-01
This paper develops a volatility formula for option on an asset from an acceleration Lagrangian model and the formula is calibrated with market data. The Black-Scholes model is a simpler case that has a velocity dependent Lagrangian. The acceleration Lagrangian is defined, and the classical solution of the system in Euclidean time is solved by choosing proper boundary conditions. The conditional probability distribution of final position given the initial position is obtained from the transition amplitude. The volatility is the standard deviation of the conditional probability distribution. Using the conditional probability and the path integral method, the martingale condition is applied, and one of the parameters in the Lagrangian is fixed. The call option price is obtained using the conditional probability and the path integral method.
Lagrangian-similarity diffusion-deposition model
International Nuclear Information System (INIS)
Horst, T.W.
1979-01-01
A Lagrangian-similarity diffusion model has been incorporated into the surface-depletion deposition model. This model predicts vertical concentration profiles far downwind of the source that agree with those of a one-dimensional gradient-transfer model
A new proposal for Lagrangian correlation coefficient
International Nuclear Information System (INIS)
Altinsoy, N.; Tugrul, A.B.
2002-01-01
The statistical description of dispersion in turbulent flow was first considered by Taylor (Proc. London Math. Soc. 20 (1921) 196) and the statistical properties of the field were determined by Lagrangian correlation coefficient R L (τ). Frenkiel (Adv. Appl. Mech. 3 (1953) 61) has proposed several simple forms for R L (τ). Some workers have investigated for a proper form of the Lagrangian correlation coefficient. In this work, a new proposal for the Lagrangian correlation coefficient is proposed and discussed. It can be written in general form with the one of the Frenkiel's (Adv. Appl. Mech. 3 (1953) 61) Lagrangian correlation coefficient. There is very satisfactory agreement between the new correlation and the experiment
Lagrangian Differentiation, Integration and Eigenvalues Problems
International Nuclear Information System (INIS)
Durand, L.
1983-01-01
Calogero recently proposed a new and very powerful method for the solution of Sturm-Liouville eigenvalue problems based on Lagrangian differentiation. In this paper, some results of a numerical investigation of Calogero's method for physical interesting problems are presented. It is then shown that one can 'invert' his differentiation technique to obtain a flexible, factorially convergent Lagrangian integration scheme which should be useful in a variety of problems, e.g. solution of integral equations
The universal lagrangian and the cosmic evolution
International Nuclear Information System (INIS)
El Tahir, A.
1984-08-01
By geometrizing Mach's Universe, we derive the most rational form of a Lagrangian which we, hence, call Universal. It contains both linear and nonlinear terms of the scalar curvature R, with constant coefficients which underlie a certain physical meaning. The metric derivable from this Lagrangian is believed to be far advanced from those derived from general relativity. A wave equation describing the overall evolution of the Universe is obtained and discussed. (author)
Energy Technology Data Exchange (ETDEWEB)
Morrison, David R., E-mail: drm@physics.ucsb.edu [Departments of Mathematics and Physics, U.C. Santa Barbara, Santa Barbara, CA 93106 (United States); Ronen Plesser, M. [Center for Geometry and Theoretical Physics, Duke University, Durham NC 27708 (United States)
2015-09-15
For complete intersection Calabi–Yau manifolds in toric varieties, Gross and Haase–Zharkov have given a conjectural combinatorial description of the special Lagrangian torus fibrations whose existence was predicted by Strominger, Yau and Zaslow. We present a geometric version of this construction, generalizing an earlier conjecture of the first author.
van Gent, P.L.; Michaelis, D; van Oudheusden, B.W.; Weiss, P.E.; de Kat, R.; Laskari, A.; Jeon, Y.J.; David, L; Schanz, D; Huhn, F.; Gesemann, S; Novara, M.; McPhaden, C.; Neeteson, N. J.; Rival, David E.; Schneiders, J.F.G.; Schrijer, F.F.J.
2017-01-01
A test case for pressure field reconstruction from particle image velocimetry (PIV) and Lagrangian particle tracking (LPT) has been developed by constructing a simulated experiment from a zonal detached eddy simulation for an axisymmetric base flow at Mach 0.7. The test case comprises sequences
Meaning of the BRS Lagrangian theory
International Nuclear Information System (INIS)
Cheng, H.; Tsai, E.
1989-01-01
A simplified treatment of the Becchi-Rouet-Stora (BRS) Lagrangian theory is presented. With this treatment we show that the BRS Lagrangian theory in general, and the Feynman-gauge field theory in particular, are effective theories, not the physical theory, and the Feynman gauge is not, strictly speaking, a gauge. The relationship between the quantum states in the BRS Lagrangian theory and those in the physical theory is explicitly given. We also show that one may obtain matrix elements of gauge-invariant operators in the physical theory by calculating corresponding ones in the BRS Lagrangian theory. The formulas which equate such matrix elements are called correspondence formulas. The correspondence formula for the S matrix enables us to equate the scattering amplitudes in the physical theory with those in the BRS Lagrangian theory, thus a proof of the unitary of the Feynman-gauge (as well as other covariant gauges) Feynman rules is rendered unnecessary. This treatment can be applied to various gauge field theories and the examples of the pure Yang-Mills theory and a gauge field theory with a Higgs field is explicitly worked out
On the existence of singularities in the geometrization of lagrangian dynamics
International Nuclear Information System (INIS)
Amaral, C.M. do; Pitanga, P.
1987-01-01
It is shown that the standard geometric picture of an important class of nonrelativistic Lagrangian motions has the origin of the generalized velocity space as a singular point. This occurs when the motion's generating force has a less than quadratic dependence on the generalized velocities. The importance cases of a gradient force-field and that of Rayleigh force-field are considered as exemples. The corresponding dynamical connections are constructed and present poles of order two one, respectively, at the origin of velocity space. This implies that well-behaved Lagrangian dinamics may originate ill-behaved gauge-fields in configuration space. (author) [pt
Nonlinear Lagrangian and the π N → π π π N process
International Nuclear Information System (INIS)
Pinto, F.A.
1976-02-01
A nonlinear Lagrangian is constructed involving only pions and nucleons consisting of a part invariant under the transformations of the group SU(2) (X) SU(2) and of a part which breaks this symmetry and contains an arbitrary parameter zeta introduced in order to allow the breaking of exact PCAC. The total cross-section for the process π N → π π π N at low incident energies of the incident pion, in the threshold approximation, is calculated utilizing this nonlinear Lagrangian. The parameter zeta appears in the total cross-section of the process π N → π π N also [pt
Lagrangian solution of supersonic real gas flows
International Nuclear Information System (INIS)
Loh, Chingyuen; Liou, Mengsing
1993-01-01
This paper details the procedure of the real gas Riemann solution in the Lagrangian approach originally proposed by Loh and Hui for perfect gases. The extension to real gases is nontrivial and requires substantial development of an exact real-gas Riemann solver for the Lagrangian form of conservation laws. The first-order Gudonov scheme is enhanced for accuracy by adding limited anti-diffusive terms according to Sweby. Extensive calculations were made to test the accuracy and robustness of the present real gas Lagrangian approach, including complex wave interactions of different types. The accuracy for capturing 2D oblique waves and slip line is clearly demonstrated. In addition, we also show the real gas effect in a generic engine nozzle
Double complexes and cohomological hierarchy in a space of weakly invariant Lagrangians of mechanics
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Saakyan, D.A.
1998-01-01
For a given configuration space M and Lie algebra G acting on M the space ν 0.0 of weakly G-invariant Lagrangians, i.e., Lagrangians whose motion equations left-hand sides are G-invariant, is studied. The problem is reformulated in terms of the double complex of Lie algebra cochains with values in the complex of Lagrangians. Calculating the cohomology of this complex by the method of spectral sequences we arrive at the hierarchy in the space ν 0.0 . The double filtration {ν s.σ }, s = 0,1,2,3,4, σ = 0,1, and the homomorphisms on every space ν s,σ are constructed. These homomorphisms take values in the cohomologies of the algebra G and the configuration space M. On one hand, every space ν s,σ in the kernel of the corresponding homomorphism, while the space itself is defined by its physical properties
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.
The Mather problem for lower semicontinuous Lagrangians
Gomes, Diogo A.; Terrone, Gabriele
2013-01-01
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.
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.
Lagrangian solution of supersonic real gas flows
Loh, Ching-Yuen; Liou, Meng-Sing
1993-01-01
The present extention of a Lagrangian approach of the Riemann solution procedure, which was originally proposed for perfect gases, to real gases, is nontrivial and requires the development of an exact real-gas Riemann solver for the Lagrangian form of the conservation laws. Calculations including complex wave interactions of various types were conducted to test the accuracy and robustness of the approach. Attention is given to the case of 2D oblique waves' capture, where a slip line is clearly in evidence; the real gas effect is demonstrated in the case of a generic engine nozzle.
On the construction of QED using ERG
International Nuclear Information System (INIS)
Sonoda, H
2007-01-01
It has been known for some time that a smooth momentum cutoff is compatible with local gauge symmetries. In this paper, we show concretely how to construct QED using the exact renormalization group (ERG). First, we give a new derivation of the Ward identity for the Wilson action using the technique of composite operators. Second, parametrizing the theory by its asymptotic behaviour for a large cutoff, we show how to fine tune the parameters to satisfy the identity. Third, we recast the identity as an invariance of the Wilson action under a nonlinear BRST transformation
Experimental investigation of Lagrangian structure functions in turbulence
DEFF Research Database (Denmark)
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...
Three-dimensional free Lagrangian hydrodynamics
International Nuclear Information System (INIS)
Trease, H.E.
1985-01-01
The purpose of the discussion is to describe the development of a 3-D free Lagrangian hyrodynamics algorithm. The 3-D algorithm is an outgrowth of an earlier 2-D free Lagrange model. Only the more pertinent issues of the free Lagrange algorithm are presented. A complete production code is being developed to support the free Lagrange algorithm described. 4 refs
Effective Lagrangian density in gauge supersymmetry
International Nuclear Information System (INIS)
Chang, S.S.
1976-01-01
In the framework of gauge supersymmetry proposed by Arnowitt and Nath, an effective Lagrangian density is formally rewritten in terms of a spontaneously broken vacuum metric and the remaining perturbative part in the gauge metric tensor. Tensor notations in the superspace are revised so that all sign factors of Grassmann parities appear more systematically
Lagrangian ocean analysis: Fundamentals and practices
van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan; Adams, Thomas P.; Berloff, Pavel; Biastoch, Arne; Blanke, Bruno; Chassignet, Eric P.; Cheng, Yu; Cotter, Colin J.; Deleersnijder, Eric; Döös, Kristofer; Drake, Henri F.; Drijfhout, Sybren; Gary, Stefan F.; Heemink, Arnold W.; Kjellsson, Joakim; Koszalka, Inga Monika; Lange, Michael; Lique, Camille; MacGilchrist, Graeme A.; Marsh, Robert; Mayorga Adame, C. Gabriela; McAdam, Ronan; Nencioli, Francesco; Paris, Claire B.; Piggott, Matthew D.; Polton, Jeff A.; Rühs, Siren; Shah, Syed H. A. M.; Thomas, Matthew D.; Wang, Jinbo; Wolfram, Phillip J.; Zanna, Laure; Zika, Jan D.
2018-01-01
Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.
QUANTIZATION OF NON-LAGRANGIAN SYSTEMS
Czech Academy of Sciences Publication Activity Database
Kochan, Denis
2009-01-01
Roč. 24, 28-29 (2009), s. 5319-5340 ISSN 0217-751X R&D Projects: GA MŠk(CZ) LC06002 Institutional research plan: CEZ:AV0Z10480505 Keywords : dissipative quantization * non-Lagrangian system * umbilical string Subject RIV: BE - Theoretical Physics Impact factor: 0.941, year: 2009
Lagrangian statistics in compressible isotropic homogeneous turbulence
Yang, Yantao; Wang, Jianchun; Shi, Yipeng; Chen, Shiyi
2011-11-01
In this work we conducted the Direct Numerical Simulation (DNS) of a forced compressible isotropic homogeneous turbulence and investigated the flow statistics from the Lagrangian point of view, namely the statistics is computed following the passive tracers trajectories. The numerical method combined the Eulerian field solver which was developed by Wang et al. (2010, J. Comp. Phys., 229, 5257-5279), and a Lagrangian module for tracking the tracers and recording the data. The Lagrangian probability density functions (p.d.f.'s) have then been calculated for both kinetic and thermodynamic quantities. In order to isolate the shearing part from the compressing part of the flow, we employed the Helmholtz decomposition to decompose the flow field (mainly the velocity field) into the solenoidal and compressive parts. The solenoidal part was compared with the incompressible case, while the compressibility effect showed up in the compressive part. The Lagrangian structure functions and cross-correlation between various quantities will also be discussed. This work was supported in part by the China's Turbulence Program under Grant No.2009CB724101.
Gravitational theory with the local quadratic Lagrangian
International Nuclear Information System (INIS)
Tentyukov, M.N.
1992-01-01
It is suggested that the vacuum gravitational equations should be derived from the local Lagrangian containing only first-order derivatives. As an example we demonstrate the properties of the derived equations by studying of the exact spherically-symmetric solutions. 23 refs
Effective lagrangian from bosonic string field theory
International Nuclear Information System (INIS)
Nakazawa, Naohito
1987-01-01
We investigate the low-energy effective action from the string field theoretical view point. The low-energy effective lagrangian for the massless mode of bosonic string is determined to the order of α'. We find a term which can not be determined from the S-matrix approach. (author)
Chaotic Lagrangian models for turbulent relative dispersion.
Lacorata, Guglielmo; Vulpiani, Angelo
2017-04-01
A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.
Construction of a Roe linearization for the ideal MHD equations
International Nuclear Information System (INIS)
Cargo, P.; Gallice, G.; Raviart, P.A.
1996-01-01
In [3], Munz has constructed a Roe linearization for the equations of gas dynamics in Lagrangian coordinates. We extend this construction to the case of the ideal magnetohydrodynamics equations again in Lagrangian coordinates. As a consequence we obtain a Roe linearization for the MHD equations in Eulerian coordinates. (author)
Relating Lagrangian and Hamiltonian Formalisms of LC Circuits
Clemente-Gallardo, Jesús; Scherpen, Jacquelien M.A.
2003-01-01
The Lagrangian formalism earlier defined for (switching) electrical circuits, is adapted to the Lagrangian formalism defined on Lie algebroids. This allows us to define regular Lagrangians and consequently, well-defined Hamiltonian descriptions of arbitrary LC networks. The relation with other
Lagrangian structures, integrability and chaos for 3D dynamical equations
International Nuclear Information System (INIS)
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 show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, 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 integrability. In particular, we show that the so-called ABC system is completely integrable if it possesses one constant of the motion
Unsteady force estimation using a Lagrangian drift-volume approach
McPhaden, Cameron J.; Rival, David E.
2018-04-01
A novel Lagrangian force estimation technique for unsteady fluid flows has been developed, using the concept of a Darwinian drift volume to measure unsteady forces on accelerating bodies. The construct of added mass in viscous flows, calculated from a series of drift volumes, is used to calculate the reaction force on an accelerating circular flat plate, containing highly-separated, vortical flow. The net displacement of fluid contained within the drift volumes is, through Darwin's drift-volume added-mass proposition, equal to the added mass of the plate and provides the reaction force of the fluid on the body. The resultant unsteady force estimates from the proposed technique are shown to align with the measured drag force associated with a rapid acceleration. The critical aspects of understanding unsteady flows, relating to peak and time-resolved forces, often lie within the acceleration phase of the motions, which are well-captured by the drift-volume approach. Therefore, this Lagrangian added-mass estimation technique opens the door to fluid-dynamic analyses in areas that, until now, were inaccessible by conventional means.
Güngör, Özenç; Starkman, Glenn D.; Stora, Raymond
This work is dedicated to the memory of Raymond Stora (1930-2015). $SU(2)_L$ is the simplest spontaneous symmetry breaking (SSB) non-Abelian gauge theory: a complex scalar doublet $\\phi=\\frac{1}{\\sqrt{2}}\\begin{bmatrix}H+i\\pi_3-\\pi_2 +i\\pi_1\\end{bmatrix}\\equiv\\frac{1}{\\sqrt{2}}\\tilde{H}e^{2i\\tilde{t}\\cdot\\tilde{\\vec{\\pi}}/}\\begin{bmatrix}10\\end{bmatrix}$ and a vector $\\vec{W}^\\mu$. In Landau gauge, $\\vec{W}^\\mu$ is transverse, $\\vec{\\tilde{\\pi}}$ are massless derivatively coupled Nambu-Goldstone bosons (NGB). A global shift symmetry enforces $m^{2}_{\\tilde{\\pi}}=0$. We observe that on-shell T-matrix elements of physical states $\\vec{W}^\\mu$,$\\phi$ are independent of global $SU(2)_{L}$ transformations, and the associated global current is exactly conserved for amplitudes of physical states. We identify two towers of "1-soft-pion" global Ward-Takahashi Identities (WTI), which govern the $\\phi$-sector, and represent a new global symmetry, $SU(2)_L\\otimes$BRST, a symmetry not of the Lagrangian but of the physical...
Topology Optimization of Passive Micromixers Based on Lagrangian Mapping Method
Directory of Open Access Journals (Sweden)
Yuchen Guo
2018-03-01
Full Text Available This paper presents an optimization-based design method of passive micromixers for immiscible fluids, which means that the Peclet number infinitely large. Based on topology optimization method, an optimization model is constructed to find the optimal layout of the passive micromixers. Being different from the topology optimization methods with Eulerian description of the convection-diffusion dynamics, this proposed method considers the extreme case, where the mixing is dominated completely by the convection with negligible diffusion. In this method, the mixing dynamics is modeled by the mapping method, a Lagrangian description that can deal with the case with convection-dominance. Several numerical examples have been presented to demonstrate the validity of the proposed method.
What If We Had A Magnetograph at Lagrangian L5?
Pevtsov, Alexei A.; Bertello, Luca; MacNeice, Peter; Petrie, Gordon
2016-01-01
Synoptic Carrington charts of magnetic field are routinely used as an input for modelings of solar wind and other aspects of space weather forecast. However, these maps are constructed using only the observations from the solar hemisphere facing Earth. The evolution of magnetic flux on the "farside" of the Sun, which may affect the topology of coronal field in the "nearside," is largely ignored. It is commonly accepted that placing a magnetograph in Lagrangian L5 point would improve the space weather forecast. However, the quantitative estimates of anticipated improvements have been lacking. We use longitudinal magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) to investigate how adding data from L5 point would affect the outcome of two major models used in space weather forecast.
Functional integral for non-Lagrangian systems
Kochan, Denis
2010-01-01
A novel functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The new approach, which we call "stringy quantization," is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force $-\\kappa[\\dot{q}]^A$. Results for $A = 1$ are compared with those obtained in the approaches by Caldirola-Kanai, Bateman and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.
Lagrangians for generalized Argyres-Douglas theories
Benvenuti, Sergio; Giacomelli, Simone
2017-10-01
We continue the study of Lagrangian descriptions of N=2 Argyres-Douglas theories. We use our recent interpretation in terms of sequential confinement to guess the Lagrangians of all the Argyres-Douglas models with Abelian three dimensional mirror. We find classes of four dimensional N=1 quivers that flow in the infrared to generalized Argyres-Douglas theories, such as the ( A k , A kN + N -1) models. We study in detail how the N=1 chiral rings map to the Coulomb and Higgs Branches of the N=2 CFT's. The three dimensional mirror RG flows are shown to land on the N=4 complete graph quivers. We also compactify to three dimensions the gauge theory dual to ( A 1, D 4), and find the expected Abelianization duality with N=4 SQED with 3 flavors.
Engineering dynamics from the Lagrangian to simulation
Gans, Roger F
2013-01-01
This engineering dynamics textbook is aimed at beginning graduate students in mechanical engineering and other related engineering disciplines who need training in dynamics as applied to engineering mechanisms. It introduces the formal mathematical development of Lagrangian mechanics (and its corollaries), while solving numerous engineering applications. The author’s goal is to instill an understanding of the basic physics required for engineering dynamics, while providing a recipe (algorithm) for the simulation of engineering mechanisms such as robots. The book is reasonably self-contained so that the practicing engineer interested in this area can also make use of it. This book is made accessible to the widest possible audience by numerous, solved examples and diagrams that apply the principles to real engineering applications. • Provides an applied textbook for intermediate/advanced engineering dynamics courses; • Discusses Lagrangian mechanics in the context of numerous engineering applications...
Lagrangian procedures for higher order field equations
International Nuclear Information System (INIS)
Bollini, C.G.
1987-01-01
A Lagrangian procedure for a pedagogical way is presented for the treatment of higher order field equations. The energy-momentum tensor and the conserved density current are built. In particular the case in which the derivatives appear only in the invariant D'Alembertian operator is discussed. Some examples are discussed. The fields are quantized and the corresponding Hamilonian which is shown not to be positive defructed. Rules are given to write the causal propagators. (author) [pt
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.
Test Particles with Acceleration-Dependent Lagrangian
Toller, M.
2005-01-01
We consider a classical test particle subject to electromagnetic and gravitational fields, described by a Lagrangian depending on the acceleration and on a fundamental length. We associate to the particle a moving local reference frame and we study its trajectory in the principal fibre bundle of all the Lorentz frames. We discuss in this framework the general form of the Lagrange equations and the connection between symmetries and conservation laws (Noether theorem). We apply these results to...
Directory of Open Access Journals (Sweden)
V. J. García-Garrido
2017-06-01
Full Text Available In this work, we study the Lagrangian footprint of the planetary waves present in the Southern Hemisphere stratosphere during the exceptional sudden Stratospheric warming event that took place during September 2002. Our focus is on constructing a simple kinematic model that retains the fundamental mechanisms responsible for complex fluid parcel evolution, during the polar vortex breakdown and its previous stages. The construction of the kinematic model is guided by the Fourier decomposition of the geopotential field. The study of Lagrangian transport phenomena in the ERA-Interim reanalysis data highlights hyperbolic trajectories, and these trajectories are Lagrangian objects that are the kinematic mechanism for the observed filamentation phenomena. Our analysis shows that the breaking and splitting of the polar vortex is justified in our model by the sudden growth of a planetary wave and the decay of the axisymmetric flow.
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
Canonical symmetry in a system with singular Lagrangian and ward identities
International Nuclear Information System (INIS)
Li Ziping
1994-01-01
An algorithm to construct the generator of gauge transformation for a constrained Hamiltonian system is given. The relationships among the coefficients connecting with first-class constraints in the generator is cleared. Based on the phase space generating function, the corresponding Ward identities in canonical formalism is deduced. The preliminary applications of above results to a model in field theory which is functionally equivalent to the mixed Chern-Simons Lagrangian is discussed in detail
Between Laws and Models: Some Philosophical Morals of Lagrangian Mechanics
Butterfield, Jeremy
2004-01-01
I extract some philosophical morals from some aspects of Lagrangian mechanics. (A companion paper will present similar morals from Hamiltonian mechanics and Hamilton-Jacobi theory.) One main moral concerns methodology: Lagrangian mechanics provides a level of description of phenomena which has been largely ignored by philosophers, since it falls between their accustomed levels--``laws of nature'' and ``models''. Another main moral concerns ontology: the ontology of Lagrangian mechanics is bot...
A Chiang-type lagrangian in CP^2
Cannas da Silva, Ana
2018-03-01
We analyse a monotone lagrangian in CP^2 that is hamiltonian isotopic to the standard lagrangian RP^2, yet exhibits a distinguishing behaviour under reduction by one of the toric circle actions, namely it intersects transversally the reduction level set and it projects one-to-one onto a great circle in CP^1. This lagrangian thus provides an example of embedded composition fitting work of Wehrheim-Woodward and Weinstein.
Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data
2015-09-30
Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...coastal ocean fields, both in Eulerian and Lagrangian forms. - Further develop and implement our GMM-DO schemes for robust Bayesian nonlinear estimation
Lagrangian model of conformal invariant interacting quantum field theory
International Nuclear Information System (INIS)
Lukierski, J.
1976-01-01
A Lagrangian model of conformal invariant interacting quantum field theory is presented. The interacting Lagrangian and free Lagrangian are derived replacing the canonical field phi by the field operator PHIsub(d)sup(c) and introducing the conformal-invariant interaction Lagrangian. It is suggested that in the conformal-invariant QFT with the dimensionality αsub(B) obtained from the bootstrep equation, the normalization constant c of the propagator and the coupling parametery do not necessarily need to satisfy the relation xsub(B) = phi 2 c 3
Lagrangians for plasmas in drift-fluid approximation
International Nuclear Information System (INIS)
Pfirsch, D.; Correa-Restrepo, D.
1996-10-01
For drift waves and related instabilities conservation laws can play a crucial role. In an ideal theory these conservation laws are guaranteed when a Lagrangian can be found from which the equations for the various quantities result by Hamilton's principle. Such a Lagrangian for plasmas in drift-fluid approximation was obtained by a heuristic method in a recent paper by Pfirsch and Correa-Restrepo. In the present paper the same Lagrangian is derived from the exact multi-fluid Lagrangian via an iterative approximation procedure which resembles the standard method usually applied to the equations of motion. That method, however, does not guarantee all the conservation laws to hold. (orig.)
Lagrangian condensation microphysics with Twomey CCN activation
Grabowski, Wojciech W.; Dziekan, Piotr; Pawlowska, Hanna
2018-01-01
We report the development of a novel Lagrangian microphysics methodology for simulations of warm ice-free clouds. The approach applies the traditional Eulerian method for the momentum and continuous thermodynamic fields such as the temperature and water vapor mixing ratio, and uses Lagrangian super-droplets to represent condensed phase such as cloud droplets and drizzle or rain drops. In other applications of the Lagrangian warm-rain microphysics, the super-droplets outside clouds represent unactivated cloud condensation nuclei (CCN) that become activated upon entering a cloud and can further grow through diffusional and collisional processes. The original methodology allows for the detailed study of not only effects of CCN on cloud microphysics and dynamics, but also CCN processing by a cloud. However, when cloud processing is not of interest, a simpler and computationally more efficient approach can be used with super-droplets forming only when CCN is activated and no super-droplet existing outside a cloud. This is possible by applying the Twomey activation scheme where the local supersaturation dictates the concentration of cloud droplets that need to be present inside a cloudy volume, as typically used in Eulerian bin microphysics schemes. Since a cloud volume is a small fraction of the computational domain volume, the Twomey super-droplets provide significant computational advantage when compared to the original super-droplet methodology. Additional advantage comes from significantly longer time steps that can be used when modeling of CCN deliquescence is avoided. Moreover, other formulation of the droplet activation can be applied in case of low vertical resolution of the host model, for instance, linking the concentration of activated cloud droplets to the local updraft speed. This paper discusses the development and testing of the Twomey super-droplet methodology, focusing on the activation and diffusional growth. Details of the activation implementation
Lagrangian condensation microphysics with Twomey CCN activation
Directory of Open Access Journals (Sweden)
W. W. Grabowski
2018-01-01
Full Text Available We report the development of a novel Lagrangian microphysics methodology for simulations of warm ice-free clouds. The approach applies the traditional Eulerian method for the momentum and continuous thermodynamic fields such as the temperature and water vapor mixing ratio, and uses Lagrangian super-droplets to represent condensed phase such as cloud droplets and drizzle or rain drops. In other applications of the Lagrangian warm-rain microphysics, the super-droplets outside clouds represent unactivated cloud condensation nuclei (CCN that become activated upon entering a cloud and can further grow through diffusional and collisional processes. The original methodology allows for the detailed study of not only effects of CCN on cloud microphysics and dynamics, but also CCN processing by a cloud. However, when cloud processing is not of interest, a simpler and computationally more efficient approach can be used with super-droplets forming only when CCN is activated and no super-droplet existing outside a cloud. This is possible by applying the Twomey activation scheme where the local supersaturation dictates the concentration of cloud droplets that need to be present inside a cloudy volume, as typically used in Eulerian bin microphysics schemes. Since a cloud volume is a small fraction of the computational domain volume, the Twomey super-droplets provide significant computational advantage when compared to the original super-droplet methodology. Additional advantage comes from significantly longer time steps that can be used when modeling of CCN deliquescence is avoided. Moreover, other formulation of the droplet activation can be applied in case of low vertical resolution of the host model, for instance, linking the concentration of activated cloud droplets to the local updraft speed. This paper discusses the development and testing of the Twomey super-droplet methodology, focusing on the activation and diffusional growth. Details of the
Effective lagrangian for Kaon-nucleon scattering
International Nuclear Information System (INIS)
Andrade, S.C.B. de; Ferreira, E.M.
1980-11-01
A model for the Kaon-nucleon interaction is investigated, based on a lagrangian which includes the Yukawa interactions of hyperons, kaons and nucleons plus contact terms representing short range interactions in each isospin state. All diagrams up to fourth order are evaluated and the partial wave S matrix elements are unitarized through diagonal Pade approximants. The results of the calculations with this model give a good description of all experimental data on both I = O and I = 1 states of the KN system at low and intermediate energies. (Author) [pt
An entropic solver for ideal Lagrangian magnetohydrodynamics
International Nuclear Information System (INIS)
Bezard, F.; Despres, B.
1999-01-01
In this paper, the authors adapt to the ideal 1D lagrangian MHD equations a class of numerical schemes of order one in time and space presented in an earlier paper and applied to the gas dynamics system. They use some properties of systems of conservation laws with zero entropy flux which describe fluid models invariant by galilean transformation and reversible for regular solutions. These numerical schemes satisfy an entropy inequality under CFL conditions. In the last section, they describe a particular scheme for the MHD equations and show with some numerical applications its robustness and accuracy. The generalization to full Eulerian multidimensional MHD will be the subject of a forthcoming paper
Transitions in turbulent rotating convection: A Lagrangian perspective : A Lagrangian perspective
Rajaei, H.; Joshi, P.R.; Alards, K.M.J.; Kunnen, R.P.J.; Toschi, F.; Clercx, H.J.H.
2016-01-01
Using measurements of Lagrangian acceleration in turbulent rotating convection and accompanying direct numerical simulations, we show that the transition between turbulent states reported earlier [e.g., S. Weiss et al., Phys. Rev. Lett. 105, 224501 (2010)] is a boundary-layer transition between the
International Nuclear Information System (INIS)
Chang, Y.W.; Chu, H.Y.; Gvildys, J.; Wang, C.Y.
1979-01-01
The analysis of fluid-structure interaction involves the calculation of both fluid transient and structure dynamics. In the structural analysis, Lagrangian meshes have been used exclusively, whereas for the fluid transient, Lagrangian, Eulerian, and arbitrary Lagrangian-Eulerian (quasi-Eulerian) meshes have been used. This paper performs an evaluation on these three types of meshes. The emphasis is placed on the applicability of the method in analyzing fluid-structure interaction problems in HCDA analysis
An objective interpretation of Lagrangian quantum mechanics
International Nuclear Information System (INIS)
Roberts, K.V.
1978-01-01
Unlike classical mechanics, the Copenhagen interpretation of quantum mechanics does not provide an objective space-time picture of the actual history of a physical system. This paper suggests how the conceptual foundations of quantum mechanics can be reformulated, without changing the mathematical content of the theory or its detailed agreement with experiment and without introducing any hidden variables, in order to provide an objective, covariant, Lagrangian description of reality which is deterministic and time-symmetric on the microscopic scale. The basis of this description can be expressed either as an action functional or as a summation over Feynman diagrams or paths. The probability laws associated with the quantum-mechanical measurement process, and the asymmetry in time of the principles of macroscopic causality and of the laws of statistical mechanics, are interpreted as consequences of the particular boundary conditions that apply to the actual universe. The objective interpretation does not include the observer and the measurement process among the fundamental concepts of the theory, but it does not entail a revision of the ideas of determinism and of time, since in a Lagrangian theory both initial and final boundary conditions on the action functional are required. (author)
Lagrangian particle method for compressible fluid dynamics
Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang
2018-06-01
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface/multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic-elliptic systems. Numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.
Generating functionals and Lagrangian partial differential equations
Energy Technology Data Exchange (ETDEWEB)
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.
Extended Lagrangian Excited State Molecular Dynamics.
Bjorgaard, J A; Sheppard, D; Tretiak, S; Niklasson, A M N
2018-02-13
An extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).
Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R
2013-09-01
We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.
Duran, R; Beron-Vera, F J; Olascoaga, M J
2018-03-26
We construct a climatology of Lagrangian coherent structures (LCSs)-the concealed skeleton that shapes transport-with a twelve-year-long data-assimilative simulation of the sea-surface circulation in the Gulf of Mexico (GoM). Computed as time-mean Cauchy-Green strain tensorlines of the climatological velocity, the climatological LCSs (cLCSs) unveil recurrent Lagrangian circulation patterns. The cLCSs strongly constrain the ensemble-mean Lagrangian circulation of the instantaneous model velocity, showing that a climatological velocity can preserve meaningful transport information. The quasi-steady transport patterns revealed by the cLCSs agree well with aspects of the GoM circulation described in several previous observational and numerical studies. For example, the cLCSs identify regions of persistent isolation, and suggest that coastal regions previously identified as high-risk for pollution impact are regions of maximal attraction. We also show that cLCSs are remarkably accurate at identifying transport patterns observed during the Deepwater Horizon and Ixtoc oil spills, and during the Grand LAgrangian Deployment (GLAD) experiment. Thus it is shown that computing cLCSs is an efficient and meaningful way of synthesizing vast amounts of Lagrangian information. The cLCS method confirms previous GoM studies, and contributes to our understanding by revealing the persistent nature of the dynamics and kinematics treated therein.
The Solution Construction of Heterotic Super-Liouville Model
Yang, Zhan-Ying; Zhen, Yi
2001-12-01
We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld-Sokolov linear system, we construct the explicit solution of the heterotic super-Liouville system in component form. We also show that the solutions are local and periodic by calculating the exchange relation of the solution. Finally starting from the action of heterotic super-Liouville model, we obtain the conserved current and conserved charge which possessed the BRST properties.
A Bernstein type result for special Lagrangian submanifolds
Tsui, Mao-Pei; Wang, Mu-Tao
2002-01-01
Let \\Sigma be a complete minimal Lagrangian submanifold of \\C^n. We identify regions in the Grassmannian of Lagrangian subspaces so that whenever the image of the Gauss map of \\Sigma lies in one of these regions, then \\Sigma is an affine space.
Modeling pollutant transport using a meshless-lagrangian particle model
International Nuclear Information System (INIS)
Carrington, D.B.; Pepper, D.W.
2002-01-01
A combined meshless-Lagrangian particle transport model is used to predict pollutant transport over irregular terrain. The numerical model for initializing the velocity field is based on a meshless approach utilizing multiquadrics established by Kansa. The Lagrangian particle transport technique uses a random walk procedure to depict the advection and dispersion of pollutants over any type of surface, including street and city canyons
The Bach-Lanczos Lagrangian in matrix relativity
International Nuclear Information System (INIS)
Maluf, J.W.
1987-01-01
The author examines the generalisation of the Bach-Lanczos Lagrangian in matrix relativity where it is no longer a topological invariant, and find that for certain structures of the matrix affine connection a Yang-Mills type Lagrangian is obtained. Thus the possibility is considered of interpreting non-Abelian gauge fields as arising from an otherwise topological invariant. (author)
The Lagrangians and Hamiltonians of damped coupled vibrations
International Nuclear Information System (INIS)
Ding Guangtao; Gan Huilan; Zheng Xianfeng; Cui Zhifeng
2012-01-01
In this paper, the analytical mechanization of two kinds of damped coupled vibrations is studied. First, by use of coordinate transformations the equations of motion are transformed into the self-ad- joint form. Secondly, the Lagrangians are obtained according to Engels method. Finally the Lagrangians and Hamiltonians of the original equations are deduced by using the inverse transformation. (authors)
Lagrangian motion, coherent structures, and lines of persistent material strain.
Samelson, R M
2013-01-01
Lagrangian motion in geophysical fluids may be strongly influenced by coherent structures that support distinct regimes in a given flow. The problems of identifying and demarcating Lagrangian regime boundaries associated with dynamical coherent structures in a given velocity field can be studied using approaches originally developed in the context of the abstract geometric theory of ordinary differential equations. An essential insight is that when coherent structures exist in a flow, Lagrangian regime boundaries may often be indicated as material curves on which the Lagrangian-mean principal-axis strain is large. This insight is the foundation of many numerical techniques for identifying such features in complex observed or numerically simulated ocean flows. The basic theoretical ideas are illustrated with a simple, kinematic traveling-wave model. The corresponding numerical algorithms for identifying candidate Lagrangian regime boundaries and lines of principal Lagrangian strain (also called Lagrangian coherent structures) are divided into parcel and bundle schemes; the latter include the finite-time and finite-size Lyapunov exponent/Lagrangian strain (FTLE/FTLS and FSLE/FSLS) metrics. Some aspects and results of oceanographic studies based on these approaches are reviewed, and the results are discussed in the context of oceanographic observations of dynamical coherent structures.
Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids
International Nuclear Information System (INIS)
Aradi, Balint; Frauenheim, Thomas
2015-01-01
A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born-Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can also be applied to a broad range of problems in materials science, chemistry, and biology
Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids.
Aradi, Bálint; Niklasson, Anders M N; Frauenheim, Thomas
2015-07-14
A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born-Oppenheimer molecular dynamics. For systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can be applied to a broad range of problems in materials science, chemistry, and biology.
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.
Jacobi equations as Lagrange equations of the deformed Lagrangian
International Nuclear Information System (INIS)
Casciaro, B.
1995-03-01
We study higher-order variational derivatives of a generic Lagrangian L 0 = L 0 (t,q,q). We introduce two new Lagrangians, L 1 and L 2 , associated to the first and second-order deformations of the original Lagrangian L 0 . In terms of these Lagrangians, we are able to establish simple relations between the variational derivatives of different orders of a Lagrangian. As a consequence of these relations the Euler-Lagrange and the Jacobi equations are obtained from a single variational principle based on L 1 . We can furthermore introduce an associated Hamiltonian H 1 = H 1 (t,q,q radical,η,η radical) with η equivalent to δq. If L 0 is independent of time then H 1 is a conserved quantity. (author). 15 refs
Hamilton-Jacobi equations and brane associated Lagrangians
International Nuclear Information System (INIS)
Baker, L.M.; Fairlie, D.B.
2001-01-01
This article seeks to relate a recent proposal for the association of a covariant Field Theory with a string or brane Lagrangian to the Hamilton-Jacobi formalism for strings and branes. It turns out that since in this special case, the Hamiltonian depends only upon the momenta of the Jacobi fields and not the fields themselves, it is the same as a Lagrangian, subject to a constancy constraint. We find that the associated Lagrangians for strings or branes have a covariant description in terms of the square root of the same Lagrangian. If the Hamilton-Jacobi function is zero, rather than a constant, then it is in in one dimension lower, reminiscent of the 'holographic' idea. In the second part of the paper, we discuss properties of these Lagrangians, which lead to what we have called 'Universal Field Equations', characteristic of covariant equations of motion
Tracking Lagrangian trajectories in position–velocity space
International Nuclear Information System (INIS)
Xu, Haitao
2008-01-01
Lagrangian particle-tracking algorithms are susceptible to intermittent loss of particle images on the sensors. The measured trajectories are often interrupted into short segments and the long-time Lagrangian statistics are difficult to obtain. We present an algorithm to connect the segments of Lagrangian trajectories from common particle-tracking algorithms. Our algorithm tracks trajectory segments in the six-dimensional position and velocity space. We describe the approach to determine parameters in the algorithm and demonstrate the validity of the algorithm with data from numerical simulations and the improvement of long-time Lagrangian statistics on experimental data. The algorithm has important applications in measurements with high particle seeding density and in obtaining multi-particle Lagrangian statistics
Reconstructing baryon oscillations: A Lagrangian theory perspective
International Nuclear Information System (INIS)
Padmanabhan, Nikhil; White, Martin; Cohn, J. D.
2009-01-01
Recently Eisenstein and collaborators introduced a method to 'reconstruct' the linear power spectrum from a nonlinearly evolved galaxy distribution in order to improve precision in measurements of baryon acoustic oscillations. We reformulate this method within the Lagrangian picture of structure formation, to better understand what such a method does, and what the resulting power spectra are. We show that reconstruction does not reproduce the linear density field, at second order. We however show that it does reduce the damping of the oscillations due to nonlinear structure formation, explaining the improvements seen in simulations. Our results suggest that the reconstructed power spectrum is potentially better modeled as the sum of three different power spectra, each dominating over different wavelength ranges and with different nonlinear damping terms. Finally, we also show that reconstruction reduces the mode-coupling term in the power spectrum, explaining why miscalibrations of the acoustic scale are reduced when one considers the reconstructed power spectrum.
Effective Chiral Lagrangians and Lattice QCD
Heitger, J; Wittig, H; Heitger, Jochen; Sommer, Rainer; Wittig, Hartmut
2000-01-01
We propose a general method to obtain accurate estimates for some of the "low-energy constants" in the one-loop effective chiral Lagrangian by means of simulating lattice QCD. In particular, the method is sensitive to those constants whose values are required to test the hypothesis of a massless up-quark. Initial tests performed in the quenched approximation confirm that good statistical precision can be achieved. As a byproduct we obtain an accurate estimate for the ratio of pseudoscalar decay constants, F_K/F_pi, in the quenched approximation, which lies 10% below the experimental result. The quantities that serve to extract the low-energy constants also allow a test of the scaling behaviour of different discretizations of QCD and a search for the effects of dynamical quarks.
Non-Lagrangian theories from brane junctions
Energy Technology Data Exchange (ETDEWEB)
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.
Non-Lagrangian theories from brane junctions
International Nuclear Information System (INIS)
Bao, Ling; Mitev, Vladimir
2013-10-01
In this article we use 5-brane junctions to study the 5D T 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 N Toda theories.
Contact manifolds, Lagrangian Grassmannians and PDEs
Directory of Open Access Journals (Sweden)
Eshkobilov Olimjon
2018-02-01
Full Text Available In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n + 1-dimensional contact manifold and the so-called Lagrangian Grassmannian bundle over the latter. This work is based on a Ph.D course given by two of the authors (G. M. and G. M.. As such, it was mainly designed as a quick introduction to the subject for graduate students. But also the more demanding reader will be gratified, thanks to the frequent references to current research topics and glimpses of higher-level mathematics, found mostly in the last sections.
On Active Current Selection for Lagrangian Profilers
Directory of Open Access Journals (Sweden)
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.
On the Lagrangian description of dissipative systems
Martínez-Pérez, N. E.; Ramírez, C.
2018-03-01
We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and conserved quantities, like the Hamiltonian, that generate symmetry transformations and do not correspond to observables. We show that there are simple relations among the equations satisfied by these two types of quantities. In the case of the damped harmonic oscillator, from the quantities obtained by the Noether theorem follows the algebra of Feshbach and Tikochinsky. Furthermore, if we consider the whole dynamics, the degrees of freedom separate into a physical and an unphysical sector. We analyze several cases, with linear and nonlinear dissipative forces; the physical consistency of the solutions is ensured, observing that the unphysical sector has always the trivial solution.
A hybrid Lagrangian Voronoi-SPH scheme
Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.
2017-11-01
A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.
Lagrangian numerical methods for ocean biogeochemical simulations
Paparella, Francesco; Popolizio, Marina
2018-05-01
We propose two closely-related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the Péclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection-reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects.
Markov Chain Monte Carlo from Lagrangian Dynamics.
Lan, Shiwei; Stathopoulos, Vasileios; Shahbaba, Babak; Girolami, Mark
2015-04-01
Hamiltonian Monte Carlo (HMC) improves the computational e ciency of the Metropolis-Hastings algorithm by reducing its random walk behavior. Riemannian HMC (RHMC) further improves the performance of HMC by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RHMC involves implicit equations that require fixed-point iterations. In some cases, the computational overhead for solving implicit equations undermines RHMC's benefits. In an attempt to circumvent this problem, we propose an explicit integrator that replaces the momentum variable in RHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamiltonian dynamics to Lagrangian dynamics. Experimental results suggests that our method improves RHMC's overall computational e ciency in the cases considered. All computer programs and data sets are available online (http://www.ics.uci.edu/~babaks/Site/Codes.html) in order to allow replication of the results reported in this paper.
LSPRAY-V: A Lagrangian Spray Module
Raju, M. S.
2015-01-01
LSPRAY-V is a Lagrangian spray solver developed for application with unstructured grids and massively parallel computers. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray encountered over a wide range of operating conditions in modern aircraft engine development. It could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-V, we have advanced the state-of-the-art in spray computations in several important ways.
Mean Lagrangian drift in continental shelf waves
Drivdal, M.; Weber, J. E. H.
2012-04-01
The time- and depth-averaged mean drift induced by barotropic continental shelf waves (CSW's) is studied theoretically for idealized shelf topography by calculating the mean volume fluxes to second order in wave amplitude. The waves suffer weak spatial damping due to bottom friction, which leads to radiation stress forcing of the mean fluxes. In terms of the total wave energy density E¯ over the shelf region, the radiation stress tensor component S¯11 for CSW's is found to be different from that of shallow water surface waves in a non-rotating ocean. For CSW's, the ratio ¯S11/¯E depends strongly on the wave number. The mean Lagrangian flow forced by the radiation stress can be subdivided into a Stokes drift and a mean Eulerian drift current. The magnitude of the latter depends on the ratio between the radiation stress and the bottom stress acting on the mean flow. When the effect of bottom friction acts equally strong on the waves and the mean current, calculations for short CSW's show that the Stokes drift and the friction-dependent wave-induced mean Eulerian current varies approximately in anti-phase over the shelf, and that the latter is numerically the largest. For long CSW's they are approximately in phase. In both cases the mean Lagrangian current, which is responsible for the net particle drift, has its largest numerical value at the coast on the shallow part of the shelf. Enhancing the effect of bottom friction on the Eulerian mean flow, results in a general current speed reduction, as well as a change in spatial structure for long waves. Applying realistic physical parameters for the continental shelf west of Norway, calculations yield along-shelf mean drift velocities for short CSW's that may be important for the transport of biological material, neutral tracers, and underwater plumes of dissolved oil from deep water drilling accidents.
International Nuclear Information System (INIS)
Blanchet, Y.; Obry, P.; Louvet, J.; Graveleau, J.
1981-04-01
Two different numerical methods have been implemented in two computer codes developed in CEA/DRNR, Cadarache, to predict the dynamic response of the containment of Super-Phenix reactor after a hypothetical energy excursion. Both codes are 2D-axisymmetric and solve the time-dependent flow of compressible fluids in the presence of deformable thin structures. The first one, called SIRIUS, uses only Lagrangian meshes; in the second one, called CASSIOPEE, the thick elastic-plastic materials are calculated in Lagrangian coordinates while fluids can be calculated either in Lagrangian or in Eulerian coordinates. The treatment of hydrodynamic, elastic-plastic thick domains then the thin shells models and the fluid-structure couplings are described in parallel for both codes. The efficiency and the limits of the previous methods are finally illustrated by comparison of measured and predicted strains of a vessel issued from one of the MARA experiments which are being purposely performed in Cadarache for validation of these codes in Super-Phenix scale models. These comparisons are encouraging and justify that the Super-Phenix reactor vessel response can be determined using the SIRIUS and CASSIOPEE codes
Shear and shearless Lagrangian structures in compound channels
Enrile, F.; Besio, G.; Stocchino, A.
2018-03-01
Transport processes in a physical model of a natural stream with a composite cross-section (compound channel) are investigated by means of a Lagrangian analysis based on nonlinear dynamical system theory. Two-dimensional free surface Eulerian experimental velocity fields of a uniform flow in a compound channel form the basis for the identification of the so-called Lagrangian Coherent Structures. Lagrangian structures are recognized as the key features that govern particle trajectories. We seek for two particular class of Lagrangian structures: Shear and shearless structures. The former are generated whenever the shear dominates the flow whereas the latter behave as jet-cores. These two type of structures are detected as ridges and trenches of the Finite-Time Lyapunov Exponents fields, respectively. Besides, shearlines computed applying the geodesic theory of transport barriers mark Shear Lagrangian Coherent Structures. So far, the detection of these structures in real experimental flows has not been deeply investigated. Indeed, the present results obtained in a wide range of the controlling parameters clearly show a different behaviour depending on the shallowness of the flow. Shear and Shearless Lagrangian Structures detected from laboratory experiments clearly appear as the flow develops in shallow conditions. The presence of these Lagrangian Structures tends to fade in deep flow conditions.
Quantizing non-Lagrangian gauge theories: an augmentation method
International Nuclear Information System (INIS)
Lyakhovich, Simon L.; Sharapov, Alexei A.
2007-01-01
We discuss a recently proposed method of quantizing general non-Lagrangian gauge theories. The method can be implemented in many different ways, in particular, it can employ a conversion procedure that turns an original non-Lagrangian field theory in d dimensions into an equivalent Lagrangian, topological field theory in d+1 dimensions. The method involves, besides the classical equations of motion, one more geometric ingredient called the Lagrange anchor. Different Lagrange anchors result in different quantizations of one and the same classical theory. Given the classical equations of motion and Lagrange anchor as input data, a new procedure, called the augmentation, is proposed to quantize non-Lagrangian dynamics. Within the augmentation procedure, the originally non-Lagrangian theory is absorbed by a wider Lagrangian theory on the same space-time manifold. The augmented theory is not generally equivalent to the original one as it has more physical degrees of freedom than the original theory. However, the extra degrees of freedom are factorized out in a certain regular way both at classical and quantum levels. The general techniques are exemplified by quantizing two non-Lagrangian models of physical interest
Canonical quantization of so-called non-Lagrangian systems
Energy Technology Data Exchange (ETDEWEB)
Gitman, D.M. [Universidade de Sao Paulo, Instituto de Fisica, Caixa Postal 66318-CEP, Sao Paulo, S.P. (Brazil); Kupriyanov, V.G. [Universidade de Sao Paulo, Instituto de Fisica, Caixa Postal 66318-CEP, Sao Paulo, S.P. (Brazil); Tomsk State University, Physics Department, Tomsk (Russian Federation)
2007-04-15
We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential equations cannot be directly identified with a set of Euler-Lagrange equations, one can reformulate such a set in an equivalent first-order form that can always be treated as the Euler-Lagrange equations of a certain action. We construct such an action explicitly. It turns out that in the general case the hamiltonization and canonical quantization of such an action are non-trivial problems, since the theory involves time-dependent constraints. We adopt the general approach of hamiltonization and canonical quantization for such theories as described in D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints (Springer, Berlin, 1990). to the case under consideration. There exists an ambiguity (that cannot be reduced to the addition of a total time derivative) in associating a Lagrange function with a given set of equations. We present a complete description of this ambiguity. The proposed scheme is applied to the quantization of a general quadratic theory. In addition, we consider the quantization of a damped oscillator and of a radiating point-like charge. (orig.)
Canonical quantization of so-called non-Lagrangian systems
International Nuclear Information System (INIS)
Gitman, D.M.; Kupriyanov, V.G.
2007-01-01
We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential equations cannot be directly identified with a set of Euler-Lagrange equations, one can reformulate such a set in an equivalent first-order form that can always be treated as the Euler-Lagrange equations of a certain action. We construct such an action explicitly. It turns out that in the general case the hamiltonization and canonical quantization of such an action are non-trivial problems, since the theory involves time-dependent constraints. We adopt the general approach of hamiltonization and canonical quantization for such theories as described in D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints (Springer, Berlin, 1990). to the case under consideration. There exists an ambiguity (that cannot be reduced to the addition of a total time derivative) in associating a Lagrange function with a given set of equations. We present a complete description of this ambiguity. The proposed scheme is applied to the quantization of a general quadratic theory. In addition, we consider the quantization of a damped oscillator and of a radiating point-like charge. (orig.)
Hamiltonian analysis for linearly acceleration-dependent Lagrangians
Energy Technology Data Exchange (ETDEWEB)
Cruz, Miguel, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Gómez-Cortés, Rosario, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx; Rojas, Efraín, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx [Facultad de Física, Universidad Veracruzana, 91000 Xalapa, Veracruz, México (Mexico); Molgado, Alberto, E-mail: miguelcruz02@uv.mx, E-mail: roussjgc@gmail.com, E-mail: molgado@fc.uaslp.mx, E-mail: efrojas@uv.mx [Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Avenida Salvador Nava S/N Zona Universitaria, CP 78290 San Luis Potosí, SLP, México (Mexico)
2016-06-15
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies 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.
A Combined Eulerian-Lagrangian Data Representation for Large-Scale Applications.
Sauer, Franz; Xie, Jinrong; Ma, Kwan-Liu
2017-10-01
The Eulerian and Lagrangian reference frames each provide a unique perspective when studying and visualizing results from scientific systems. As a result, many large-scale simulations produce data in both formats, and analysis tasks that simultaneously utilize information from both representations are becoming increasingly popular. However, due to their fundamentally different nature, drawing correlations between these data formats is a computationally difficult task, especially in a large-scale setting. In this work, we present a new data representation which combines both reference frames into a joint Eulerian-Lagrangian format. By reorganizing Lagrangian information according to the Eulerian simulation grid into a "unit cell" based approach, we can provide an efficient out-of-core means of sampling, querying, and operating with both representations simultaneously. We also extend this design to generate multi-resolution subsets of the full data to suit the viewer's needs and provide a fast flow-aware trajectory construction scheme. We demonstrate the effectiveness of our method using three large-scale real world scientific datasets and provide insight into the types of performance gains that can be achieved.
An investigation of singular Lagrangians as field systems
International Nuclear Information System (INIS)
Rabei, E.M.
1995-07-01
The link between the treatment of singular Lagrangians as field systems and the general approach is studied. It is shown that singular Lagrangians as field systems are always in exact agreement with the general approach. Two examples and the singular Lagrangian with zero rank Hessian matrix are studied. The equations of motion in the field systems are equivalent to the equations which contain acceleration, and the constraints are equivalent to the equations which do not contain acceleration in the general approach treatment. (author). 10 refs
Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations
International Nuclear Information System (INIS)
Mestdag, T; Crampin, M
2008-01-01
We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated with Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper, we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincare equations in a new fashion and we show how solutions of the Euler-Lagrange equations can be reconstructed with the help of the mechanical connection. Illustrative examples confirm the theory
Approximate Noether symmetries and collineations for regular perturbative Lagrangians
Paliathanasis, Andronikos; Jamal, Sameerah
2018-01-01
Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.
Lagrangian relaxation based algorithm for trigeneration planning with storages
DEFF Research Database (Denmark)
Rong, Aiying; Lahdelma, Risto; Luh, Peter
2008-01-01
of three energy commodities follows a joint characteristic. This paper presents a Lagrangian relaxation (LR) based algorithm for trigeneration planning with storages based on deflected subgradient optimization method. The trigeneration planning problem is modeled as a linear programming (LP) problem...... an effective method for the long-term planning problem based on the proper strategy to form Lagrangian subproblems and solve the Lagrangian dual (LD) problem based on deflected subgradient optimization method. We also develop a heuristic for restoring feasibility from the LD solution. Numerical results based...
The 3D Lagrangian Integral Method. Henrik Koblitz Rasmussen
DEFF Research Database (Denmark)
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...... Integral Method" to simulate viscoelastic flow, the governing equations are solved for the particle positions (Lagrangian kinematics). Therefore, the transient motion of surfaces can be followed in a particularly simple fashion even in 3D viscoelastic flow. The "3D Lagrangian Integral Method" is described...
The complete lowest order chiral Lagrangian from a little box
International Nuclear Information System (INIS)
DeGrand, T.; Schaefer, S.
2007-09-01
We recently performed a pilot study determining the parameters of the leading order chiral Lagrangian from distributions of the eigenvalues of a quenched Dirac operator coupled to an imaginary isospin chemical potential. (orig.)
Weak stability of Lagrangian solutions to the semigeostrophic equations
International Nuclear Information System (INIS)
Faria, Josiane C O; Lopes Filho, Milton C; Nussenzveig Lopes, Helena J
2009-01-01
In (Cullen and Feldman 2006 SIAM J. Math. Anal. 37 137–95), Cullen and Feldman proved the existence of Lagrangian solutions for the semigeostrophic system in physical variables with initial potential vorticity in L p , p > 1. Here, we show that a subsequence of the Lagrangian solutions corresponding to a strongly convergent sequence of initial potential vorticities in L 1 converges strongly in L q , q < ∞, to a Lagrangian solution, in particular extending the existence result of Cullen and Feldman to the case p = 1. We also present a counterexample for Lagrangian solutions corresponding to a sequence of initial potential vorticities converging in BM. The analytical tools used include techniques from optimal transportation, Ambrosio's results on transport by BV vector fields and Orlicz spaces
Ambiguities in the Lagrangians formalism: the time-dependent case
International Nuclear Information System (INIS)
Moreira, D.T.
1986-01-01
An intrinsic formulation of the equivalence problem for time-dependent Lagrangians is given. A new demostration of a theorem derived by Henneaux (1982) is obtained. The relationship to transformation groups is discussed. (Author) [pt
Second post-Newtonian Lagrangian dynamics of spinning compact binaries
Energy Technology Data Exchange (ETDEWEB)
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.)
Low energy effective Lagrangians in open superstring theory
International Nuclear Information System (INIS)
Medina, Ricardo
2008-01-01
The low energy effective Lagrangian describes the interactions of the massless modes of String Theory. Present work is being done to obtain all alpha' 3 terms (bosonic and fermionic) by means of the known 5-point amplitudes and SUSY
Hydrodynamical model based on a bag-like Lagrangian
International Nuclear Information System (INIS)
Chiu, C.B.; Lam, C.S.; Wang, K.H.
1976-06-01
Equations of motion of hydrodynamical model are derived from a bag-like Lagrangian by using the technique of information theory. Comments on the break-up of the system and on the properties of decay products are included
Effective Lagrangians for quantum many-body systems
Czech Academy of Sciences Publication Activity Database
Andersen, J. O.; Brauner, Tomáš; Hofmann, C. P.; Vuorinen, A.
2014-01-01
Roč. 2014, č. 8 (2014), 088 ISSN 1029-8479 Institutional support: RVO:61389005 Keywords : spontaneous symmetry breaking * chiral lagrangian s * global symmetries Subject RIV: BE - Theoretical Physics Impact factor: 6.111, year: 2014
Directory of Open Access Journals (Sweden)
Francisco de Assis Corrêa
2006-05-01
Full Text Available O problema de localização de máxima cobertura (MCLP procura localizar facilidades visando a maximizar a população atendida, considerando uma dada distância ou tempo padrão de serviço. Várias extensões desse modelo têm sido propostas para aumentar a sua aplicabilidade. Entre elas, existem modelos probabilísticos para localização-alocação de máxima cobertura com restrições no tempo de espera ou no comprimento da fila para sistemas congestionados, que levam em conta um ou vários servidores por facilidade. A proposta deste trabalho é a de resolver um modelo para um servidor por facilidade por meio da relaxação lagrangeana e do Algoritmo Genético Construtivo. Os resultados dos testes obtidos nessas abordagens são apresentados e comparados.The Maximal Covering Location Problem (MCLP seeks to locate facilities in order to maximize the serviced population, considering a given distance or standard service time. Various extensions of this model have been proposed to enhance its applicability, e.g., probabilistic models for maximum location-allocation coverage with waiting time or queue length constraints for congested systems, taking into account one or more servers per service center. In this paper we present two procedures for solving a probabilistic model, which considers one server per center, using Lagrangian relaxation and the Constructive Genetic Algorithm. Extensive tests of these approaches are presented and their results compared.
One-loop effective lagrangians after matching
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
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.
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).
LSPRAY-IV: A Lagrangian Spray Module
Raju, M. S.
2012-01-01
LSPRAY-IV is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray. Some important research areas covered as a part of the code development are: (1) the extension of combined CFD/scalar-Monte- Carlo-PDF method to spray modeling, (2) the multi-component liquid spray modeling, and (3) the assessment of various atomization models used in spray calculations. The current version contains the extension to the modeling of superheated sprays. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers.
Flux form Semi-Lagrangian methods for parabolic problems
Directory of Open Access Journals (Sweden)
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.
Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics
Webb, G. M.; Anco, S. C.
2016-02-01
The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.
Sequential weak continuity of null Lagrangians at the boundary
Czech Academy of Sciences Publication Activity Database
Kalamajska, A.; Kraemer, S.; Kružík, Martin
2014-01-01
Roč. 49, 3/4 (2014), s. 1263-1278 ISSN 0944-2669 R&D Projects: GA ČR GAP201/10/0357 Institutional support: RVO:67985556 Keywords : null Lagrangians * nonhomogeneous nonlinear mappings * sequential weak/in measure continuity Subject RIV: BA - General Mathematics Impact factor: 1.518, year: 2014 http://library.utia.cas.cz/separaty/2013/MTR/kruzik-sequential weak continuity of null lagrangians at the boundary.pdf
On the dynamics of second-order Lagrangian systems
Directory of Open Access Journals (Sweden)
Ronald Adams
2017-04-01
Full Text Available In this article we are concerned with improving the twist condition for second-order Lagrangian systems. We characterize a local Twist property and demonstrate how results on the existence of simple closed characteristics can be extended in the case of the Swift-Hohenberg / extended Fisher-Kolmogorov Lagrangian. Finally, we describe explicit evolution equations for broken geodesic curves that could be used to investigate more general systems or closed characteristics.
Semi-Lagrangian methods in air pollution models
Directory of Open Access Journals (Sweden)
A. B. Hansen
2011-06-01
Full Text Available Various semi-Lagrangian methods are tested with respect to advection in air pollution modeling. The aim is to find a method fulfilling as many of the desirable properties by Rasch andWilliamson (1990 and Machenhauer et al. (2008 as possible. The focus in this study is on accuracy and local mass conservation.
The methods tested are, first, classical semi-Lagrangian cubic interpolation, see e.g. Durran (1999, second, semi-Lagrangian cubic cascade interpolation, by Nair et al. (2002, third, semi-Lagrangian cubic interpolation with the modified interpolation weights, Locally Mass Conserving Semi-Lagrangian (LMCSL, by Kaas (2008, and last, semi-Lagrangian cubic interpolation with a locally mass conserving monotonic filter by Kaas and Nielsen (2010.
Semi-Lagrangian (SL interpolation is a classical method for atmospheric modeling, cascade interpolation is more efficient computationally, modified interpolation weights assure mass conservation and the locally mass conserving monotonic filter imposes monotonicity.
All schemes are tested with advection alone or with advection and chemistry together under both typical rural and urban conditions using different temporal and spatial resolution. The methods are compared with a current state-of-the-art scheme, Accurate Space Derivatives (ASD, see Frohn et al. (2002, presently used at the National Environmental Research Institute (NERI in Denmark. To enable a consistent comparison only non-divergent flow configurations are tested.
The test cases are based either on the traditional slotted cylinder or the rotating cone, where the schemes' ability to model both steep gradients and slopes are challenged.
The tests showed that the locally mass conserving monotonic filter improved the results significantly for some of the test cases, however, not for all. It was found that the semi-Lagrangian schemes, in almost every case, were not able to outperform the current ASD scheme
Lagrangian structures in time-periodic vortical flows
Directory of Open Access Journals (Sweden)
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.
Heister, Timo
2012-01-29
Efficient preconditioning for Oseen-type problems is an active research topic. We present a novel approach leveraging stabilization for inf-sup stable discretizations. The Grad-Div stabilization shares the algebraic properties with an augmented Lagrangian-type term. Both simplify the approximation of the Schur complement, especially in the convection-dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov-type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. © 2012 John Wiley & Sons, Ltd.
Heister, Timo; Rapin, Gerd
2012-01-01
Efficient preconditioning for Oseen-type problems is an active research topic. We present a novel approach leveraging stabilization for inf-sup stable discretizations. The Grad-Div stabilization shares the algebraic properties with an augmented Lagrangian-type term. Both simplify the approximation of the Schur complement, especially in the convection-dominated case. We exploit this for the construction of the preconditioner. Solving the discretized Oseen problem with an iterative Krylov-type method shows that the outer iteration numbers are retained independent of mesh size, viscosity, and finite element order. Thus, the preconditioner is very competitive. © 2012 John Wiley & Sons, Ltd.
A Computational Realization of a Semi-Lagrangian Method for Solving the Advection Equation
Directory of Open Access Journals (Sweden)
Alexander Efremov
2014-01-01
Full Text Available A parallel implementation of a method of the semi-Lagrangian type for the advection equation on a hybrid architecture computation system is discussed. The difference scheme with variable stencil is constructed on the base of an integral equality between the neighboring time levels. The proposed approach allows one to avoid the Courant-Friedrichs-Lewy restriction on the relation between time step and mesh size. The theoretical results are confirmed by numerical experiments. Performance of a sequential algorithm and several parallel implementations with the OpenMP and CUDA technologies in the C language has been studied.
General conditions for the existence of non-standard Lagrangians for dissipative dynamical systems
International Nuclear Information System (INIS)
Musielak, Z.E.
2009-01-01
Equations of motion describing dissipative dynamical systems with coefficients varying either in time or in space are considered. To identify the equations that admit a Lagrangian description, two classes of non-standard Lagrangians are introduced and general conditions required for the existence of these Lagrangians are determined. The conditions are used to obtain some non-standard Lagrangians and derive equations of motion resulting from these Lagrangians.
Bayesian Lagrangian Data Assimilation and Drifter Deployment Strategies
Dutt, A.; Lermusiaux, P. F. J.
2017-12-01
Ocean currents transport a variety of natural (e.g. water masses, phytoplankton, zooplankton, sediments, etc.) and man-made materials and other objects (e.g. pollutants, floating debris, search and rescue, etc.). Lagrangian Coherent Structures (LCSs) or the most influential/persistent material lines in a flow, provide a robust approach to characterize such Lagrangian transports and organize classic trajectories. Using the flow-map stochastic advection and a dynamically-orthogonal decomposition, we develop uncertainty prediction schemes for both Eulerian and Lagrangian variables. We then extend our Bayesian Gaussian Mixture Model (GMM)-DO filter to a joint Eulerian-Lagrangian Bayesian data assimilation scheme. The resulting nonlinear filter allows the simultaneous non-Gaussian estimation of Eulerian variables (e.g. velocity, temperature, salinity, etc.) and Lagrangian variables (e.g. drifter/float positions, trajectories, LCSs, etc.). Its results are showcased using a double-gyre flow with a random frequency, a stochastic flow past a cylinder, and realistic ocean examples. We further show how our Bayesian mutual information and adaptive sampling equations provide a rigorous efficient methodology to plan optimal drifter deployment strategies and predict the optimal times, locations, and types of measurements to be collected.
Scale-by-scale contributions to Lagrangian particle acceleration
Lalescu, Cristian C.; Wilczek, Michael
2017-11-01
Fluctuations on a wide range of scales in both space and time are characteristic of turbulence. Lagrangian particles, advected by the flow, probe these fluctuations along their trajectories. In an effort to isolate the influence of the different scales on Lagrangian statistics, we employ direct numerical simulations (DNS) combined with a filtering approach. Specifically, we study the acceleration statistics of tracers advected in filtered fields to characterize the smallest temporal scales of the flow. Emphasis is put on the acceleration variance as a function of filter scale, along with the scaling properties of the relevant terms of the Navier-Stokes equations. We furthermore discuss scaling ranges for higher-order moments of the tracer acceleration, as well as the influence of the choice of filter on the results. Starting from the Lagrangian tracer acceleration as the short time limit of the Lagrangian velocity increment, we also quantify the influence of filtering on Lagrangian intermittency. Our work complements existing experimental results on intermittency and accelerations of finite-sized, neutrally-buoyant particles: for the passive tracers used in our DNS, feedback effects are neglected such that the spatial averaging effect is cleanly isolated.
The PDF method for Lagrangian two-phase flow simulations
International Nuclear Information System (INIS)
Minier, J.P.; Pozorski, J.
1996-04-01
A recent turbulence model put forward by Pope (1991) in the context of PDF modelling has been used. In this approach, the one-point joint velocity-dissipation pdf equation is solved by simulating the instantaneous behaviour of a large number of Lagrangian fluid particles. Closure of the evolution equations of these Lagrangian particles is based on stochastic models and more specifically on diffusion processes. Such models are of direct use for two-phase flow modelling where the so-called fluid seen by discrete inclusions has to be modelled. Full Lagrangian simulations have been performed for shear-flows. It is emphasized that this approach gives far more information than traditional turbulence closures (such as the K-ε model) and therefore can be very useful for situations involving complex physics. It is also believed that the present model represents the first step towards a complete Lagrangian-Lagrangian model for dispersed two-phase flow problems. (authors). 21 refs., 6 figs
Diffusion coefficient adaptive correction in Lagrangian puff model
International Nuclear Information System (INIS)
Tan Wenji; Wang Dezhong; Ma Yuanwei; Ji Zhilong
2014-01-01
Lagrangian puff model is widely used in the decision support system for nuclear emergency management. The diffusion coefficient is one of the key parameters impacting puff model. An adaptive method was proposed in this paper, which could correct the diffusion coefficient in Lagrangian puff model, and it aimed to improve the accuracy of calculating the nuclide concentration distribution. This method used detected concentration data, meteorological data and source release data to estimate the actual diffusion coefficient with least square method. The diffusion coefficient adaptive correction method was evaluated by Kincaid data in MVK, and was compared with traditional Pasquill-Gifford (P-G) diffusion scheme method. The results indicate that this diffusion coefficient adaptive correction method can improve the accuracy of Lagrangian puff model. (authors)
Minimal local Lagrangians for higher-spin geometry
International Nuclear Information System (INIS)
Francia, Dario; Sagnotti, Augusto
2005-01-01
The Fronsdal Lagrangians for free totally symmetric rank-s tensors φ μ 1 ...μ s 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 α μ 1 ...μ s-3 and a rank-(s-4) Lagrange multiplier β μ 1 ...μ s-4 . In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors ψ μ 1 ...μ n can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n-2) compensator ξ μ 1 ...μ n-2 and a rank-(n-3) Lagrange multiplier λ μ 1 ...μ n-3
Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics.
Martínez, Enrique; Cawkwell, Marc J; Voter, Arthur F; Niklasson, Anders M N
2015-04-21
Extended Lagrangian Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended Lagrangian Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached at each time step. The thermostated extended Lagrangian framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.
The semi-Lagrangian method on curvilinear grids
Directory of Open Access Journals (Sweden)
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.
Seakeeping with the semi-Lagrangian particle finite element method
Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio
2017-07-01
The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.
Nonleptonic decay of charmed mesons and chiral lagrangians
International Nuclear Information System (INIS)
Kalinovskij, Yu.L.; Pervushin, V.N.
1978-01-01
Nonleptonic decays of charmed mesons in chiral theory are considered. The lagrangian of strong interaction is taken to be invariant under the SU(4)xSU(4) group. Symmetry breaking is chosen according to the (4,4sup(*))+(4sup(*),4) simplest representation of the SU(4)xSU(4) group. The lagrangian of weak interaction is taken in the ''current x current'' form and satisfies exactly the rule probabilities of decays for D and F mesons are compared with available experimental data
Mean-Lagrangian formalism and covariance of fluid turbulence.
Ariki, Taketo
2017-05-01
Mean-field-based Lagrangian framework is developed for the fluid turbulence theory, which enables physically objective discussions, especially, of the history effect. Mean flow serves as a purely geometrical object of Lie group theory, providing useful operations to measure the objective rate and history integration of the general tensor field. The proposed framework is applied, on the one hand, to one-point closure model, yielding an objective expression of the turbulence viscoelastic effect. Application to two-point closure, on the other hand, is also discussed, where natural extension of known Lagrangian correlation is discovered on the basis of an extended covariance group.
Power corrections to the HTL effective Lagrangian of QED
Carignano, Stefano; Manuel, Cristina; Soto, Joan
2018-05-01
We present compact expressions for the power corrections to the hard thermal loop (HTL) Lagrangian of QED in d space dimensions. These are corrections of order (L / T) 2, valid for momenta L ≪ T, where T is the temperature. In the limit d → 3 we achieve a consistent regularization of both infrared and ultraviolet divergences, which respects the gauge symmetry of the theory. Dimensional regularization also allows us to witness subtle cancellations of infrared divergences. We also discuss how to generalize our results in the presence of a chemical potential, so as to obtain the power corrections to the hard dense loop (HDL) Lagrangian.
Complex nonlinear Lagrangian for the Hasegawa-Mima equation
International Nuclear Information System (INIS)
Dewar, R.L.; Abdullatif, R.F.; Sangeetha, G.G.
2005-01-01
The Hasegawa-Mima equation is the simplest nonlinear single-field model equation that captures the essence of drift wave dynamics. Like the Schroedinger equation it is first order in time. However its coefficients are real, so if the potential φ is initially real it remains real. However, by embedding φ in the space of complex functions a simple Lagrangian is found from which the Hasegawa-Mima equation may be derived from Hamilton's Principle. This Lagrangian is used to derive an action conservation equation which agrees with that of Biskamp and Horton. (author)
International Nuclear Information System (INIS)
Boergers, C.; Peskin, C.S.
1987-01-01
In the Lagrangian fractional step method introduced in this paper, the fluid velocity and pressure are defined on a collection of N fluid markers. At each time step, these markers are used to generate a Voronoi diagram, and this diagram is used to construct finite-difference operators corresponding to the divergence, gradient, and Laplacian. The splitting of the Navier--Stokes equations leads to discrete Helmholtz and Poisson problems, which we solve using a two-grid method. The nonlinear convection terms are modeled simply by the displacement of the fluid markers. We have implemented this method on a periodic domain in the plane. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams, and we report on numerical results which indicate the the fractional step method is convergent of first order. The overall work per time step is proportional to N log N. copyright 1987 Academic Press, Inc
Lindner, Michael; Donner, Reik V
2017-03-01
We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a directed network that describes the exchange of mass between distinct regions of the flow domain. By studying different measures characterizing flow network connectivity at different time-scales, we are able to identify the location of dynamically invariant structures and regions of maximum dispersion. Specifically, our approach allows us to delimit co-existing flow regimes with different dynamics. To validate our findings, we compare several network characteristics to the well-established finite-time Lyapunov exponents and apply a receiver operating characteristic analysis to identify network measures that are particularly useful for unveiling the skeleton of Lagrangian chaos.
Constructive approach to supergravity
International Nuclear Information System (INIS)
Milton, K.A.; Urrutia, L.F.; Finkelstein, R.J.
1980-01-01
Starting from a first-order formulation of the Lagrangian of noninteracting massless helicity-2 and helicity-3/2 particles, global supersymmetry transformations are deduced. Then, allowing the supersymmetry transformations to become local requires, if supersymmetry is to be maintained, the introduction of a unique primitive interaction through the 'gravitino' stress tensor and torsion. Finally, the imposition of exact supersymmetry invariance leads by a short, constructive process to full supergravity and the complete form of the super-symmetry transformations. In particular, no explicit use is made of general coordinate invariance, and the self-consistency of the gravitational coupling emerges from the local supersymmetry requirement alone. (author)
IMPOSING A LAGRANGIAN PARTICLE FRAMEWORK ON AN EULERIAN HYDRODYNAMICS INFRASTRUCTURE IN FLASH
International Nuclear Information System (INIS)
Dubey, A.; Daley, C.; Weide, K.; Graziani, C.; ZuHone, J.; Ricker, P. M.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid-structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash
Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
Constructive use of holographic projections
International Nuclear Information System (INIS)
Schroer, Bert
2008-01-01
Revisiting the old problem of existence of interacting models of QFT with new conceptual ideas and mathematical tools, one arrives at a novel view about the nature of QFT. The recent success of algebraic methods in establishing the existence of factorizing models suggests new directions for a more intrinsic constructive approach beyond Lagrangian quantization. Holographic projection simplifies certain properties of the bulk theory and hence is a promising new tool for these new attempts. (author)
Constructive use of holographic projections
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Institut fuer Theoretische Physik der FU, Berlin (Germany)
2008-07-01
Revisiting the old problem of existence of interacting models of QFT with new conceptual ideas and mathematical tools, one arrives at a novel view about the nature of QFT. The recent success of algebraic methods in establishing the existence of factorizing models suggests new directions for a more intrinsic constructive approach beyond Lagrangian quantization. Holographic projection simplifies certain properties of the bulk theory and hence is a promising new tool for these new attempts. (author)
Implicit Lagrangian equations and the mathematical modeling of physical systems
Moreau, Luc; van der Schaft, Arjan
2002-01-01
We introduce a class of optimal control problems on manifolds which gives rise (via the Pontryagin maximum principle) to a class of implicit Lagrangian systems (a notion which is introduced in the paper). We apply this to the mathematical modeling of interconnected mechanical systems and mechanical
Matter composition at high density by effective scaled lagrangian
Energy Technology Data Exchange (ETDEWEB)
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.)
Classical dynamical variables for the Wess-Zumino matter Lagrangian
International Nuclear Information System (INIS)
Domenech, G.; Buenos Aires Univ. Nacional; Levinas, M.; Buenos Aires Univ. Nacional; Umerez, N.
1989-01-01
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. (orig.)
Lagrangian fluid dynamics using the Voronoi-Delauanay mesh
International Nuclear Information System (INIS)
Dukowicz, J.K.
1981-01-01
A Lagrangian technique for numerical fluid dynamics is described. This technique makes use of the Voronoi mesh to efficiently locate new neighbors, and it uses the dual (Delaunay) triangulation to define computational cells. This removes all topological restrictions and facilitates the solution of problems containing interfaces and multiple materials. To improve computational accuracy a mesh smoothing procedure is employed
Extended Lagrangian formalism for rheonomic systems with variable mass
Directory of Open Access Journals (Sweden)
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.
Infinitely many inequivalent field theories from one Lagrangian
100__; Mavromatos, Nick E.; Sarkar, Sarben
2014-01-01
Logarithmic time-like Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field $\\phi$. In Euclidean space the Lagrangian of such a theory, $L=\\frac{1}{2}(\
Formation control of marine surface craft: a Lagrangian approach
DEFF Research Database (Denmark)
Ihle, Ivar-Andre F.; Jouffroy, Jerome; Fossen, Thor I.
2006-01-01
This paper presents a method for formation control of marine surface craft inspired by Lagrangian mechanics. The desired formation configuration and response of the marine surface craft are given as a set of constraints in analytical mechanics. Thus, constraints forces arise and feedback from...
An unconditionally stable fully conservative semi-Lagrangian method
Lentine, Michael; Gré tarsson, Jó n Tó mas; Fedkiw, Ronald
2011-01-01
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
Behaviour of Lagrangian triangular mixed fluid finite elements
Indian Academy of Sciences (India)
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 ...
Towards Selective Tidal-Stream Transport for Lagrangian profilers
DEFF Research Database (Denmark)
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...
Lagrangian Approach to Study Catalytic Fluidized Bed Reactors
Madi, Hossein; Hossein Madi Team; Marcelo Kaufman Rechulski Collaboration; Christian Ludwig Collaboration; Tilman Schildhauer Collaboration
2013-03-01
Lagrangian approach of fluidized bed reactors is a method, which simulates the movement of catalyst particles (caused by the fluidization) by changing the gas composition around them. Application of such an investigation is in the analysis of the state of catalysts and surface reactions under quasi-operando conditions. The hydrodynamics of catalyst particles within a fluidized bed reactor was studied to improve a Lagrangian approach. A fluidized bed methanation employed in the production of Synthetic Natural Gas from wood was chosen as the case study. The Lagrangian perspective was modified and improved to include different particle circulation patterns, which were investigated through this study. Experiments were designed to evaluate the concepts of the model. The results indicate that the setup is able to perform the designed experiments and a good agreement between the simulation and the experimental results were observed. It has been shown that fluidized bed reactors, as opposed to fixed beds, can be used to avoid the deactivation of the methanation catalyst due to carbon deposits. Carbon deposition on the catalysts tested with the Lagrangian approach was investigated by temperature programmed oxidation (TPO) analysis of ex-situ catalyst samples. This investigation was done to identify the effects of particles velocity and their circulation patterns on the amount and type of deposited carbon on the catalyst surface. Ecole Polytechnique Federale de Lausanne(EPFL), Paul Scherrer Institute (PSI)
High-Order Hamilton's Principle and the Hamilton's Principle of High-Order Lagrangian Function
International Nuclear Information System (INIS)
Zhao Hongxia; Ma Shanjun
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.
Implications of Lagrangian transport for coupled chemistry-climate simulations
Stenke, A.; Dameris, M.; Grewe, V.; Garny, H.
2008-10-01
For the first time a purely Lagrangian transport algorithm is applied in a fully coupled chemistry-climate model (CCM). We use the Lagrangian scheme ATTILA for the transport of water vapour, cloud water and chemical trace species in the ECHAM4.L39(DLR)/CHEM (E39C) CCM. The advantage of the Lagrangian approach is that it is numerically non-diffusive and therefore maintains steeper and more realistic gradients than the operational semi-Lagrangian transport scheme. In case of radiatively active species changes in the simulated distributions feed back to model dynamics which in turn affect the modelled transport. The implications of the Lagrangian transport scheme for stratospheric model dynamics and tracer distributions in the upgraded model version E39C-ATTILA (E39C-A) are evaluated by comparison with observations and results of the E39C model with the operational semi-Lagrangian advection scheme. We find that several deficiencies in stratospheric dynamics in E39C seem to originate from a pronounced modelled wet bias and an associated cold bias in the extra-tropical lowermost stratosphere. The reduction of the simulated moisture and temperature bias in E39C-A leads to a significant advancement of stratospheric dynamics in terms of the mean state as well as annual and interannual variability. As a consequence of the favourable numerical characteristics of the Lagrangian transport scheme and the improved model dynamics, E39C-A generally shows more realistic stratospheric tracer distributions: Compared to E39C high stratospheric chlorine (Cly) concentrations extend further downward and agree now well with analyses derived from observations. Therefore E39C-A realistically covers the altitude of maximum ozone depletion in the stratosphere. The location of the ozonopause, i.e. the transition from low tropospheric to high stratospheric ozone values, is also clearly improved in E39C-A. Furthermore, the simulated temporal evolution of stratospheric Cly in the past is
The topology of Lagrangian foliations of integrable systems with hyperelliptic Hamiltonian
International Nuclear Information System (INIS)
Kudryavtseva, Elena A; Lepskii, Timur A
2011-01-01
We study the integrable Hamiltonian systems (C 2 ,Re(dz and dw),H=Ref(z,w)) with the additional first integral F=Imf which correspond to the complex Hamiltonian systems (C 2 ,dz and dw,f(z,w)) with a hyperelliptic Hamiltonian f(z,w)=z 2 +P n (w), n element of N. For n≥3 the system has incomplete flows on any Lagrangian leaf f -1 (a). The topology of the Lagrangian foliation of such systems in a small neighbourhood of any leaf f -1 (a) is described in terms of the number n and the combinatorial type of the leaf--the set of multiplicities of the critical points of the function f that belong to the leaf. For odd n, a complex analogue of Liouville's theorem is obtained for those systems corresponding to polynomials P n (w) with simple real roots. In particular, a set of complex canonical variables analogous to action-angle variables is constructed in a small neighbourhood of the leaf f -1 (0). Bibliography: 12 titles.
Next generation extended Lagrangian first principles molecular dynamics.
Niklasson, Anders M N
2017-08-07
Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.
Energy Technology Data Exchange (ETDEWEB)
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.
Partial quantization of Lagrangian-Hamiltonian systems
International Nuclear Information System (INIS)
Amaral, C.M. do; Soares Filho, P.C.
1979-05-01
A classical variational principle is constructed in the Weiss form, for dynamical systems with support spaces of the configuration-phase kind. This extended principle rules the dynamics of classical systems, partially Hamiltonian, in interaction with Lagrangean parameterized subsidiary dynamics. The variational family of equations obtained, consists of an equation of the Hamilton-Jacobi type, coupled to a family of differential equations of the Euler-Lagrange form. The basic dynamical function appearing in the equations is a function of the Routh kind. By means of an ansatz induced by the variationally obtained family, a generalized set of equation, is proposed constituted by a wave equation of Schroedinger type, coupled to a family of equations formaly analog to those Euler-Lagrange equations. A basic operator of Routh type appears in our generalized set of equations. This operator describes the interaction between a quantized Hamiltonian dynamics, with a parameterized classical Lagrangean dynamics in semi-classical closed models. (author) [pt
Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids
Energy Technology Data Exchange (ETDEWEB)
Sambasivan, Shiv Kumar [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory; Burton, Donald E. [Los Alamos National Laboratory; Christon, Mark A. [Los Alamos National Laboratory
2012-07-19
A finite volume cell-centered Lagrangian scheme for solving large deformation problems is constructed based on the hypo-elastic model and using the mimetic theory. Rigorous analysis in the context of gas and solid dynamics, and arbitrary polygonal meshes, is presented to demonstrate the ability of cell-centered schemes in mimicking the continuum properties and principles at the discrete level. A new mimetic formulation based gradient evaluation technique and physics-based, frame independent and symmetry preserving slope limiters are proposed. Furthermore, a physically consistent dissipation model is employed which is both robust and inexpensive to implement. The cell-centered scheme along with these additional new features are applied to solve solids undergoing elasto-plastic deformation.
Albaugh, Alex; Head-Gordon, Teresa; Niklasson, Anders M N
2018-02-13
Generalized extended Lagrangian Born-Oppenheimer molecular dynamics (XLBOMD) methods provide a framework for fast iteration-free simulations of models that normally require expensive electronic ground state optimizations prior to the force evaluations at every time step. XLBOMD uses dynamically driven auxiliary degrees of freedom that fluctuate about a variationally optimized ground state of an approximate "shadow" potential which approximates the true reference potential. While the requirements for such shadow potentials are well understood, constructing such potentials in practice has previously been ad hoc, and in this work, we present a systematic development of XLBOMD shadow potentials that match the reference potential to any order. We also introduce a framework for combining friction-like dissipation for the auxiliary degrees of freedom with general-order integration, a combination that was not previously possible. These developments are demonstrated with a simple fluctuating charge model and point induced dipole polarization models.
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 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...
A Discrete Approach to Meshless Lagrangian Solid Modeling
Directory of Open Access Journals (Sweden)
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.
Regularization of Hamilton-Lagrangian guiding center theories
International Nuclear Information System (INIS)
Correa-Restrepo, D.; Wimmel, H.K.
1985-04-01
The Hamilton-Lagrangian guiding-center (G.C.) theories of Littlejohn, Wimmel, and Pfirsch show a singularity for B-fields with non-vanishing parallel curl at a critical value of vsub(parallel), which complicates applications. The singularity is related to a sudden breakdown, at a critical vsub(parallel), of gyration in the exact particle mechanics. While the latter is a real effect, the G.C. singularity can be removed. To this end a regularization method is defined that preserves the Hamilton-Lagrangian structure and the conservation theorems. For demonstration this method is applied to the standard G.C. theory (without polarization drift). Liouville's theorem and G.C. kinetic equations are also derived in regularized form. The method could equally well be applied to the case with polarization drift and to relativistic G.C. theory. (orig.)
An algorithm for discovering Lagrangians automatically from data
Directory of Open Access Journals (Sweden)
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.
Hadronic interactions from effective chiral Lagrangians of quarks and gluons
International Nuclear Information System (INIS)
Krein, G.
1996-06-01
We discuss the combined used of the techniques of effective chiral field theory and the field theoretic method known as Fock-Tani representation to derive effective hadron interactions. The Fock-Tani method is based on a change of representation by means of a unitary transformation such that the composite hadrons are redescribed by elementary-particle field operators. Application of the unitary transformation on the microscopic quark-quark interaction derived from a chiral effective Lagrangian leads to chiral effective interactions describing all possible processes involving hadrons and their constituents. The formalism is illustrated by deriving the one-pion-exchange potential between the nucleons using the quark-gluon effective chiral Lagrangian of Manohar and Georgi. We also present the results of a study of the saturation properties of the nuclear matter using this formalism. (author). 9 refs., 2 figs
A non-conventional discontinuous Lagrangian for viscous flow
Marner, F.
2017-01-01
Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided. PMID:28386415
Lagrangian space consistency relation for large scale structure
International Nuclear Information System (INIS)
Horn, Bart; Hui, Lam; Xiao, Xiao
2015-01-01
Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias and Riotto and Peloso and Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present. The simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space
Bohr--Sommerfeld Lagrangians of moduli spaces of Higgs bundles
DEFF Research Database (Denmark)
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...
Pure spinors, free differential algebras, and the supermembrane
International Nuclear Information System (INIS)
Fre, Pietro; Grassi, Pietro Antonio
2007-01-01
The Lagrangian formalism for the supermembrane in any 11d supergravity background is constructed in the pure spinor framework. Our gauge-fixed action is manifestly BRST, supersymmetric, and 3d Lorentz invariant. The relation between the Free Differential Algebras (FDA) underlying 11d supergravity and the BRST symmetry of the membrane action is exploited. The 'gauge-fixing' has a natural interpretation as the variation of the Chevalley cohomology class needed for the extension of 11d super-Poincare superalgebra to M-theory FDA. We study the solution of the pure spinor constraints in full detail
Pure spinors, free differential algebras, and the supermembrane
Energy Technology Data Exchange (ETDEWEB)
Fre, Pietro [Dipartimento di Fisica Teorica, Universita di Torino, and INFN-Sezione di Torino, Via P. Giuria 1, I-10125 Turin (Italy); Grassi, Pietro Antonio [Centro Studi e Ricerche E. Fermi, Compendio Viminale, I-00184 Rome (Italy) and DISTA, Universita del Piemonte Orientale, and INFN-Sezione di Torino, Via Bellini 25/G, Alessandria 15100 (Italy) and CERN, Theory Unit, CH-1211 Geneva 23 (Switzerland)]. E-mail: pgrassi@insti.physics.sunysb.edu
2007-02-12
The Lagrangian formalism for the supermembrane in any 11d supergravity background is constructed in the pure spinor framework. Our gauge-fixed action is manifestly BRST, supersymmetric, and 3d Lorentz invariant. The relation between the Free Differential Algebras (FDA) underlying 11d supergravity and the BRST symmetry of the membrane action is exploited. The 'gauge-fixing' has a natural interpretation as the variation of the Chevalley cohomology class needed for the extension of 11d super-Poincare superalgebra to M-theory FDA. We study the solution of the pure spinor constraints in full detail.
A Lagrangian PFEM approach for non-Newtonian viscoplastic materials
Larese, A.
2017-01-01
This paper presents the application of a stabilized mixed Particle Finite Element Method (PFEM) to the solution of viscoplastic non-Newtonian flows. The application of the proposed model to the deformation of granular non-cohesive material is analysed. A variable yield threshold modified Bingham model is presented, using a Mohr Coulomb resistance criterion. Since the granular material is expected to undergo severe deformation, a Lagrangian approach is preferred to a fixed mesh one. PFEM i...
Accidental symmetries and the effective Lagrangian of string theory
International Nuclear Information System (INIS)
Ovrut, B.A.
1989-01-01
In this paper the relationship between accidental worldsheet symmetries of the string generating functional and target space invariance groups is discussed. Accidental symmetries are used to derive the invariance groups and effective low energy Lagrangian for the bosonic string, and the heterotic string compactified to four-dimensions on Z N orbifolds. The necessity of a new type of Green-Schwarz mechanism, associated with the auxiliary vector field in the four-dimensional N = 1 supergravity multiplet, is shown using these methods
Lagrangian measurements of sulfur dioxide to sulfate conversion rates
Energy Technology Data Exchange (ETDEWEB)
Zak, B D
1981-12-01
On the basis of Project MISTT data and proposed homogenous gas phase oxidation mechanisms for sulfur dioxide, it has been suggested that the degree of mixing with background air, the chemical composition of the background air, and the intensity of the sunlight available are key factors determining the rate of sulfur dioxide to sulfate conversion. These hypotheses are examined in light of Lagrangian measrements of conversion rates in power plant plumes made during the Tennessee Plume Study and Project Da Vinci. It is found that the Lagrangian conversion rate measurements are consistent with these hypotheses. It has also been suggested that the concentration of ozone may serve as a workable surrogate for the concentrations of the free radicals involved in the homogeneous gas phase mechanism. The night-time Lagrangian data remind one that the gross difference in mean lifetime of ozone and free radicals can lead to situations in which the ozone concentration is not a good surrogate for the free radical concentrations.
A new circulation type classification based upon Lagrangian air trajectories
Directory of Open Access Journals (Sweden)
Alexandre M. Ramos
2014-10-01
Full Text Available A new classification method of the large-scale circulation characteristic for a specific target area (NW Iberian Peninsula is presented, based on the analysis of 90-h backward trajectories arriving in this area calculated with the 3-D Lagrangian particle dispersion model FLEXPART. A cluster analysis is applied to separate the backward trajectories in up to five representative air streams for each day. Specific measures are then used to characterise the distinct air streams (e.g., curvature of the trajectories, cyclonic or anticyclonic flow, moisture evolution, origin and length of the trajectories. The robustness of the presented method is demonstrated in comparison with the Eulerian Lamb weather type classification.A case study of the 2003 heatwave is discussed in terms of the new Lagrangian circulation and the Lamb weather type classifications. It is shown that the new classification method adds valuable information about the pertinent meteorological conditions, which are missing in an Eulerian approach. The new method is climatologically evaluated for the five-year time period from December 1999 to November 2004. The ability of the method to capture the inter-seasonal circulation variability in the target region is shown. Furthermore, the multi-dimensional character of the classification is shortly discussed, in particular with respect to inter-seasonal differences. Finally, the relationship between the new Lagrangian classification and the precipitation in the target area is studied.
Lagrangian generic second order traffic flow models for node
Directory of Open Access Journals (Sweden)
Asma Khelifi
2018-02-01
Full Text Available This study sheds light on higher order macroscopic traffic flow modeling on road networks, thanks to the generic second order models (GSOM family which embeds a myriad of traffic models. It has been demonstrated that such higher order models are easily solved in Lagrangian coordinates which are compatible with both microscopic and macroscopic descriptions. The generalized GSOM model is reformulated in the Lagrangian coordinate system to develop a more efficient numerical method. The difficulty in applying this approach on networks basically resides in dealing with node dynamics. Traffic flow characteristics at node are different from that on homogeneous links. Different geometry features can lead to different critical research issues. For instance, discontinuity in traffic stream can be an important issue for traffic signal operations, while capacity drop may be crucial for lane-merges. The current paper aims to establish and analyze a new adapted node model for macroscopic traffic flow models by applying upstream and downstream boundary conditions on the Lagrangian coordinates in order to perform simulations on networks of roads, and accompanying numerical method. The internal node dynamics between upstream and downstream links are taken into account of the node model. Therefore, a numerical example is provided to underscore the efficiency of this approach. Simulations show that the discretized node model yields accurate results. Additional kinematic waves and contact discontinuities are induced by the variation of the driver attribute.
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.
Lagrangian formulation of the general relativistic Poynting-Robertson effect
De Falco, Vittorio; Battista, Emmanuele; Falanga, Maurizio
2018-04-01
We propose the Lagrangian formulation for describing the motion of a test particle in a general relativistic, stationary, and axially symmetric spacetime. The test particle is also affected by a radiation field, modeled as a coherent flux of photons traveling along the null geodesics of the background spacetime, including the general relativistic Poynting-Robertson effect. The innovative part of this work is to prove the existence of the potential linked to the dissipative action caused by the Poynting-Robertson effect in general relativity through the help of an integrating factor, depending on the energy of the system. Generally, such kinds of inverse problems involving dissipative effects might not admit a Lagrangian formulation; especially, in general relativity, there are no examples of such attempts in the literature so far. We reduce this general relativistic Lagrangian formulation to the classic case in the weak-field limit. This approach facilitates further studies in improving the treatment of the radiation field, and it contains, for example, some implications for a deeper comprehension of the gravitational waves.
Lagrangian statistics in weakly forced two-dimensional turbulence.
Rivera, Michael K; Ecke, Robert E
2016-01-01
Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.
Acoustic streaming: an arbitrary Lagrangian-Eulerian perspective.
Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco
2017-08-25
We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.
International Nuclear Information System (INIS)
Stoks, V.G.J.
1997-01-01
We present a chiral-invariant meson-baryon Lagrangian which describes the interactions of the baryon octet with the lowest-mass meson nonets. The nonlinear realization of the chiral symmetry generates pair-meson interaction vertices. The corresponding pair-meson coupling constants can all be expressed in terms of the meson-nucleon-nucleon pseudovector, scalar, and vector coupling constants, and their corresponding F/(F+D) ratios, and for which empirical estimates are given. We show that it is possible to construct an NN potential of reasonable quality satisfying these theoretical and empirical constraints. (orig.)
Ghoussoub, Nassif; Tzou, Leo
2005-01-01
Anti-selfdual Lagrangians on a state space lift to path space provided one adds a suitable selfdual boundary Lagrangian. This process can be iterated by considering the path space as a new state space for the newly obtained anti-selfdual Lagrangian. We give here two applications for these remarkable permanence properties. In the first, we establish for certain convex-concave Hamiltonians ${\\cal H}$ on a --possibly infinite dimensional--symplectic space $H^2$, the existence of a solution for t...
Near-Surface Monsoonal Circulation of the Vietnam East Sea from Lagrangian Drifters
2015-09-30
Sea from Lagrangian Drifters Luca Centurioni Scripps Institution of Oceanography 9500 Gilman Drive Mail Code 0213 La Jolla, California 92103...Contribute to the study of coastal and open ocean current systems in sparsely sampled regions such us the South China Sea (SCS), using a Lagrangian ...We intend to make new Lagrangian and Eulerian observations to measure the seasonal circulation 1) in the coastal waters of Vietnam and 2) in the SCS
Synthetic three-dimensional turbulent passive scalar fields via the minimal Lagrangian map
Rosales, Carlos
2011-07-01
A method for simple but realistic generation of three-dimensional synthetic turbulent passive scalar fields is presented. The method is an extension of the minimal turnover Lagrangian map approach (MTLM) [C. Rosales and C. Meneveau, Phys. Rev. E 78, 016313 (2008)] formulated for the generation of synthetic turbulent velocity fields. In this development, the minimal Lagrangian map is applied to deform simultaneously a vector field and an advected scalar field. This deformation takes place over a hierarchy of spatial scales encompassing a range from integral to dissipative scales. For each scale, fluid particles are mapped transporting the scalar property, without interaction or diffusional effects, from their initial configuration to new positions determined only by their velocity at the beginning of the motion and a parameter chosen to accumulate deformation for the equivalent of the phenomenological "turn-over" time scale. The procedure is studied for the case of inertial-convective regime. It is found that many features of passive scalar turbulence are well reproduced by this simple kinematical construction. Fundamental statistics of the resulting synthetic scalar fields, evaluated through the flatness and probability density functions of the scalar gradient and scalar increments, reproduce quite well the known statistical characteristics of passive scalars in turbulent fields. High-order statistics are also consistent with those observed in real hydrodynamic turbulence. The anomalous scaling of real turbulence is well reproduced for different kind of structure functions, with good quantitative agreement in general, for the scaling exponents. The spatial structure of the scalar field is also quite realistic, as well as several characteristics of the dissipation fields for the scalar variance and kinetic energy. Similarly, the statistical geometry at dissipative scales that ensues from the coupling of velocity and scalar gradients behaves in agreement with what is
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 improved Lagrangian relaxation and dual ascent approach to facility location problems
DEFF Research Database (Denmark)
Jörnsten, Kurt; Klose, Andreas
2016-01-01
not be reduced to the same extent as in the case of ordinary semi-Lagrangian relaxation. Hence, an effective method for optimizing the Lagrangian dual function is of utmost importance for obtaining a computational advantage from the simplified Lagrangian dual function. In this paper, we suggest a new dual ascent...... 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...
Dispersion upscaling from a pore scale characterization of Lagrangian velocities
Turuban, Régis; de Anna, Pietro; Jiménez-Martínez, Joaquín; Tabuteau, Hervé; Méheust, Yves; Le Borgne, Tanguy
2013-04-01
Mixing and reactive transport are primarily controlled by the interplay between diffusion, advection and reaction at pore scale. Yet, how the distribution and spatial correlation of the velocity field at pore scale impact these processes is still an open question. Here we present an experimental investigation of the distribution and correlation of pore scale velocities and its relation with upscaled dispersion. We use a quasi two-dimensional (2D) horizontal set up, consisting of two glass plates filled with cylinders representing the grains of the porous medium : the cell is built by soft lithography technique, wich allows for full control of the system geometry. The local velocity field is quantified from particle tracking velocimetry using microspheres that are advected with the pore scale flow. Their displacement is purely advective, as the particle size is chosen large enough to avoid diffusion. We thus obtain particle trajectories as well as lagrangian velocities in the entire system. The measured velocity field shows the existence of a network of preferential flow paths in channels with high velocities, as well as very low velocity in stagnation zones, with a non Gaussian distribution. Lagrangian velocities are long range correlated in time, which implies a non-fickian scaling of the longitudinal variance of particle positions. To upscale this process we develop an effective transport model, based on correlated continous time random walk, which is entirely parametrized by the pore scale velocity distribution and correlation. The model predictions are compared with conservative tracer test data for different Peclet numbers. Furthermore, we investigate the impact of different pore geometries on the distribution and correlation of Lagrangian velocities and we discuss the link between these properties and the effective dispersion behavior.
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.
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.
Lagrangian 3D tracking of fluorescent microscopic objects in motion
Darnige, T.; Figueroa-Morales, N.; Bohec, P.; Lindner, A.; Clément, E.
2016-01-01
We describe the development of a tracking device, mounted on an epi-fluorescent inverted microscope, suited to obtain time resolved 3D Lagrangian tracks of fluorescent passive or active micro-objects in micro-fluidic devices. The system is based on real-time image processing, determining the displacement of a x,y mechanical stage to keep the chosen object at a fixed position in the observation frame. The z displacement is based on the refocusing of the fluorescent object determining the displ...
N =1 Lagrangians for generalized Argyres-Douglas theories
Agarwal, Prarit; Sciarappa, Antonio; Song, Jaewon
2017-10-01
We find N = 1 Lagrangian gauge theories that flow to generalized ArgyresDouglas theories with N = 2 supersymmetry. We find that certain SU quiver gauge theories flow to generalized Argyres-Douglas theories of type ( A k-1 , A mk-1) and ( I m,km , S). We also find quiver gauge theories of SO/Sp gauge groups flowing to the ( A 2 m-1 , D 2 mk+1), ( A 2 m , D 2 m( k-1)+ k ) and D m(2 k + 2) m(2 k + 2) [ m] theories.
Uses of the chiral Lagrangian at the SSC
International Nuclear Information System (INIS)
Dawson, S.
1992-09-01
In the event that the SSC does not observe any resonances such as a Higgs boson or a techni-rho meson, we would like to know if the SSC can still discover something about the nature of the electroweak symmetry breaking. In particular, we consider the question of whether there is a ''no-lose'' corollary at the SSC. We will use chiral Lagrangian techniques to address this question and analyze their utility for studying events containing W and Z gauge bosons at the SSC
Non-linear effective Lagrangian treatment of 'Penguin' interaction
International Nuclear Information System (INIS)
Pham, T.N.
1984-01-01
Using the non-linear effective lagrangian technique, we show explicitly that only derivative coupling is allowed for the K - π, K -> 2 π and K -> 3 π transitions induced by the ΔS = 1 Penguin operator of SVZ in agreement with chiral symmetry requirements. From a derivative coupling (3, anti 3) mass term and the SU(3) breaking effect for fsub(K)/fsub(π), we estimate the strength of the Penguin interactions and find it too small to account for the ΔI = 1/2 amplitude. (orig.)
Lagrangian formulation of a consistent relativistic guiding center theory
International Nuclear Information System (INIS)
Wimmel, H.K.
1983-02-01
A new relativistic guiding center mechanics is presented that conserves energy (in time-independent fields) and satisfies a Liouville's theorem. The theory reduces to Littlejohn's theory in the non-relativistic limit and agrees to leading orders in epsilon identical rsub(g)/L with the relativistic theory by Morozov and Solov'ev (which generally lacks a Liouville's theorem). The new theory is developed from an appropriate Lagrangian and is supplemented by a collisionless relativistic kinetic equation for the guiding centers. Moment equations for guiding center density and energy density are also derived. (orig.)
Using Upper Tolerances in Lagrangian Relaxation for the DCMSTP
DEFF Research Database (Denmark)
Turkensteen, Marcel
, and if the constraint is not binding and the penalty value is positive, the penalty value is decreased. A condition for optimality is that the constraints with slack have a penalty value of zero. In Lagrangian relaxation, it generally takes a long time until the penalty values converge. Therefore, the result is often...... will contain at least d edges adjacent to the vertex. Thus, we can determine by how much the penalty values can be increased without creating both slack and a positive penalty for any constraint. Using this finding, our approach is able to obtain accurate penalty values quickly....
LAGRANGIAN MODELING OF A SUSPENDED-SEDIMENT PULSE.
Schoellhamer, David H.
1987-01-01
The one-dimensional Lagrangian Transport Model (LTM) has been applied in a quasi two-dimensional manner to simulate the transport of a slug injection of microbeads in steady experimental flows. A stationary bed segment was positioned below each parcel location to simulate temporary storage of beads on the bottom of the flume. Only one degree of freedom was available for all three bead simulations. The results show the versatility of the LTM and the ability of the LTM to accurately simulate transport of fine suspended sediment.
A Satellite-Based Lagrangian View on Phytoplankton Dynamics
Lehahn, Yoav; d'Ovidio, Francesco; Koren, Ilan
2018-01-01
The well-lit upper layer of the open ocean is a dynamical environment that hosts approximately half of global primary production. In the remote parts of this environment, distant from the coast and from the seabed, there is no obvious spatially fixed reference frame for describing the dynamics of the microscopic drifting organisms responsible for this immense production of organic matter—the phytoplankton. Thus, a natural perspective for studying phytoplankton dynamics is to follow the trajectories of water parcels in which the organisms are embedded. With the advent of satellite oceanography, this Lagrangian perspective has provided valuable information on different aspects of phytoplankton dynamics, including bloom initiation and termination, spatial distribution patterns, biodiversity, export of carbon to the deep ocean, and, more recently, bottom-up mechanisms that affect the distribution and behavior of higher-trophic-level organisms. Upcoming submesoscale-resolving satellite observations and swarms of autonomous platforms open the way to the integration of vertical dynamics into the Lagrangian view of phytoplankton dynamics.
Progress toward the effective Quantum Chromodynamic Lagrangian from symmetry considerations
International Nuclear Information System (INIS)
Salomone, A.N.
1982-01-01
The properties of an effective Lagrangian which satisfies both the axial and trace anomaly equations of Quantum Chromodynamics are investigated both from the theoretical and phenomenological points of view. The model Lagrangian requires that chiral symmetry be broken spontaneously. The non-linear approximation of the model illuminates eta-glue duality or mixing. The phase transition behavior of the model of Quantum Chromodynamics can be studied as the numbers of flavors and the vacuum angle are varied by analyzing a simple mechanical analog. The analog of the model is similar to the massive Schwinger model. The possibility of a physical scalar glue state is discussed and it is shown that it is characterized by a pronounced eta to two glue decay width. A nonperturbative Quantum Chromodynamic vacuum is seen to follow directly from satisfying the trace anomaly. The quark matter meson, eta, is at least as prominent as the glueball, iota, in the gluon dominated reaction psi to gamma plus anything. An associated large breaking of flavor SU(3) is shown to be ameliorated as the model is made more realistic by lowering scalar meson masses from infinity. The pi delta decay of the iota (1440) can be reasonably well estimated without the need of introducing any new parameters
The Gaussian streaming model and convolution Lagrangian effective field theory
Energy Technology Data Exchange (ETDEWEB)
Vlah, Zvonimir [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94306 (United States); Castorina, Emanuele; White, Martin, E-mail: zvlah@stanford.edu, E-mail: ecastorina@berkeley.edu, E-mail: mwhite@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States)
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.
A new Lagrangian method for real gases at supersonic speed
Loh, C. Y.; Liou, Meng-Sing
1992-01-01
With the renewed interest in high speed flights, the real gas effect is of theoretical as well as practical importance. In the past decade, upwind splittings or Godunov-type Riemann solutions have received tremendous attention and as a result significant progress has been made both in the ideal and non-ideal gas. In this paper, we propose a new approach that is formulated using the Lagrangian description, for the calculation of supersonic/hypersonic real gas inviscid flows. This new formulation avoids the grid generation step which is automatically obtained as the solution procedure marches in the 'time-like' direction. As a result, no remapping is required and the accuracy is faithfully maintained in the Lagrangian level. In this paper, we give numerical results for a variety of real gas problems consisting of essential elements in high speed flows, such as shock waves, expansion waves, slip surfaces and their interactions. Finally, calculations for flows in a generic inlet and nozzle are presented.
Next Generation Extended Lagrangian Quantum-based Molecular Dynamics
Negre, Christian
2017-06-01
A new framework for extended Lagrangian first-principles molecular dynamics simulations is presented, which overcomes shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while maintaining important advantages of the unified extended Lagrangian formulation of density functional theory pioneered by Car and Parrinello three decades ago. The new framework allows, for the first time, energy conserving, linear-scaling Born-Oppenheimer molecular dynamics simulations, which is necessary to study larger and more realistic systems over longer simulation times than previously possible. Expensive, self-consinstent-field optimizations are avoided and normal integration time steps of regular, direct Born-Oppenheimer molecular dynamics can be used. Linear scaling electronic structure theory is presented using a graph-based approach that is ideal for parallel calculations on hybrid computer platforms. For the first time, quantum based Born-Oppenheimer molecular dynamics simulation is becoming a practically feasible approach in simulations of +100,000 atoms-representing a competitive alternative to classical polarizable force field methods. In collaboration with: Anders Niklasson, Los Alamos National Laboratory.
A Lagrangian mixing frequency model for transported PDF modeling
Turkeri, Hasret; Zhao, Xinyu
2017-11-01
In this study, a Lagrangian mixing frequency model is proposed for molecular mixing models within the framework of transported probability density function (PDF) methods. The model is based on the dissipations of mixture fraction and progress variables obtained from Lagrangian particles in PDF methods. The new model is proposed as a remedy to the difficulty in choosing the optimal model constant parameters when using conventional mixing frequency models. The model is implemented in combination with the Interaction by exchange with the mean (IEM) mixing model. The performance of the new model is examined by performing simulations of Sandia Flame D and the turbulent premixed flame from the Cambridge stratified flame series. The simulations are performed using the pdfFOAM solver which is a LES/PDF solver developed entirely in OpenFOAM. A 16-species reduced mechanism is used to represent methane/air combustion, and in situ adaptive tabulation is employed to accelerate the finite-rate chemistry calculations. The results are compared with experimental measurements as well as with the results obtained using conventional mixing frequency models. Dynamic mixing frequencies are predicted using the new model without solving additional transport equations, and good agreement with experimental data is observed.
A few words about resonances in the electroweak effective Lagrangian
Energy Technology Data Exchange (ETDEWEB)
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.
Lagrangian Statistics and Intermittency in Gulf of Mexico.
Lin, Liru; Zhuang, Wei; Huang, Yongxiang
2017-12-12
Due to the nonlinear interaction between different flow patterns, for instance, ocean current, meso-scale eddies, waves, etc, the movement of ocean is extremely complex, where a multiscale statistics is then relevant. In this work, a high time-resolution velocity with a time step 15 minutes obtained by the Lagrangian drifter deployed in the Gulf of Mexico (GoM) from July 2012 to October 2012 is considered. The measured Lagrangian velocity correlation function shows a strong daily cycle due to the diurnal tidal cycle. The estimated Fourier power spectrum E(f) implies a dual-power-law behavior which is separated by the daily cycle. The corresponding scaling exponents are close to -1.75 and -2.75 respectively for the time scale larger (resp. 0.1 ≤ f ≤ 0.4 day -1 ) and smaller (resp. 2 ≤ f ≤ 8 day -1 ) than 1 day. A Hilbert-based approach is then applied to this data set to identify the possible multifractal property of the cascade process. The results show an intermittent dynamics for the time scale larger than 1 day, while a less intermittent dynamics for the time scale smaller than 1 day. It is speculated that the energy is partially injected via the diurnal tidal movement and then transferred to larger and small scales through a complex cascade process, which needs more studies in the near future.
Multiphase Interface Tracking with Fast Semi-Lagrangian Contouring.
Li, Xiaosheng; He, Xiaowei; Liu, Xuehui; Zhang, Jian J; Liu, Baoquan; Wu, Enhua
2016-08-01
We propose a semi-Lagrangian method for multiphase interface tracking. In contrast to previous methods, our method maintains an explicit polygonal mesh, which is reconstructed from an unsigned distance function and an indicator function, to track the interface of arbitrary number of phases. The surface mesh is reconstructed at each step using an efficient multiphase polygonization procedure with precomputed stencils while the distance and indicator function are updated with an accurate semi-Lagrangian path tracing from the meshes of the last step. Furthermore, we provide an adaptive data structure, multiphase distance tree, to accelerate the updating of both the distance function and the indicator function. In addition, the adaptive structure also enables us to contour the distance tree accurately with simple bisection techniques. The major advantage of our method is that it can easily handle topological changes without ambiguities and preserve both the sharp features and the volume well. We will evaluate its efficiency, accuracy and robustness in the results part with several examples.
The Monotonic Lagrangian Grid for Rapid Air-Traffic Evaluation
Kaplan, Carolyn; Dahm, Johann; Oran, Elaine; Alexandrov, Natalia; Boris, Jay
2010-01-01
The Air Traffic Monotonic Lagrangian Grid (ATMLG) is presented as a tool to evaluate new air traffic system concepts. The model, based on an algorithm called the Monotonic Lagrangian Grid (MLG), can quickly sort, track, and update positions of many aircraft, both on the ground (at airports) and in the air. The underlying data structure is based on the MLG, which is used for sorting and ordering positions and other data needed to describe N moving bodies and their interactions. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. Recent upgrades to ATMLG include adding blank place-holders within the MLG data structure, which makes it possible to dynamically change the MLG size and also improves the quality of the MLG grid. Additional upgrades include adding FAA flight plan data, such as way-points and arrival and departure times from the Enhanced Traffic Management System (ETMS), and combining the MLG with the state-of-the-art strategic and tactical conflict detection and resolution algorithms from the NASA-developed Stratway software. In this paper, we present results from our early efforts to couple ATMLG with the Stratway software, and we demonstrate that it can be used to quickly simulate air traffic flow for a very large ETMS dataset.
A Lagrangian dynamic subgrid-scale model turbulence
Meneveau, C.; Lund, T. S.; Cabot, W.
1994-01-01
A new formulation of the dynamic subgrid-scale model is tested in which the error associated with the Germano identity is minimized over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to flows in complex geometries that do not possess homogeneous directions. The characteristic Lagrangian time scale over which the averaging is performed is chosen such that the model is purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested successfully in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are superior to those of the plane-averaged dynamic model. The relationship between the averaged terms in the model and vortical structures (worms) that appear in the LES is investigated. Computational overhead is kept small (about 10 percent above the CPU requirements of the volume or plane-averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.
Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics.
Campos, Joventino Oliveira; Dos Santos, Rodrigo Weber; Sundnes, Joakim; Rocha, Bernardo Martins
2018-04-01
Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi-incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the numerical solution of the model. The near-incompressibility is known to cause numerical issues such as the well-known locking phenomenon and ill-conditioning of the stiffness matrix. In this work, the augmented Lagrangian method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. Numerical results of the augmented Lagrangian method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance. Copyright © 2017 John Wiley & Sons, Ltd.
A Satellite-Based Lagrangian View on Phytoplankton Dynamics.
Lehahn, Yoav; d'Ovidio, Francesco; Koren, Ilan
2018-01-03
The well-lit upper layer of the open ocean is a dynamical environment that hosts approximately half of global primary production. In the remote parts of this environment, distant from the coast and from the seabed, there is no obvious spatially fixed reference frame for describing the dynamics of the microscopic drifting organisms responsible for this immense production of organic matter-the phytoplankton. Thus, a natural perspective for studying phytoplankton dynamics is to follow the trajectories of water parcels in which the organisms are embedded. With the advent of satellite oceanography, this Lagrangian perspective has provided valuable information on different aspects of phytoplankton dynamics, including bloom initiation and termination, spatial distribution patterns, biodiversity, export of carbon to the deep ocean, and, more recently, bottom-up mechanisms that affect the distribution and behavior of higher-trophic-level organisms. Upcoming submesoscale-resolving satellite observations and swarms of autonomous platforms open the way to the integration of vertical dynamics into the Lagrangian view of phytoplankton dynamics.
Fingerprints of heavy scales in electroweak effective Lagrangians
Pich, Antonio; Rosell, Ignasi; Santos, Joaquín; Sanz-Cillero, Juan José
2017-04-01
The couplings of the electroweak effective theory contain information on the heavy-mass scales which are no-longer present in the low-energy Lagrangian. We build a general effective Lagrangian, implementing the electroweak chiral symmetry breaking SU(2) L ⊗ SU(2) R → SU(2) L+ R , which couples the known particle fields to heavier states with bosonic quantum numbers J P = 0± and 1±. We consider colour-singlet heavy fields that are in singlet or triplet representations of the electroweak group. Integrating out these heavy scales, we analyze the pattern of low-energy couplings among the light fields which are generated by the massive states. We adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs, without making any assumption about its possible doublet structure. Special attention is given to the different possible descriptions of massive spin-1 fields and the differences arising from naive implementations of these formalisms, showing their full equivalence once a proper short-distance behaviour is required.
Fingerprints of heavy scales in electroweak effective Lagrangians
Energy Technology Data Exchange (ETDEWEB)
Pich, Antonio [Departament de Física Teòrica, IFIC, Universitat de València - CSIC,Apt. Correus 22085, E-46071 València (Spain); Rosell, Ignasi [Departamento de Matemáticas, Física y Ciencias Tecnológicas,Universidad CEU Cardenal Herrera, E-46115 Alfara del Patriarca, València (Spain); Santos, Joaquín [Departament de Física Teòrica, IFIC, Universitat de València - CSIC,Apt. Correus 22085, E-46071 València (Spain); Sanz-Cillero, Juan José [Departamento de Física Teórica I, Universidad Complutense de Madrid,E-28040 Madrid (Spain)
2017-04-04
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){sub L}⊗SU(2){sub R}→SU(2){sub L+R}, which couples the known particle fields to heavier states with bosonic quantum numbers J{sup P}=0{sup ±} and 1{sup ±}. We consider colour-singlet heavy fields that are in singlet or triplet representations of the electroweak group. Integrating out these heavy scales, we analyze the pattern of low-energy couplings among the light fields which are generated by the massive states. We adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs, without making any assumption about its possible doublet structure. Special attention is given to the different possible descriptions of massive spin-1 fields and the differences arising from naive implementations of these formalisms, showing their full equivalence once a proper short-distance behaviour is required.
Nonlinear realizations and effective Lagrangian densities for nonlinear σ-models
International Nuclear Information System (INIS)
Hamilton-Charlton, Jason Dominic
2003-01-01
Nonlinear realizations of the groups SU(N), SO(m) and SO(t,s) are analysed, described by the coset spaces SU(N) / SU(N-1) x U(1), SO(m) / SO(m-1), SO(1,m-1) / SO(1,m-2) and SO(m) / SO(m-2 x SO(2). The analysis consists of determining the transformation properties of the Goldstone Bosons, constructing the most general possible Lagrangian for the realizations, and as a result identifying the coset space metric. We view the λ matrices of SU(N) as being the basis of an (N 2 - 1) dimensional real vector space, and from this we learn how to construct the basis of a Cartan Subspace associated with a vector. This results in a mathematical structure which allows us to find expressions for coset representative elements used in the analysis. This structure is not only relevant to SU(N) breaking models, but may also be used to find results in SO(m) and SO(1,m - 1) breaking models. (author)
Relativistic particle dynamics: Lagrangian proof of the no-interaction theorem
International Nuclear Information System (INIS)
Marmo, G.; Mukunda, N.; Sudarshan, E.C.G.
1983-11-01
An economical proof is given, in the Lagrangian framework, of the No Interaction Theorem of relativistic particle mechanics. It is based on the assumption that there is a Lagrangian, which if singular is allowed to lead at most to primary first class constraints. The proof works with Lagrange rather than Poisson brackets, leading to considerable simplifications compared to other proofs
Schroeder, Craig; Zheng, Wen; Fedkiw, Ronald
2012-01-01
-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
Ćaǧatay Uçgun, Filiz; Esen, Oǧul; Gümral, Hasan
2018-01-01
We present Skinner-Rusk and Hamiltonian formalisms of second order degenerate Clément and Sarıoğlu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed to obtain Hamiltonian realizations of Lagrangian theories. The Gotay-Nester-Hinds algorithm is used to investigate Skinner-Rusk formalisms of these systems.
Syed, H.A.M.S.; Primeau, F.W.; Deleersnijder, E.L.C.; Heemink, A.W.
2017-01-01
Lagrangian forward and backward models are introduced into a coarse-grid ocean global circulation model to trace the ventilation routes of the deep North Pacific Ocean. The random walk aspect in the Lagrangian model is dictated by a rotated isopycnal diffusivity tensor in the circulation model,
Lagrangian and Hamiltonian Formulation of Transmission Line Systems with Boundary Energy Flow
Jeltsema, Dimitri; Schaft, Arjan J. van der
The classical Lagrangian and Hamiltonian formulation of an electrical transmission line is reviewed and extended to allow for varying boundary conditions, The method is based on the definition of an infinite-dimensional analogue of the affine Lagrangian and Hamiltonian input-output systems
Lagrangian viscoelastic flow computations using a generalized molecular stress function model
DEFF Research Database (Denmark)
Rasmussen, Henrik K.
2002-01-01
A new finite 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 represents a further development of the 3D Lagrangian integral method (3D-LIM) from a Rivlin...
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
Benzi, R.; Biferale, L.; Fisher, R.T.; Lamb, D.Q.; Toschi, F.
2009-01-01
We report a detailed study of Eulerian and Lagrangian statistics from high resolution Direct Numerical Simulations of isotropic weakly compressible turbulence. Reynolds number at the Taylor microscale is estimated to be around 600. Eulerian and Lagrangian statistics is evaluated over a huge data
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.
A new method to calibrate Lagrangian model with ASAR images for oil slick trajectory.
Tian, Siyu; Huang, Xiaoxia; Li, Hongga
2017-03-15
Since Lagrangian model coefficients vary with different conditions, it is necessary to calibrate the model to obtain optimal coefficient combination for special oil spill accident. This paper focuses on proposing a new method to calibrate Lagrangian model with time series of Envisat ASAR images. Oil slicks extracted from time series images form a detected trajectory of special oil slick. Lagrangian model is calibrated by minimizing the difference between simulated trajectory and detected trajectory. mean center position distance difference (MCPD) and rotation difference (RD) of Oil slicks' or particles' standard deviational ellipses (SDEs) are calculated as two evaluations. The two parameters are taken to evaluate the performance of Lagrangian transport model with different coefficient combinations. This method is applied to Penglai 19-3 oil spill accident. The simulation result with calibrated model agrees well with related satellite observations. It is suggested the new method is effective to calibrate Lagrangian model. Copyright © 2016 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Amitava Choudhuri; Subrata Ghosh; Talukdar, B.
2011-01-01
We identify two alternative Lagrangian representations for the damped harmonic oscillator characterised by a frictional coefficient γ. The first one is explicitly time independent while the second one involves time parameter explicitly. With separate attention to both Lagrangians we make use of the Noether theorem to compute the variational symmetries and conservation laws in order to study how association between them changes as one goes from one representation to the other. In the case of time independent representation squeezing symmetry leads to conservation of angular momentum for γ = 0, while for the time-dependent Lagrangian the same conserved quantity results from rotational invariance. The Lie algebra (g) of the symmetry vectors that leaves the action corresponding to the time-independent Lagrangian invariant is semi-simple. On the other hand, g is only a simple Lie algebra for the action characterised by the time-dependent Lagrangian. (authors)
Bustamante, M D
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 show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, 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 integrability. In particular, w...
Energy Technology Data Exchange (ETDEWEB)
Bustamante, Miguel D [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile (Chile); Hojman, Sergio A [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile (Chile)
2003-01-10
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 show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behaviour has not been verified up to now. The Euler-Lagrange equations we get for these systems usually present 'time reparametrization' invariance, 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 integrability. In particular, we show that the so-called ABC system is completely integrable if it possesses one constant of the motion.
Lagrangian 3D tracking of fluorescent microscopic objects in motion
Darnige, T.; Figueroa-Morales, N.; Bohec, P.; Lindner, A.; Clément, E.
2017-05-01
We describe the development of a tracking device, mounted on an epi-fluorescent inverted microscope, suited to obtain time resolved 3D Lagrangian tracks of fluorescent passive or active micro-objects in microfluidic devices. The system is based on real-time image processing, determining the displacement of a x, y mechanical stage to keep the chosen object at a fixed position in the observation frame. The z displacement is based on the refocusing of the fluorescent object determining the displacement of a piezo mover keeping the moving object in focus. Track coordinates of the object with respect to the microfluidic device as well as images of the object are obtained at a frequency of several tenths of Hertz. This device is particularly well adapted to obtain trajectories of motile micro-organisms in microfluidic devices with or without flow.
Directory of Open Access Journals (Sweden)
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.
An augmented Lagrangian multi-scale dictionary learning algorithm
Directory of Open Access Journals (Sweden)
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.
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
Conformal, Riemannian and Lagrangian geometry the 2000 Barrett lectures
Chang, Sun-Yung A; Grove, Karsten; Yang, Paul C; Freire, Alexandre
2002-01-01
Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactifications of manifolds and on Yamabe-type variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially in connection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus...
Collision avoidance for multiple Lagrangian dynamical systems with gyroscopic forces
Directory of Open Access Journals (Sweden)
Lorenzo Sabattini
2017-01-01
Full Text Available This article introduces a novel methodology for dealing with collision avoidance for groups of mobile robots. In particular, full dynamics are considered, since each robot is modeled as a Lagrangian dynamical system moving in a three-dimensional environment. Gyroscopic forces are utilized for defining the collision avoidance control strategy: This kind of forces leads to avoiding collisions, without interfering with the convergence properties of the multi-robot system’s desired control law. Collision avoidance introduces, in fact, a perturbation on the nominal behavior of the system: We define a method for choosing the direction of the gyroscopic force in an optimal manner, in such a way that perturbation is minimized. Collision avoidance and convergence properties are analytically demonstrated, and simulation results are provided for validation purpose.
The canonical Lagrangian approach to three-space general relativity
Shyam, Vasudev; Venkatesh, Madhavan
2013-07-01
We study the action for the three-space formalism of general relativity, better known as the Barbour-Foster-Ó Murchadha action, which is a square-root Baierlein-Sharp-Wheeler action. In particular, we explore the (pre)symplectic structure by pulling it back via a Legendre map to the tangent bundle of the configuration space of this action. With it we attain the canonical Lagrangian vector field which generates the gauge transformations (3-diffeomorphisms) and the true physical evolution of the system. This vector field encapsulates all the dynamics of the system. We also discuss briefly the observables and perennials for this theory. We then present a symplectic reduction of the constrained phase space.
Numerical methods for Lagrangian hydrodynamics applied to inertial fusion
International Nuclear Information System (INIS)
Maire, P.H.; Breil, J.; Galera, S.; Schurtz, G.
2009-01-01
CHIC is a code of Lagrangian hydrodynamics and implosion that has been developed since 2003 for the simulation of plasma experiments concerning inertial fusion. The transport of electron energy is assured with the Spitzer-Harm diffusion model with flux limiter. The propagation of the laser beams inside the plasma is computed by an algorithm of 3-dimensional beam launching that takes into account refraction as well as collisional absorption. The self-generated transverse magnetic fields are assessed by a magnetohydrodynamics model that stems from a generalized Ohm's law. The coupling with electron energy transport is assured with Braginskii conduction model. The validation of this code has been performed with various plasma experiments. (A.C.)
A Lagrangian meshfree method applied to linear and nonlinear elasticity.
Walker, Wade A
2017-01-01
The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.
Lagrangian investigations of vorticity dynamics in compressible turbulence
Parashar, Nishant; Sinha, Sawan Suman; Danish, Mohammad; Srinivasan, Balaji
2017-10-01
In this work, we investigate the influence of compressibility on vorticity-strain rate dynamics. Well-resolved direct numerical simulations of compressible homogeneous isotropic turbulence performed over a cubical domain of 10243 are employed for this study. To clearly identify the influence of compressibility on the time-dependent dynamics (rather than on the one-time flow field), we employ a well-validated Lagrangian particle tracker. The tracker is used to obtain time correlations between the instantaneous vorticity vector and the strain-rate eigenvector system of an appropriately chosen reference time. In this work, compressibility is parameterized in terms of both global (turbulent Mach number) and local parameters (normalized dilatation-rate and flow field topology). Our investigations reveal that the local dilatation rate significantly influences these statistics. In turn, this observed influence of the dilatation rate is predominantly associated with rotation dominated topologies (unstable-focus-compressing, stable-focus-stretching). We find that an enhanced dilatation rate (in both contracting and expanding fluid elements) significantly enhances the tendency of the vorticity vector to align with the largest eigenvector of the strain-rate. Further, in fluid particles where the vorticity vector is maximally misaligned (perpendicular) at the reference time, vorticity does show a substantial tendency to align with the intermediate eigenvector as well. The authors make an attempt to provide physical explanations of these observations (in terms of moment of inertia and angular momentum) by performing detailed calculations following tetrads {approach of Chertkov et al. ["Lagrangian tetrad dynamics and the phenomenology of turbulence," Phys. Fluids 11(8), 2394-2410 (1999)] and Xu et al. ["The pirouette effect in turbulent flows," Nat. Phys. 7(9), 709-712 (2011)]} in a compressible flow field.
Atmospheric rivers moisture transport from a Lagrangian perspective
Ramos, A. M.; Nieto, R.; Tomé, R.; Gimeno, L.; Trigo, R. M.; Liberato, M. L. R.; Lavers, D. A.
2015-12-01
An automated atmospheric rivers (ARs) detection algorithm is used for the North Atlantic Ocean Basin allowing the identification of the major ARs that affected western European coasts between 1979 and 2014 over the winter half-year (October to March). The entire west coast of Europe was divided into five domains, namely, the Iberian Peninsula (9.75° W; 36-43.75° N), France (4.5° W; 43.75-50° N), UK (4.5° W; 50-59° N), southern Scandinavia and the Netherlands (5.25° E; 50-59° N), and northern Scandinavia (5.25° E; 59-70° N). Following the identification of the main ARs that made landfall in western Europe, a Lagrangian analysis was then applied in order to identify the main sources of moisture that reach each domain. The Lagrangian dataset used was obtained from the FLEXPART model global simulation from 1979 to 2012, where the atmosphere was divided into approximately 2.0 million parcels, and it was forced by ERA-Interim reanalysis on a 1° latitude-longitude grid. Results show that, in general, for all regions considered, the major climatological source of moisture extends along the subtropical North Atlantic, from the Florida Peninsula (northward of 20° N), to each sink region, with the nearest coast to each sink region always appearing as a local maximum of evaporation. In addition, during the AR events, the Atlantic subtropical source is reinforced and displaced, with a slight northward movement of the moisture sources is found when the sink region is positioned at higher latitudes. In conclusion, the results confirm the advection of moisture linked to ARs from subtropical ocean areas, but also the existence of a tropical one, and the mid-latitude sources further the analysed longitude along the North Atlantic is located eastward.
L-GRAAL: Lagrangian graphlet-based network aligner.
Malod-Dognin, Noël; Pržulj, Nataša
2015-07-01
Discovering and understanding patterns in networks of protein-protein interactions (PPIs) is a central problem in systems biology. Alignments between these networks aid functional understanding as they uncover important information, such as evolutionary conserved pathways, protein complexes and functional orthologs. A few methods have been proposed for global PPI network alignments, but because of NP-completeness of underlying sub-graph isomorphism problem, producing topologically and biologically accurate alignments remains a challenge. We introduce a novel global network alignment tool, Lagrangian GRAphlet-based ALigner (L-GRAAL), which directly optimizes both the protein and the interaction functional conservations, using a novel alignment search heuristic based on integer programming and Lagrangian relaxation. We compare L-GRAAL with the state-of-the-art network aligners on the largest available PPI networks from BioGRID and observe that L-GRAAL uncovers the largest common sub-graphs between the networks, as measured by edge-correctness and symmetric sub-structures scores, which allow transferring more functional information across networks. We assess the biological quality of the protein mappings using the semantic similarity of their Gene Ontology annotations and observe that L-GRAAL best uncovers functionally conserved proteins. Furthermore, we introduce for the first time a measure of the semantic similarity of the mapped interactions and show that L-GRAAL also uncovers best functionally conserved interactions. In addition, we illustrate on the PPI networks of baker's yeast and human the ability of L-GRAAL to predict new PPIs. Finally, L-GRAAL's results are the first to show that topological information is more important than sequence information for uncovering functionally conserved interactions. L-GRAAL is coded in C++. Software is available at: http://bio-nets.doc.ic.ac.uk/L-GRAAL/. n.malod-dognin@imperial.ac.uk Supplementary data are available at
Lagrangian mixed layer modeling of the western equatorial Pacific
Shinoda, Toshiaki; Lukas, Roger
1995-01-01
Processes that control the upper ocean thermohaline structure in the western equatorial Pacific are examined using a Lagrangian mixed layer model. The one-dimensional bulk mixed layer model of Garwood (1977) is integrated along the trajectories derived from a nonlinear 1 1/2 layer reduced gravity model forced with actual wind fields. The Global Precipitation Climatology Project (GPCP) data are used to estimate surface freshwater fluxes for the mixed layer model. The wind stress data which forced the 1 1/2 layer model are used for the mixed layer model. The model was run for the period 1987-1988. This simple model is able to simulate the isothermal layer below the mixed layer in the western Pacific warm pool and its variation. The subduction mechanism hypothesized by Lukas and Lindstrom (1991) is evident in the model results. During periods of strong South Equatorial Current, the warm and salty mixed layer waters in the central Pacific are subducted below the fresh shallow mixed layer in the western Pacific. However, this subduction mechanism is not evident when upwelling Rossby waves reach the western equatorial Pacific or when a prominent deepening of the mixed layer occurs in the western equatorial Pacific or when a prominent deepening of the mixed layer occurs in the western equatorial Pacific due to episodes of strong wind and light precipitation associated with the El Nino-Southern Oscillation. Comparison of the results between the Lagrangian mixed layer model and a locally forced Eulerian mixed layer model indicated that horizontal advection of salty waters from the central Pacific strongly affects the upper ocean salinity variation in the western Pacific, and that this advection is necessary to maintain the upper ocean thermohaline structure in this region.
Rossi, V.; Dubois, M.; Ser-Giacomi, E.; Monroy, P.; Lopez, C.; Hernandez-Garcia, E.
2016-02-01
Assessing the spatial structure and dynamics of marine populations is still a major challenge for ecologists. The necessity to manage marine resources from a large-scale perspective and considering the whole ecosystem is now recognized but the absence of appropriate tools to address these objectives limits the implementation of globally pertinent conservation planning. Inspired from Network Theory, we present a new methodological framework called Lagrangian Flow Network which allows a systematic characterization of multi-scale dispersal and connectivity of early life history stages of marine organisms. The network is constructed by subdividing the basin into an ensemble of equal-area subregions which are interconnected through the transport of propagules by ocean currents. The present version allows the identification of hydrodynamical provinces and the computation of various connectivity proxies measuring retention and exchange of larvae. Due to our spatial discretization and subsequent network representation, as well as our Lagrangian approach, further methodological improvements are handily accessible. These future developments include a parametrization of habitat patchiness, the implementation of realistic larval traits and the consideration of abiotic variables (e.g. temperature, salinity, planktonic resources...) and their effects on larval production and survival. While the model is potentially tunable to any species whose biological traits and ecological preferences are precisely known, it can also be used in a more generic configuration by efficient computing and analysis of a large number of experiments with relevant ecological parameters. It permits a better characterization of population connectivity at multiple scales and it informs its ecological and managerial interpretations.
An online-coupled NWP/ACT model with conserved Lagrangian levels
Sørensen, B.; Kaas, E.; Lauritzen, P. H.
2012-04-01
Numerical weather and climate modelling is under constant development. Semi-implicit semi-Lagrangian (SISL) models have proven to be numerically efficient in both short-range weather forecasts and climate models, due to the ability to use long time steps. Chemical/aerosol feedback mechanism are becoming more and more relevant in NWP as well as climate models, since the biogenic and anthropogenic emissions can have a direct effect on the dynamics and radiative properties of the atmosphere. To include chemical feedback mechanisms in the NWP models, on-line coupling is crucial. In 3D semi-Lagrangian schemes with quasi-Lagrangian vertical coordinates the Lagrangian levels are remapped to Eulerian model levels each time step. This remapping introduces an undesirable tendency to smooth sharp gradients and creates unphysical numerical diffusion in the vertical distribution. A semi-Lagrangian advection method is introduced, it combines an inherently mass conserving 2D semi-Lagrangian scheme, with a SISL scheme employing both hybrid vertical coordinates and a fully Lagrangian vertical coordinate. This minimizes the vertical diffusion and thus potentially improves the simulation of the vertical profiles of moisture, clouds, and chemical constituents. Since the Lagrangian levels suffer from traditional Lagrangian limitations caused by the convergence and divergence of the flow, remappings to the Eulerian model levels are generally still required - but this need only be applied after a number of time steps - unless dynamic remapping methods are used. For this several different remapping methods has been implemented. The combined scheme is mass conserving, consistent, and multi-tracer efficient.
A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics
Directory of Open Access Journals (Sweden)
E. Kaas
2013-11-01
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.
International Nuclear Information System (INIS)
Loubere, Raphael; Maire, Pierre-Henri; Vachal, Pavel
2013-01-01
The aim of the present work is the 3D extension of a general formalism to derive a staggered discretization for Lagrangian hydrodynamics on unstructured grids. The classical compatible discretization is used; namely, momentum equation is discretized using the fundamental concept of subcell forces. Specific internal energy equation is obtained using total energy conservation. The subcell force is derived by invoking the Galilean invariance and thermodynamic consistency. A general form of the subcell force is provided so that a cell entropy inequality is satisfied. The subcell force consists of a classical pressure term plus a tensorial viscous contribution proportional to the difference between the node velocity and the cell-centered velocity. This cell-centered velocity is an extra degree of freedom solved with a cell-centered approximate Riemann solver. The second law of thermodynamics is satisfied by construction of the local positive definite subcell tensor involved in the viscous term. A particular expression of this tensor is proposed. A more accurate extension of this discretization both in time and space is also provided using a piecewise linear reconstruction of the velocity field and a predictor-corrector time discretization. Numerical tests are presented in order to assess the efficiency of this approach in 3D. Sanity checks show that the 3D extension of the 2D approach reproduces 1D and 2D results. Finally, 3D problems such as Sedov, Noh, and Saltzman are simulated. (authors)
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-Hamiltonian unified formalism for autonomous higher order dynamical systems
International Nuclear Information System (INIS)
Prieto-Martinez, Pedro Daniel; Roman-Roy, Narciso
2011-01-01
The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view. (paper)
Leading-order classical Lagrangians for the nonminimal standard-model extension
Reis, J. A. A. S.; Schreck, M.
2018-03-01
In this paper, we derive the general leading-order classical Lagrangian covering all fermion operators of the nonminimal standard-model extension (SME). Such a Lagrangian is considered to be the point-particle analog of the effective field theory description of Lorentz violation that is provided by the SME. At leading order in Lorentz violation, the Lagrangian obtained satisfies the set of five nonlinear equations that govern the map from the field theory to the classical description. This result can be of use for phenomenological studies of classical bodies in gravitational fields.
Development of a multimaterial, two-dimensional, arbitrary Lagrangian-Eulerian mesh computer program
International Nuclear Information System (INIS)
Barton, R.T.
1982-01-01
We have developed a large, multimaterial, two-dimensional Arbitrary Lagrangian-Eulerian (ALE) computer program. The special feature of an ALE mesh is that it can be either an embedded Lagrangian mesh, a fixed Eulerian mesh, or a partially embedded, partially remapped mesh. Remapping is used to remove Lagrangian mesh distortion. This general purpose program has been used for astrophysical modeling, under the guidance of James R. Wilson. The rationale behind the development of this program will be used to highlight several important issues in program design
Augmented Lagrangian for shallow viscoplastic flow with topography
Ionescu, Ioan R.
2013-06-01
In this paper we have developed a robust numerical algorithm for the visco-plastic Saint-Venant model with topography. For the time discretization an implicit (backward) Euler scheme was used. To solve the resulting nonlinear equations, a four steps iterative algorithm was proposed. To handle the non-differentiability of the plastic terms an iterative decomposition-coordination formulation coupled with the augmented Lagrangian method was adopted. The proposed algorithm is consistent, i.e. if the convergence is achieved then the iterative solution satisfies the nonlinear system at each time iteration. The equations for the velocity field are discretized using the finite element method, while a discontinuous Galerkin method, with an upwind choice of the flux, is adopted for solving the hyperbolic equations that describe the evolution of the thickness. The algorithm permits to solve alternatively, at each iteration, the equations for the velocity field and for the thickness. The iterative decomposition coordination formulation coupled with the augmented Lagrangian method works very well and no instabilities are present. The proposed algorithm has a very good convergence rate, with the exception of large Reynolds numbers (Re≫1000), not involved in the applications concerned by the shallow viscoplastic model. The discontinuous Galerkin technique assure the mass conservation of the shallow system. The model has the exact C-property for a plane bottom and an asymptotic C-property for a general topography. Some boundary value problems were selected to analyze the robustness of the numerical algorithm and the predictive capabilities of the mechanical model. The comparison with an exact rigid flow solution illustrates the accuracy of the numerical scheme in handling the non-differentiability of the plastic terms. The influence of the mesh and of the time step are investigated for the flow of a Bingham fluid in a talweg. The role of the material cohesion in stopping a
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean.
Beron-Vera, Francisco J; Olascoaga, María J; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan
2015-08-01
Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.
Kuhn, Alexander; Engelke, Wito; Rö ssl, Christian; Hadwiger, Markus; Theisel, Holger
2013-01-01
of given particle trajectories and without additional flow map derivatives. We demonstrate its application for a set of computational fluid dynamic examples, as well as trajectories acquired by Lagrangian methods, and discuss its benefits and limitations
A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
Li, Wenliang
2018-04-01
We propose a framework for Lorentz-invariant Lagrangian field theories where Ostrogradsky's scalar ghosts could be absent. A key ingredient is the generalized Kronecker delta. The general Lagrangians are reformulated in the language of differential forms. The absence of higher order equations of motion for the scalar modes stems from the basic fact that every exact form is closed. The well-established Lagrangian theories for spin-0, spin-1, p-form, spin-2 fields have natural formulations in this framework. We also propose novel building blocks for Lagrangian field theories. Some of them are novel nonlinear derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar ghosts are absent in these fully nonlinear theories.
Comment on ''Canonical formalism for Lagrangians with nonlocality of finite extent''
International Nuclear Information System (INIS)
Llosa, Josep
2003-01-01
The paper by Woodward [Phys. Rev. A 62, 052105 (2000)] claimed to have proved that Lagrangian theories with a nonlocality of finite extent are necessarily unstable. In this Comment we propose that this conclusion is false
Extension of the chiral perturbation theory meson Lagrangian to order p{sup 6}
Energy Technology Data Exchange (ETDEWEB)
Fearing, H W; Scherer, S
1994-08-01
We have derived the most general chirally invariant Lagrangian L{sub 6} for the meson sector at order p{sup 6}. The result provides an extension of the standard Gasser-Leutwyler Lagrangian L{sub 4} to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the derivation was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The equation of motion terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating p{sup 6} contributions to simple processes. (author). 53 refs., 10 tabs.
Heuristic approach to Satellite Range Scheduling with Bounds using Lagrangian Relaxation.
Energy Technology Data Exchange (ETDEWEB)
Brown, Nathanael J. K.; Arguello, Bryan; Nozick, Linda Karen; Xu, Ningxiong [Cornell
2017-03-01
This paper focuses on scheduling antennas to track satellites using a heuristic method. In order to validate the performance of the heuristic, bounds are developed using Lagrangian relaxation. The performance of the algorithm is established using several illustrative problems.
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.
Attili, Antonio; Bisetti, Fabrizio
2013-01-01
. 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
International Nuclear Information System (INIS)
Gogala, B.
1983-01-01
The equations of the gauge theory of gravitation are derived from a complex quadratic Lagrangian with torsion. The derivation is performed in a coordinate basis in a completely covariant way. (author)
Extension of the renormalizability criterion to the case of arbitrary unperturbed Lagrangian
International Nuclear Information System (INIS)
Grozin, A.G.
1979-01-01
Extension of the renormalizability criterium of the perturbation theory is generalized in the case, when an unperturbed lagrangian is not a lagrangian of free fields L 0 . The derivating functional of the Green function, written in the form of a function integral is disintegrated by the perturbed lagrangian L 1 when building the perturbation theory. Described are ultraviolet divergences and possibilities of their elimination in eucledian space. The criterion permits to state extension renormalizability of the perturbation theory for eVery point L 0 and the direction L 1 assigned in this point in linear space of different lagrangians. According to the Weinberg theorem the grade asymptotics of Green functions is not changed at slight shift from the initial point in the supernormalized direction. For any point and any direction the extension of the perturbation theory is supernormalized in this space
Collaborative Research: Lagrangian Modeling of Dispersion in the Planetary Boundary Layer
National Research Council Canada - National Science Library
Weil, Jeffrey
2003-01-01
...), using Lagrangian "particle" models coupled with large-eddy simulation (LES) fields. A one-particle model for the mean concentration field was enhanced by a theoretically improved treatment of the LES subgrid-scale (SGS) velocities...
Further Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions
Directory of Open Access Journals (Sweden)
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.
Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...
Lagrangian Assimilation of Satellite Data for Climate Studies in the Arctic
Lindsay, Ronald W.; Zhang, Jin-Lun; Stern, Harry
2004-01-01
Under this grant we have developed and tested a new Lagrangian model of sea ice. A Lagrangian model keeps track of material parcels as they drift in the model domain. Besides providing a natural framework for the assimilation of Lagrangian data, it has other advantages: 1) a model that follows material elements is well suited for a medium such as sea ice in which an element retains its identity for a long period of time; 2) model cells can be added or dropped as needed, allowing the spatial resolution to be increased in areas of high variability or dense observations; 3) ice from particular regions, such as the marginal seas, can be marked and traced for a long time; and 4) slip lines in the ice motion are accommodated more naturally because there is no internal grid. Our work makes use of these strengths of the Lagrangian formulation.
National Research Council Canada - National Science Library
Shao, Y
2004-01-01
Lagrangian Stochastic (LS) particle models have proven to be a useful computational tool for the description and prediction of dispersion of pollutant releases in complex meteorological situations (e.g...
AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...
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.
Lagrangian Description of Nonadiabatic Particle Motion in Spherical Tori
Energy Technology Data Exchange (ETDEWEB)
R.B. White; Yu.V. Yakovenko; Ya.I. Kolesnichenko
2002-06-21
The ability of a device to provide adiabatic motion of charged particles is crucial for magnetic confinement. As the magnetic field in the present-day spherical tori, e.g., MAST and NSTX, is much lower than in the conventional tokamaks, effects of the finite Larmor radius (FLR) on the motion of fast ions are of importance in these devices, affecting the stochasticity threshold for the interaction of the ions with electromagnetic perturbations. In addition, FLR by itself may result in non-conservation (jumps) of the magnetic moment of particles [4]. In this work we propose a Lagrangian approach to description of the resonant collisionless motion of charged particles under a perturbation, allowing for FLR. The work generalizes results of Ref. [1], where only time-independent perturbations were considered. The approach is used to find the stochasticity thresholds for the Goldston-White-Boozer (GWB) diffusion [2] and the cyclotron-resonance-induced (CRI) diffusion (for the case of the firs t cyclotron resonance, the latter was discovered in Ref. [3]). In addition, a new expression for the magnetic moment variation caused by FLR is found.
Dynamic isoperimetry and the geometry of Lagrangian coherent structures
International Nuclear Information System (INIS)
Froyland, Gary
2015-01-01
The study of transport and mixing processes in dynamical systems is particularly important for the analysis of mathematical models of physical systems. We propose a novel, direct geometric method to identify subsets of phase space that remain strongly coherent over a finite time duration. This new method is based on a dynamic extension of classical (static) isoperimetric problems; the latter are concerned with identifying submanifolds with the smallest boundary size relative to their volume.The present work introduces dynamic isoperimetric problems; the study of sets with small boundary size relative to volume as they are evolved by a general dynamical system. We formulate and prove dynamic versions of the fundamental (static) isoperimetric (in)equalities; a dynamic Federer–Fleming theorem and a dynamic Cheeger inequality. We introduce a new dynamic Laplace operator and describe a computational method to identify coherent sets based on eigenfunctions of the dynamic Laplacian.Our results include formal mathematical statements concerning geometric properties of finite-time coherent sets, whose boundaries can be regarded as Lagrangian coherent structures. The computational advantages of our new approach are a well-separated spectrum for the dynamic Laplacian, and flexibility in appropriate numerical approximation methods. Finally, we demonstrate that the dynamic Laplace operator can be realised as a zero-diffusion limit of a newly advanced probabilistic transfer operator method [9] for finding coherent sets, which is based on small diffusion. Thus, the present approach sits naturally alongside the probabilistic approach [9], and adds a formal geometric interpretation. (paper)
MESOILT2, a Lagrangian trajectory climatological dispersion model
International Nuclear Information System (INIS)
Ramsdell, J.V. Jr.; Burk, K.W.
1991-03-01
The objective of the Hanford Environmental Dose Reconstruction (HEDR) Project is to estimate the radiation dose that individuals could have received as a result of emissions from nuclear operations at the Hanford Site. An independent Technical Steering Panel (TSP) directs the project, which is conducted by the Pacific Northwest Laboratory (PNL). The TSP directed PNL to demonstrate that its recommended approach for dose reconstruction is technically feasible and practical. This demonstration was Phase 1 of the project. This report is specifically concerned with the approach that PNL recommends for dealing with the atmospheric pathway. The TSP established a model domain for the atmospheric pathway for Phase 1 that includes 10 counties in Washington and Oregon and covers several thousand square miles. It is unrealistic to assume that atmospheric models which estimate transport and diffusion based on the meteorological conditions near the point of release of material at the time of release are adequate for a region this large. As a result, PNL recommended use of a Lagrangian trajectory, puff dispersion model for the Phase I study. This report describes the MESOILT2 computer code and the atmospheric transport, diffusion, deposition, and depletion models used in Phase I. The contents of the report include a technical description of the models, a user's guide for the codes, and descriptions of the individual code elements. 53 refs., 17 figs., 5 tabs
Lagrangian speckle model and tissue-motion estimation--theory.
Maurice, R L; Bertrand, M
1999-07-01
It is known that when a tissue is subjected to movements such as rotation, shearing, scaling, etc., changes in speckle patterns that result act as a noise source, often responsible for most of the displacement-estimate variance. From a modeling point of view, these changes can be thought of as resulting from two mechanisms: one is the motion of the speckles and the other, the alterations of their morphology. In this paper, we propose a new tissue-motion estimator to counteract these speckle decorrelation effects. The estimator is based on a Lagrangian description of the speckle motion. This description allows us to follow local characteristics of the speckle field as if they were a material property. This method leads to an analytical description of the decorrelation in a way which enables the derivation of an appropriate inverse filter for speckle restoration. The filter is appropriate for linear geometrical transformation of the scattering function (LT), i.e., a constant-strain region of interest (ROI). As the LT itself is a parameter of the filter, a tissue-motion estimator can be formulated as a nonlinear minimization problem, seeking the best match between the pre-tissue-motion image and a restored-speckle post-motion image. The method is tested, using simulated radio-frequency (RF) images of tissue undergoing axial shear.
International Nuclear Information System (INIS)
Oliphant, T.A.; Morel, J.E.; Gula, W.P.; Pfeufer, G.W.
1997-01-01
The cell-centered diffusion differencing scheme presented by Morel et al. has been applied to magnetic diffusion associated with Lagrangian hydrodynamic codes. Thus, the method applies to non-orthogonal meshes. Although the present application involves structured meshes, the method applies equally well to unstructured meshes. Morel's example of application is to 2D diffusion using Ficke's law. Thus, a volume integral approach is applied to the divergence operator. In 2D magnetic diffusion symmetry allows the use of an area integral approach involving the field components normal to the area, e.g. A-theta and B-theta. Instead of a divergence of a term proportional to the field gradient a curl of a term proportional to the curl of the field is used. An essential fact that allows this procedure is that the solenoidal property of the magnetic field is automatic. In the case of 3D it is necessary to return to the volumetric integral approach and to use rectangular components of the vector potential. Successful benchmarks have been run in comparison with the 1D code RAVEN. A typical example is that of a metal cylinder being compressed by a magnetic field applied at the outer boundary. So far, the 3D diffusion model has been tested in the orthogonal case and found to preserve the linear, homogeneous solution. Results of these and further tests are presented
A multivector derivative approach to Lagrangian field theory
International Nuclear Information System (INIS)
Lasenby, A.; Gull, S.; Doran, C.
1993-01-01
A new calculus, based upon the multivector derivative, is developed for Lagrangian mechanics and field theory, providing streamlined and rigorous derivations of the Euler-Lagrange equations. A more general form of Noether's theorem is found which is appropriate to both discrete and continuous symmetries. This is used to find the conjugate currents of the Dirac theory, where it improves on techniques previously used for analyses of local observables. General formulas for the canonical stress-energy and angular-momentum tensors are derived, with spinors and vectors treated in a unified way. It is demonstrated that the antisymmetric terms in the stress-energy tensor are crucial to the correct treatment of angular momentum. The multivector derivative is extended to provide a functional calculus for linear functions which is more compact and more powerful than previous formalisms. This is demonstrated in a reformulation of the functional derivative with respect to the metric, which is then used to recover the full canonical stress-energy tensor. Unlike conventional formalisms, which result in a symmetric stress-energy tensor, this reformulation retains the potentially important antisymmetric contribution. 23 refs
Phenomenology of the Higgs effective Lagrangian via FEYNRULES
International Nuclear Information System (INIS)
Alloul, Adam; Fuks, Benjamin; 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-Higgs production. We finally study contact interactions of gauge and Higgs bosons to fermions
Phenomenology of the Higgs effective Lagrangian via FEYNRULES
Energy Technology Data Exchange (ETDEWEB)
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-...
Parallel MR image reconstruction using augmented Lagrangian methods.
Ramani, Sathish; Fessler, Jeffrey A
2011-03-01
Magnetic resonance image (MRI) reconstruction using SENSitivity Encoding (SENSE) requires regularization to suppress noise and aliasing effects. Edge-preserving and sparsity-based regularization criteria can improve image quality, but they demand computation-intensive nonlinear optimization. In this paper, we present novel methods for regularized MRI reconstruction from undersampled sensitivity encoded data--SENSE-reconstruction--using the augmented Lagrangian (AL) framework for solving large-scale constrained optimization problems. We first formulate regularized SENSE-reconstruction as an unconstrained optimization task and then convert it to a set of (equivalent) constrained problems using variable splitting. We then attack these constrained versions in an AL framework using an alternating minimization method, leading to algorithms that can be implemented easily. The proposed methods are applicable to a general class of regularizers that includes popular edge-preserving (e.g., total-variation) and sparsity-promoting (e.g., l(1)-norm of wavelet coefficients) criteria and combinations thereof. Numerical experiments with synthetic and in vivo human data illustrate that the proposed AL algorithms converge faster than both general-purpose optimization algorithms such as nonlinear conjugate gradient (NCG) and state-of-the-art MFISTA.
Reaction enhancement of initially distant scalars by Lagrangian coherent structures
International Nuclear Information System (INIS)
Pratt, Kenneth R.; Crimaldi, John P.; Meiss, James D.
2015-01-01
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
Lagrangian pathways of upwelling in the Southern Ocean
Viglione, Giuliana A.; Thompson, Andrew F.
2016-08-01
The spatial and temporal variability of upwelling into the mixed layer in the Southern Ocean is studied using a 1/10° ocean general circulation model. Virtual drifters are released in a regularly spaced pattern across the Southern Ocean at depths of 250, 500, and 1000 m during both summer and winter months. The drifters are advected along isopycnals for a period of 4 years, unless they outcrop into the mixed layer, where lateral advection and a parameterization of vertical mixing are applied. The focus of this study is on the discrete exchange between the model mixed layer and the interior. Localization of interior-mixed layer exchange occurs downstream of major topographic features across the Indian and Pacific basins, creating "hotspots" of outcropping. Minimal outcropping occurs in the Atlantic basin, while 59% of drifters outcrop in the Pacific sector and in Drake Passage (the region from 140° W to 40° W), a disproportionately large amount even when considering the relative basin sizes. Due to spatial and temporal variations in mixed layer depth, the Lagrangian trajectories provide a statistical measure of mixed layer residence times. For each exchange into the mixed layer, the residence time has a Rayleigh distribution with a mean of 30 days; the cumulative residence time of the drifters is 261 ± 194 days, over a period of 4 years. These results suggest that certain oceanic gas concentrations, such as CO2 and 14C, will likely not reach equilibrium with the atmosphere before being resubducted.
Lagrangian Description of Nonadiabatic Particle Motion in Spherical Tori
International Nuclear Information System (INIS)
White, R.B.; Yakovenko, Yu.V.; Kolesnichenko, Ya.I.
2002-01-01
The ability of a device to provide adiabatic motion of charged particles is crucial for magnetic confinement. As the magnetic field in the present-day spherical tori, e.g., MAST and NSTX, is much lower than in the conventional tokamaks, effects of the finite Larmor radius (FLR) on the motion of fast ions are of importance in these devices, affecting the stochasticity threshold for the interaction of the ions with electromagnetic perturbations. In addition, FLR by itself may result in non-conservation (jumps) of the magnetic moment of particles [4]. In this work we propose a Lagrangian approach to description of the resonant collisionless motion of charged particles under a perturbation, allowing for FLR. The work generalizes results of Ref. [1], where only time-independent perturbations were considered. The approach is used to find the stochasticity thresholds for the Goldston-White-Boozer (GWB) diffusion [2] and the cyclotron-resonance-induced (CRI) diffusion (for the case of the first cyclotron resonance, the latter was discovered in Ref. [3]). In addition, a new expression for the magnetic moment variation caused by FLR is found
Loop calculations in the three dimensional Gribov-Zwanziger Lagrangian
International Nuclear Information System (INIS)
Gracey, J.A.
2010-01-01
The three dimensional Gribov-Zwanziger Lagrangian is analysed at one and two loops. Specifically, the two loop gap equation is evaluated and the Gribov mass is expressed in terms of the coupling constant. The one loop corrections to the propagators of all the fields are determined. It is shown that when the gap equation is satisfied the Faddeev-Popov ghost and both Bose and Grassmann localizing ghosts all enhance in the infrared limit at one loop. This verifies that the Kugo-Ojima confinement criterion holds to this order and we also show that both Grassmann ghosts are enhanced at two loops. For the Bose ghost we determine the full form of the propagator in the zero momentum limit for both the transverse and longitudinal pieces and confirm Zwanziger's recent general analysis for the low energy behaviour. We provide an alternative but equivalent version of the horizon condition expressing it as the vacuum expectation value of an operator involving only the localizing Bose ghost field. The one loop static potential is also determined. (orig.)
Option pricing: Stock price, stock velocity and the acceleration Lagrangian
Baaquie, Belal E.; Du, Xin; Bhanap, Jitendra
2014-12-01
The industry standard Black-Scholes option pricing formula is based on the current value of the underlying security and other fixed parameters of the model. The Black-Scholes formula, with a fixed volatility, cannot match the market's option price; instead, it has come to be used as a formula for generating the option price, once the so called implied volatility of the option is provided as additional input. The implied volatility not only is an entire surface, depending on the strike price and maturity of the option, but also depends on calendar time, changing from day to day. The point of view adopted in this paper is that the instantaneous rate of return of the security carries part of the information that is provided by implied volatility, and with a few (time-independent) parameters required for a complete pricing formula. An option pricing formula is developed that is based on knowing the value of both the current price and rate of return of the underlying security which in physics is called velocity. Using an acceleration Lagrangian model based on the formalism of quantum mathematics, we derive the pricing formula for European call options. The implied volatility of the market can be generated by our pricing formula. Our option price is applied to foreign exchange rates and equities and the accuracy is compared with Black-Scholes pricing formula and with the market price.
A Lagrangian View of Stratospheric Trace Gas Distributions
Schoeberl, M. R.; Sparling, L.; Dessler, A.; Jackman, C. H.; Fleming, E. L.
1998-01-01
As a result of photochemistry, some relationship between the stratospheric age-of-air and the amount of tracer contained within an air sample is expected. The existence of such a relationship allows inferences about transport history to be made from observations of chemical tracers. This paper lays down the conceptual foundations for the relationship between age and tracer amount, developed within a Lagrangian framework. In general, the photochemical loss depends not only on the age of the parcel but also on its path. We show that under the "average path approximation" that the path variations are less important than parcel age. The average path approximation then allows us to develop a formal relationship between the age spectrum and the tracer spectrum. Using the relation between the tracer and age spectra, tracer-tracer correlations can be interpreted as resulting from mixing which connects parts of the single path photochemistry curve, which is formed purely from the action of photochemistry on an irreducible parcel. This geometric interpretation of mixing gives rise to constraints on trace gas correlations, and explains why some observations are do not fall on rapid mixing curves. This effect is seen in the ATMOS observations.
Tracking plastics in the Mediterranean: 2D Lagrangian model.
Liubartseva, S; Coppini, G; Lecci, R; Clementi, E
2018-04-01
Drift of floating debris is studied with a 2D Lagrangian model with stochastic beaching and sedimentation of plastics. An ensemble of >10 10 virtual particles is tracked from anthropogenic sources (coastal human populations, rivers, shipping lanes) to environmental destinations (sea surface, coastlines, seabed). Daily analyses of ocean currents and waves provided by CMEMS at a horizontal resolution of 1/16° are used to force the plastics. High spatio-temporal variability in sea-surface plastic concentrations without any stable long-term accumulations is found. Substantial accumulation of plastics is detected on coastlines and the sea bottom. The most contaminated areas are in the Cilician subbasin, Catalan Sea, and near the Po River Delta. Also, highly polluted local patches in the vicinity of sources with limited circulation are identified. An inverse problem solution, used to quantify the origins of plastics, shows that plastic pollution of every Mediterranean country is caused primarily by its own terrestrial sources. Copyright © 2018 Elsevier Ltd. All rights reserved.
The Monotonic Lagrangian Grid for Fast Air-Traffic Evaluation
Alexandrov, Natalia; Kaplan, Carolyn; Oran, Elaine; Boris, Jay
2010-01-01
This paper describes the continued development of a dynamic air-traffic model, ATMLG, intended for rapid evaluation of rules and methods to control and optimize transport systems. The underlying data structure is based on the Monotonic Lagrangian Grid (MLG), which is used for sorting and ordering positions and other data needed to describe N moving bodies, and their interactions. In ATMLG, the MLG is combined with algorithms for collision avoidance and updating aircraft trajectories. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. In this paper, we use ATMLG to examine how the ability to maintain a required separation between aircraft decreases as the number of aircraft in the volume increases. This requires keeping track of the primary and subsequent collision avoidance maneuvers necessary to maintain a five mile separation distance between all aircraft. Simulation results show that the number of collision avoidance moves increases exponentially with the number of aircraft in the volume.
Existence of Periodic Orbits with Zeno Behavior in Completed Lagrangian Hybrid Systems
Or, Yizhar; Ames, Aaron D.
2009-01-01
In this paper, we consider hybrid models of mechanical systems undergoing impacts, Lagrangian hybrid systems, and study their periodic orbits in the presence of Zeno behavior-an infinite number of impacts occurring in finite time. The main result of this paper is explicit conditions under which the existence of stable periodic orbits for a Lagrangian hybrid system with perfectly plastic impacts implies the existence of periodic orbits in the same system with non-plastic impacts. Such periodic...
A conservative scheme for 2D and 3D adaptive semi-Lagrangian advection
Behrens, Jörn; Mentrup, Lars
2005-01-01
This article describes a 2D and 3D adaptive and mass conservingsemi-Lagrangian advection scheme for atmospheric transport problems. Fromthe integral form of the conservation law we derive a semi-Lagrangian schemebased on conservation of mass along trajectories. The mapping of mass fromthe old (adaptively refined and possibly different) grid to the upstream controlvolume is performed by a mass packet based scheme, essentially consistingof a sub-grid discretization. We validate the new adaptive...
Relating Lagrangian passive scalar scaling exponents to Eulerian scaling exponents in turbulence
Schmitt , François G
2005-01-01
Intermittency is a basic feature of fully developed turbulence, for both velocity and passive scalars. Intermittency is classically characterized by Eulerian scaling exponent of structure functions. The same approach can be used in a Lagrangian framework to characterize the temporal intermittency of the velocity and passive scalar concentration of a an element of fluid advected by a turbulent intermittent field. Here we focus on Lagrangian passive scalar scaling exponents, and discuss their p...
Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.
Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun
2013-01-01
An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.
Energy Technology Data Exchange (ETDEWEB)
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 third-order asymptotic solution of nonlinear standing water waves in Lagrangian coordinates
International Nuclear Information System (INIS)
Yang-Yih, Chen; Hung-Chu, Hsu
2009-01-01
Asymptotic solutions up to third-order which describe irrotational finite amplitude standing waves are derived in Lagrangian coordinates. The analytical Lagrangian solution that is uniformly valid for large times satisfies the irrotational condition and the pressure p = 0 at the free surface, which is in contrast with the Eulerian solution existing under a residual pressure at the free surface due to Taylor's series expansion. In the third-order Lagrangian approximation, the explicit parametric equation and the Lagrangian wave frequency of water particles could be obtained. In particular, the Lagrangian mean level of a particle motion that is a function of vertical label is found as a part of the solution which is different from that in an Eulerian description. The dynamic properties of nonlinear standing waves in water of a finite depth, including particle trajectory, surface profile and wave pressure are investigated. It is also shown that the Lagrangian solution is superior to an Eulerian solution of the same order for describing the wave shape and the kinematics above the mean water level. (general)
BRST Quantisation of Histories Electrodynamics
Noltingk, D.
2001-01-01
This paper is a continuation of earlier work where a classical history theory of pure electrodynamics was developed in which the the history fields have \\emph{five} components. The extra component is associated with an extra constraint, thus enlarging the gauge group of histories electrodynamics. In this paper we quantise the classical theory developed previously by two methods. Firstly we quantise the reduced classical history space, to obtain a reduced quantum history theory. Secondly we qu...
these systems can improve water quality, engineers and scientists construct systems that replicate the functions of natural wetlands. Constructed wetlands are treatment systems that use natural processes
Lagrangian Particle Tracking Simulation for Warm-Rain Processes in Quasi-One-Dimensional Domain
Kunishima, Y.; Onishi, R.
2017-12-01
Conventional cloud simulations are based on the Euler method and compute each microphysics process in a stochastic way assuming infinite numbers of particles within each numerical grid. They therefore cannot provide the Lagrangian statistics of individual particles in cloud microphysics (i.e., aerosol particles, cloud particles, and rain drops) nor discuss the statistical fluctuations due to finite number of particles. We here simulate the entire precipitation process of warm-rain, with tracking individual particles. We use the Lagrangian Cloud Simulator (LCS), which is based on the Euler-Lagrangian framework. In that framework, flow motion and scalar transportation are computed with the Euler method, and particle motion with the Lagrangian one. The LCS tracks particle motions and collision events individually with considering the hydrodynamic interaction between approaching particles with a superposition method, that is, it can directly represent the collisional growth of cloud particles. It is essential for trustworthy collision detection to take account of the hydrodynamic interaction. In this study, we newly developed a stochastic model based on the Twomey cloud condensation nuclei (CCN) activation for the Lagrangian tracking simulation and integrated it into the LCS. Coupling with the Euler computation for water vapour and temperature fields, the initiation and condensational growth of water droplets were computed in the Lagrangian way. We applied the integrated LCS for a kinematic simulation of warm-rain processes in a vertically-elongated domain of, at largest, 0.03×0.03×3000 (m3) with horizontal periodicity. Aerosol particles with a realistic number density, 5×107 (m3), were evenly distributed over the domain at the initial state. Prescribed updraft at the early stage initiated development of a precipitating cloud. We have confirmed that the obtained bulk statistics fairly agree with those from a conventional spectral-bin scheme for a vertical column
Applications of the representation of the Heisenberg-Euler Lagrangian by means of special functions
International Nuclear Information System (INIS)
Valluri, S.R.; Lamm, D.R.; Mielniczuk, W.J.
1993-01-01
A convenient series representation for the real part of the Heisenberg-Euler Lagrangian density of quantum electrodynamics for arbitrary nonvanishing electric fields, E, and magnetic fields, B, has been previously provided by Mielniczuk. Using this representation, numerical information for the Lagrangian is presented for the range 0 cr ≤ 5 and 0 cr ≤ 10 (subscript cr stands for critical) with the electric and magnetic fields parallel and E cr ∼ 1.7 X 10 16 V cm -1 and B cr ∼ 4.4 X 10 13 G. It was found that for a fixed electric field, the Lagrangian is monotonically increasing with increasing magnetic field strength. However, for a fixed magnetic field, the Lagrangian exhibits a positively valued maximum before turning monotonically decreasing with increasing electric field strength. Further, the series representation is extended to the case of vanishing electric or magnetic field. Numerical results for these special cases are in very close agreement with previous results, which indicated a maximum value for the Lagrangian density for B = 0 at E/E cr ∼ 3. Also, the techniques developed for deriving the real part of the Heisenberg-Euler Lagrangian are applied to the imaginary part to deduce a similar, convenient series representation that agrees with the previous results derived by others for the special case of a vanishing magnetic field. Possible applications of this Lagrangian to quantum chromodynamics are discussed. This series representation will be of use in calculations of a quantum-electrodynamical field energy density in the absence of real charges, and for calculations of polarization and magnetization of the vacuum. More accurate calculations of the cross-section scattering of light by light in the presence of a constant, homogeneous magnetic and (or) electric field are possible with the aid of this series representation. (author)
Evaluation of wastewater contaminant transport in surface waters using verified Lagrangian sampling.
Antweiler, Ronald C; Writer, Jeffrey H; Murphy, Sheila F
2014-02-01
Contaminants released from wastewater treatment plants can persist in surface waters for substantial distances. Much research has gone into evaluating the fate and transport of these contaminants, but this work has often assumed constant flow from wastewater treatment plants. However, effluent discharge commonly varies widely over a 24-hour period, and this variation controls contaminant loading and can profoundly influence interpretations of environmental data. We show that methodologies relying on the normalization of downstream data to conservative elements can give spurious results, and should not be used unless it can be verified that the same parcel of water was sampled. Lagrangian sampling, which in theory samples the same water parcel as it moves downstream (the Lagrangian parcel), links hydrologic and chemical transformation processes so that the in-stream fate of wastewater contaminants can be quantitatively evaluated. However, precise Lagrangian sampling is difficult, and small deviations - such as missing the Lagrangian parcel by less than 1h - can cause large differences in measured concentrations of all dissolved compounds at downstream sites, leading to erroneous conclusions regarding in-stream processes controlling the fate and transport of wastewater contaminants. Therefore, we have developed a method termed "verified Lagrangian" sampling, which can be used to determine if the Lagrangian parcel was actually sampled, and if it was not, a means for correcting the data to reflect the concentrations which would have been obtained had the Lagrangian parcel been sampled. To apply the method, it is necessary to have concentration data for a number of conservative constituents from the upstream, effluent, and downstream sites, along with upstream and effluent concentrations that are constant over the short-term (typically 2-4h). These corrections can subsequently be applied to all data, including non-conservative constituents. Finally, we show how data
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
Felici, Helene Marie
1992-01-01
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.
Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality
International Nuclear Information System (INIS)
Avan, Jean; Caudrelier, Vincent; Doikou, Anastasia; Kundu, Anjan
2016-01-01
We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized by the fact that the zero-curvature representation of the NLEE can be realized by two Hamiltonian formulations stemming from two distinct choices of the configuration space, yielding two inequivalent Poisson structures on the corresponding phase space and two distinct Hamiltonians. This is fundamentally different from the standard bi-Hamiltonian or generally multitime structure. The first formulation chooses purely space-dependent fields as configuration space; it yields the standard Poisson structure for NLS. The other one is new: it chooses purely time-dependent fields as configuration space and yields a different Poisson structure at each level of the hierarchy. The corresponding NLEE becomes a space evolution equation. We emphasize the role of the Lagrangian formulation as a unifying framework for deriving both Poisson structures, using ideas from covariant field theory. One of our main results is to show that the two matrices of the Lax pair satisfy the same form of ultralocal Poisson algebra (up to a sign) characterized by an r-matrix structure, whereas traditionally only one of them is involved in the classical r-matrix method. We construct explicit dual hierarchies of Hamiltonians, and Lax representations of the triggered dynamics, from the monodromy matrices of either Lax matrix. An appealing procedure to build a multi-dimensional lattice of Lax pair, through successive uses of the dual Poisson structures, is briefly introduced.
Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality
Energy Technology Data Exchange (ETDEWEB)
Avan, Jean, E-mail: Jean.Avan@u-cergy.fr [Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, F-95302 Cergy-Pontoise (France); Caudrelier, Vincent, E-mail: v.caudrelier@city.ac.uk [Department of Mathematics, City University London, Northampton Square, EC1V 0HB London (United Kingdom); Doikou, Anastasia, E-mail: A.Doikou@hw.ac.uk [Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh (United Kingdom); Kundu, Anjan, E-mail: Anjan.Kundu@saha.ac.in [Saha Institute of Nuclear Physics, Theory Division, Kolkata (India)
2016-01-15
We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equation (NLEE) in the hierarchy, dual integrable structures are characterized by the fact that the zero-curvature representation of the NLEE can be realized by two Hamiltonian formulations stemming from two distinct choices of the configuration space, yielding two inequivalent Poisson structures on the corresponding phase space and two distinct Hamiltonians. This is fundamentally different from the standard bi-Hamiltonian or generally multitime structure. The first formulation chooses purely space-dependent fields as configuration space; it yields the standard Poisson structure for NLS. The other one is new: it chooses purely time-dependent fields as configuration space and yields a different Poisson structure at each level of the hierarchy. The corresponding NLEE becomes a space evolution equation. We emphasize the role of the Lagrangian formulation as a unifying framework for deriving both Poisson structures, using ideas from covariant field theory. One of our main results is to show that the two matrices of the Lax pair satisfy the same form of ultralocal Poisson algebra (up to a sign) characterized by an r-matrix structure, whereas traditionally only one of them is involved in the classical r-matrix method. We construct explicit dual hierarchies of Hamiltonians, and Lax representations of the triggered dynamics, from the monodromy matrices of either Lax matrix. An appealing procedure to build a multi-dimensional lattice of Lax pair, through successive uses of the dual Poisson structures, is briefly introduced.
Lagrangian relaxation technique in power systems operation planning: Multipliers updating problem
Energy Technology Data Exchange (ETDEWEB)
Ruzic, S. [Electric Power Utility of Serbia, Belgrade (Yugoslavia)
1995-11-01
All Lagrangian relaxation based approaches to the power systems operation planning have an important common part: the Lagrangian multipliers correction procedure. It is the subject of this paper. Different approaches presented in the literature are discussed and an original method for the Lagrangian multipliers updating is proposed. The basic idea of this new method is to update Lagrangian multipliers trying to satisfy Khun-Tucker optimality conditions. Instead of the dual function maximization the `distance of optimality function` is defined and minimized. If Khun-Tucker optimality conditions are satisfied the value of this function is in range (-1,0); otherwise the function has a big positive value. This method called `the distance of optimality method` takes into account future changes in planning generations due to the Lagrangian multipliers updating. The influence of changes in a multiplier associated to one system constraint to the satisfaction of some other system requirements is also considered. The numerical efficiency of the proposed method is analyzed and compared with results obtained using the sub-gradient technique. 20 refs, 2 tabs
Jakovetic, Dusan; Xavier, João; Moura, José M. F.
2011-08-01
We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x=x^\\star. The objective function of the corresponding optimization problem is the sum of private (known only by a node,) convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, decentralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l_1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.
Geometric Lagrangian approach to the physical degree of freedom count in field theory
Díaz, Bogar; Montesinos, Merced
2018-05-01
To circumvent some technical difficulties faced by the geometric Lagrangian approach to the physical degree of freedom count presented in the work of Díaz, Higuita, and Montesinos [J. Math. Phys. 55, 122901 (2014)] that prevent its direct implementation to field theory, in this paper, we slightly modify the geometric Lagrangian approach in such a way that its resulting version works perfectly for field theory (and for particle systems, of course). As in previous work, the current approach also allows us to directly get the Lagrangian constraints, a new Lagrangian formula for the counting of the number of physical degrees of freedom, the gauge transformations, and the number of first- and second-class constraints for any action principle based on a Lagrangian depending on the fields and their first derivatives without performing any Dirac's canonical analysis. An advantage of this approach over the previous work is that it also allows us to handle the reducibility of the constraints and to get the off-shell gauge transformations. The theoretical framework is illustrated in 3-dimensional generalized general relativity (Palatini and Witten's exotic actions), Chern-Simons theory, 4-dimensional BF theory, and 4-dimensional general relativity given by Palatini's action with a cosmological constant.
Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex
Curbelo, Jezabel; José García-Garrido, Víctor; Mechoso, Carlos Roberto; Mancho, Ana Maria; Wiggins, Stephen; Niang, Coumba
2017-07-01
In this paper we study the three-dimensional (3-D) Lagrangian structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using Lagrangian descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of Lagrangian transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the Lagrangian structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex Lagrangian patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.
International Nuclear Information System (INIS)
Levi, A.R.; Lubicz, V.; Rebbi, C.
1997-01-01
We discuss a general strategy to compute the coefficients of the QCD chiral Lagrangian using lattice QCD with Wilson fermions. This procedure requires the introduction of a lattice chiral Lagrangian as an intermediate step in the calculation. The QCD chiral Lagrangian is then obtained by expanding the lattice effective theory in increasing powers of the lattice spacing and the external momenta. In order to investigate the general structure of the lattice effective Lagrangian, we perform an analytical calculation at the leading order of the strong-coupling and large-N expansion. We find that the explicit chiral symmetry breaking, introduced on the lattice by the Wilson term, is reproduced in the effective theory by a set of additional terms, which do not have direct correspondence in the continuum chiral Lagrangian. We argue that these terms can be conveniently reabsorbed by a suitable renormalization procedure. This is shown explicitly at the leading order of the strong-coupling and large-N expansion. In fact, we find that at this order, as is known to be the case in the opposite weak-coupling limit, the vector and axial Ward identities of the continuum theory are reproduced on the lattice provided that the bare quark mass and the lattice operators are properly renormalized. copyright 1997 The American Physical Society
International Nuclear Information System (INIS)
Ritus, V.I.
1987-01-01
This chapter gives methods of formulating the Lagrangian function of an intense field and its asymptotic properties are investigated. Section 2 gives a derivation of the correction pounds to the Lagrangian function resulting from the change in the radiation interaction of the vacuum electrons induced by a constant external field. Section 3 is devoted to the renormalization of the external field as well as the charge and mass of the electron. Like charge renormalization, mass renormalization is performed within the scope of the calculation of the Lagrangian function of the electromagnetic field (without separate consideration of the mass operator or the position of the pole of the Green function of the electron) using a general physical renormalization principle requiring vanishing of the radiation corrections to the observed charge and mass when the field is switched off. This calculation process is performed explicitly in Section 4 where the imaginary part of the Lagrangian function is calculated for weak and strong fields. Here it is noted that the asymptotic behavior of the Lagrangian function with large fields coincides with logarithmic accuracy to the asymptotic behavior of a polarized function with large momenta
Pellicer, Eugenio; Teixeira, José C; Moura, Helder P; Catalá, Joaquín
2014-01-01
The management of construction projects is a wide ranging and challenging discipline in an increasingly international industry, facing continual challenges and demands for improvements in safety, in quality and cost control, and in the avoidance of contractual disputes. Construction Management grew out of a Leonardo da Vinci project to develop a series of Common Learning Outcomes for European Managers in Construction. Financed by the European Union, the project aimed to develop a library of basic materials for developing construction management skills for use in a pan-European context. Focused exclusively on the management of the construction phase of a building project from the contractor's point of view, Construction Management covers the complete range of topics of which mastery is required by the construction management professional for the effective delivery of new construction projects. With the continued internationalisation of the construction industry, Construction Management will be required rea...
Directory of Open Access Journals (Sweden)
Brent Knutson
2015-01-01
Full Text Available We present a study of three-dimensional Lagrangian coherent structures (LCS near the Hong Kong International Airport and relate to previous developments of two-dimensional (2D LCS analyses. The LCS are contrasted among three independent models and against 2D coherent Doppler light detection and ranging (LIDAR data. Addition of the velocity information perpendicular to the LIDAR scanning cone helps solidify flow structures inferred from previous studies; contrast among models reveals the intramodel variability; and comparison with flight data evaluates the performance among models in terms of Lagrangian analyses. We find that, while the three models and the LIDAR do recover similar features of the windshear experienced by a landing aircraft (along the landing trajectory, their Lagrangian signatures over the entire domain are quite different—a portion of each numerical model captures certain features resembling those LCS extracted from independent 2D LIDAR analyses based on observations.
Directory of Open Access Journals (Sweden)
Brian Jonathan Wolk
2017-01-01
Full Text Available This paper introduces an alternative formalism for deriving the Dirac operator and equation. The use of this formalism concomitantly generates a separate operator coupled to the Dirac operator. When operating on a Clifford field, this coupled operator produces field components which are formally equivalent to the field components of Maxwell's electromagnetic field tensor. Consequently, the Lagrangian of the associated coupled field exhibits internal local gauge symmetry. The coupled field Lagrangian is seen to be equivalent to the Lagrangian of Quantum Electrodynamics. Received: 8 November 2016, Accepted: 4 January 2017; Edited by: D. Gomez Dumm; DOI: http://dx.doi.org/10.4279/PIP.090002 Cite as: B J Wolk, Papers in Physics 9, 090002 (2017
Cotter, C J; Gottwald, G A; Holm, D D
2017-09-01
In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.
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,...
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Gaida, R.P.; Kluchkousky, Ya.B.; Tretyak, V.I.
1987-01-01
In the present report the main attention is paid to the interrelations of various three-dimensional approaches and to the relation of the latter to the Fokker-type action formalism; the problem of the correspondence between three-dimensional descriptions and singular Lagrangian formalism will be shortly concerned. The authors start with the three-dimensional Lagrangian formulation of the classical RDIT. The generality of this formalism enables, similarly as in the non-relativistic case, to consider it as a central link explaining naturally a number of features of other three-dimensional approaches, namely Newtonian (based directly on second order equations of motion) and Hamiltonian ones). It is also capable of describing four-dimensional manifestly covariant models using Fokker action integrals and singular Lagrangians
Lagrangian Timescales of Southern Ocean Upwelling in a Hierarchy of Model Resolutions
Drake, Henri F.; Morrison, Adele K.; Griffies, Stephen M.; Sarmiento, Jorge L.; Weijer, Wilbert; Gray, Alison R.
2018-01-01
In this paper we study upwelling pathways and timescales of Circumpolar Deep Water (CDW) in a hierarchy of models using a Lagrangian particle tracking method. Lagrangian timescales of CDW upwelling decrease from 87 years to 31 years to 17 years as the ocean resolution is refined from 1° to 0.25° to 0.1°. We attribute some of the differences in timescale to the strength of the eddy fields, as demonstrated by temporally degrading high-resolution model velocity fields. Consistent with the timescale dependence, we find that an average Lagrangian particle completes 3.2 circumpolar loops in the 1° model in comparison to 0.9 loops in the 0.1° model. These differences suggest that advective timescales and thus interbasin merging of upwelling CDW may be overestimated by coarse-resolution models, potentially affecting the skill of centennial scale climate change projections.
Electroweak chiral Lagrangian from a natural topcolor-assisted technicolor model
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Lang Junyi; Jiang Shaozhou; Wang Qing
2009-01-01
Based on previous studies on computing coefficients of the electroweak chiral Lagrangian from C. T. Hill's schematic topcolor-assisted technicolor model, we generalize the calculation to K. Lane's prototype natural topcolor-assisted technicolor model. We find that typical features of the model are qualitatively similar to those of Hill's, but Lane's model prefers a smaller technicolor group and the Z ' mass must be smaller than 400 GeV. Furthermore, the S parameter is around the order of +1, mainly due to the existence of three doublets of techniquarks. We obtain the values for all coefficients of the electroweak chiral Lagrangian up to the order p 4 . Apart from large negative four-fermion coupling values, the extended technicolor impacts on the electroweak chiral Lagrangian coefficients are small, since the techniquark self energy, which determines these coefficients, in general receives almost no influence from the extended technicolor induced four-fermion interactions except for its large momentum tail.
Space-Time Transformation in Flux-form Semi-Lagrangian Schemes
Directory of Open Access Journals (Sweden)
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.
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.
Evaluation of wastewater contaminant transport in surface waters using verified Lagrangian sampling
Antweiler, Ronald C.; Writer, Jeffrey H.; Murphy, Sheila F.
2014-01-01
Contaminants released from wastewater treatment plants can persist in surface waters for substantial distances. Much research has gone into evaluating the fate and transport of these contaminants, but this work has often assumed constant flow from wastewater treatment plants. However, effluent discharge commonly varies widely over a 24-hour period, and this variation controls contaminant loading and can profoundly influence interpretations of environmental data. We show that methodologies relying on the normalization of downstream data to conservative elements can give spurious results, and should not be used unless it can be verified that the same parcel of water was sampled. Lagrangian sampling, which in theory samples the same water parcel as it moves downstream (the Lagrangian parcel), links hydrologic and chemical transformation processes so that the in-stream fate of wastewater contaminants can be quantitatively evaluated. However, precise Lagrangian sampling is difficult, and small deviations – such as missing the Lagrangian parcel by less than 1 h – can cause large differences in measured concentrations of all dissolved compounds at downstream sites, leading to erroneous conclusions regarding in-stream processes controlling the fate and transport of wastewater contaminants. Therefore, we have developed a method termed “verified Lagrangian” sampling, which can be used to determine if the Lagrangian parcel was actually sampled, and if it was not, a means for correcting the data to reflect the concentrations which would have been obtained had the Lagrangian parcel been sampled. To apply the method, it is necessary to have concentration data for a number of conservative constituents from the upstream, effluent, and downstream sites, along with upstream and effluent concentrations that are constant over the short-term (typically 2–4 h). These corrections can subsequently be applied to all data, including non-conservative constituents. Finally, we
Lagrangian statistics and flow topology in forced two-dimensional turbulence.
Kadoch, B; Del-Castillo-Negrete, D; Bos, W J T; Schneider, K
2011-03-01
A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.
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Burdík, C; Reshetnyak, A
2012-01-01
We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux Y(s 1 ,..., s k ) with κ ≥ 2 rows on d-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for κ = 2 Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic sp(2κ) algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin (s 1 , s 2 ) is derived.
Lagrangian analysis of multiscale particulate flows with the particle finite element method
Oñate, Eugenio; Celigueta, Miguel Angel; Latorre, Salvador; Casas, Guillermo; Rossi, Riccardo; Rojek, Jerzy
2014-05-01
We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.
A coherent structure approach for parameter estimation in Lagrangian Data Assimilation
Maclean, John; Santitissadeekorn, Naratip; Jones, Christopher K. R. T.
2017-12-01
We introduce a data assimilation method to estimate model parameters with observations of passive tracers by directly assimilating Lagrangian Coherent Structures. Our approach differs from the usual Lagrangian Data Assimilation approach, where parameters are estimated based on tracer trajectories. We employ the Approximate Bayesian Computation (ABC) framework to avoid computing the likelihood function of the coherent structure, which is usually unavailable. We solve the ABC by a Sequential Monte Carlo (SMC) method, and use Principal Component Analysis (PCA) to identify the coherent patterns from tracer trajectory data. Our new method shows remarkably improved results compared to the bootstrap particle filter when the physical model exhibits chaotic advection.
Gravitational Lagrangians, Mach's Principle, and the Equivalence Principle in an Expanding Universe
Essén, Hanno
2014-08-01
Gravitational Lagrangians as derived by Fock for the Einstein-Infeld-Hoffmann approach, and by Kennedy assuming only a fourth rank tensor interaction, contain long range interactions. Here we investigate how these affect the local dynamics when integrated over an expanding universe out to the Hubble radius. Taking the cosmic expansion velocity into account in a heuristic manner it is found that these long range interactions imply Mach's principle, provided the universe has the critical density, and that mass is renormalized. Suitable higher order additions to the Lagrangians make the formalism consistent with the equivalence principle.
International Nuclear Information System (INIS)
Boman, R.; Papeleux, L.; Ponthot, J. P.
2007-01-01
In this paper, the Arbitrary Lagrangian Eulerian formalism is used to compute the steady state of a 2D metal cutting operation and a 3D U-shaped cold roll forming process. Compared to the Lagrangian case, this method allows the use of a refined mesh near the tools, leading to an accurate representation of the chip formation (metal cutting) and the bending of the sheet (roll forming) with a limited computational time. The main problem of this kind of simulation is the rezoning of the nodes on the free surfaces of the sheet. A modified iterative isoparametric smoother is used to manage this geometrically complex and CPU expensive task
Lagrangian statistics of mesoscale turbulence in a natural environment: The Agulhas return current.
Carbone, Francesco; Gencarelli, Christian N; Hedgecock, Ian M
2016-12-01
The properties of mesoscale geophysical turbulence in an oceanic environment have been investigated through the Lagrangian statistics of sea surface temperature measured by a drifting buoy within the Agulhas return current, where strong temperature mixing produces locally sharp temperature gradients. By disentangling the large-scale forcing which affects the small-scale statistics, we found that the statistical properties of intermittency are identical to those obtained from the multifractal prediction in the Lagrangian frame for the velocity trajectory. The results suggest a possible universality of turbulence scaling.