Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system
Battista, Emmanuele; Dell'Agnello, Simone; Esposito, Giampiero; Simo, Jules
2015-01-01
Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical...
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.
Orbital maneuvers between the Lagrangian points and the primaries in the Earth-Sun system
Prado, Antônio F. B. Almeida
2006-01-01
This paper is concerned with trajectories to transfer a spacecraft between the Lagrangian points of the Sun-Earth system and the primaries. The Lagrangian points have important applications in astronautics, since they are equilibrium points of the equation of motion and very good candidates to locate a satellite or a space station. The planar circular restricted three-body problem in two dimensions is used as the model for the Sun-Earth system, and Lamaître regularization is used to avoid sin...
International Nuclear Information System (INIS)
Claisse, A.; Després, B.; Labourasse, E.; Ledoux, F.
2012-01-01
The aim of this paper is the numerical simulation of compressible hydrodynamic strong implosions, which take place for instance in Inertial Confinement Fusion. It focuses in particular on two crucial issues, for such calculations: very low CFL number at the implosion center and approximation error on the initial geometry. Thus, we propose an exceptional points method, which is translation invariant and suitable to curved meshes. This method is designed for cell-centered Lagrangian schemes (GLACE, EUCCLHYD). Several numerical examples on significant test cases are presented to show the relevance of our approach.
Webb, G. M.; Zank, G. P.
2007-01-01
We explore the role of the Lagrangian map for Lie symmetries in magnetohydrodynamics (MHD) and gas dynamics. By converting the Eulerian Lie point symmetries of the Galilei group to Lagrange label space, in which the Eulerian position coordinate x is regarded as a function of the Lagrange fluid labels x0 and time t, one finds that there is an infinite class of symmetries in Lagrange label space that map onto each Eulerian Lie point symmetry of the Galilei group. The allowed transformation of the Lagrangian fluid labels x0 corresponds to a fluid relabelling symmetry, including the case where there is no change in the fluid labels. We also consider a class of three, well-known, scaling symmetries for a gas with a constant adiabatic index γ. These symmetries map onto a modified form of the fluid relabelling symmetry determining equations, with non-zero source terms. We determine under which conditions these symmetries are variational or divergence symmetries of the action, and determine the corresponding Lagrangian and Eulerian conservation laws by use of Noether's theorem. These conservation laws depend on the initial entropy, density and magnetic field of the fluid. We derive the conservation law corresponding to the projective symmetry in gas dynamics, for the case γ = (n + 2)/n, where n is the number of Cartesian space coordinates, and the corresponding result for two-dimensional (2D) MHD, for the case γ = 2. Lie algebraic structures in Lagrange label space corresponding to the symmetries are investigated. The Lie algebraic symmetry relations between the fluid relabelling symmetries in Lagrange label space, and their commutators with a linear combination of the three symmetries with a constant adiabatic index are delineated.
International Nuclear Information System (INIS)
Webb, G M; Zank, G P
2007-01-01
We explore the role of the Lagrangian map for Lie symmetries in magnetohydrodynamics (MHD) and gas dynamics. By converting the Eulerian Lie point symmetries of the Galilei group to Lagrange label space, in which the Eulerian position coordinate x is regarded as a function of the Lagrange fluid labels x 0 and time t, one finds that there is an infinite class of symmetries in Lagrange label space that map onto each Eulerian Lie point symmetry of the Galilei group. The allowed transformation of the Lagrangian fluid labels x 0 corresponds to a fluid relabelling symmetry, including the case where there is no change in the fluid labels. We also consider a class of three, well-known, scaling symmetries for a gas with a constant adiabatic index γ. These symmetries map onto a modified form of the fluid relabelling symmetry determining equations, with non-zero source terms. We determine under which conditions these symmetries are variational or divergence symmetries of the action, and determine the corresponding Lagrangian and Eulerian conservation laws by use of Noether's theorem. These conservation laws depend on the initial entropy, density and magnetic field of the fluid. We derive the conservation law corresponding to the projective symmetry in gas dynamics, for the case γ = (n + 2)/n, where n is the number of Cartesian space coordinates, and the corresponding result for two-dimensional (2D) MHD, for the case γ = 2. Lie algebraic structures in Lagrange label space corresponding to the symmetries are investigated. The Lie algebraic symmetry relations between the fluid relabelling symmetries in Lagrange label space, and their commutators with a linear combination of the three symmetries with a constant adiabatic index are delineated
A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics
Energy Technology Data Exchange (ETDEWEB)
Franceschini, Andrea; Ferronato, Massimiliano, E-mail: massimiliano.ferronato@unipd.it; Janna, Carlo; Teatini, Pietro
2016-06-01
The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion according to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions. - Highlights: • A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable also in realistic applications.
Lunar and Lagrangian Point L1/L2 CubeSat Communication and Navigation Considerations
Schaire, Scott; Wong, Yen; Bussey, George; Shelton, Marta; Folta, Dave; Gramling, Cheryl; Celeste, Peter; Anderson, Mike; Perrotto, Trish; Malphrus, Benjamin; Kruth, Jeff
2017-01-01
CubeSats have grown in sophistication to the point that relatively low-cost mission solutions could be undertaken for planetary exploration. There are unique considerations for lunar and L1/L2 CubeSat communication and navigation compared with low earth orbit CubeSats. This paper explores those considerations as they relate to the Lunar IceCube Mission. The Lunar IceCube is a CubeSat mission led by Morehead State University with participation from NASA Goddard Space Flight Center, Jet Propuls...
Integrability from point symmetries in a family of cosmological Horndeski Lagrangians
Dimakis, N.; Giacomini, Alex; Paliathanasis, Andronikos
2017-07-01
For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lemaître-Robertson-Walker space-time. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. The de Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally, we discuss how singular solutions provides nonsingular universes in a different frame and vice versa.
Integrability from point symmetries in a family of cosmological Horndeski Lagrangians
Energy Technology Data Exchange (ETDEWEB)
Dimakis, N.; Giacomini, Alex [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Paliathanasis, Andronikos [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Durban University of Technology, Institute of Systems Science, Durban (South Africa)
2017-07-15
For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lemaitre-Robertson-Walker space-time. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. The de Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally, we discuss how singular solutions provides nonsingular universes in a different frame and vice versa. (orig.)
Lunar and Lagrangian Point L1 L2 CubeSat Communication and Navigation Considerations
Schaire, Scott; Wong, Yen F.; Altunc, Serhat; Bussey, George; Shelton, Marta; Folta, Dave; Gramling, Cheryl; Celeste, Peter; Anderson, Mile; Perrotto, Trish;
2017-01-01
CubeSats have grown in sophistication to the point that relatively low-cost mission solutions could be undertaken for planetary exploration. There are unique considerations for lunar and L1/L2 CubeSat communication and navigation compared with low earth orbit CubeSats. This paper explores those considerations as they relate to the Lunar IceCube Mission. The Lunar IceCube is a CubeSat mission led by Morehead State University with participation from NASA Goddard Space Flight Center, Jet Propulsion Laboratory, the Busek Company and Vermont Tech. It will search for surface water ice and other resources from a high inclination lunar orbit. Lunar IceCube is one of a select group of CubeSats designed to explore beyond low-earth orbit that will fly on NASA’s Space Launch System (SLS) as secondary payloads for Exploration Mission (EM) 1. Lunar IceCube and the EM-1 CubeSats will lay the groundwork for future lunar and L1/L2 CubeSat missions. This paper discusses communication and navigation needs for the Lunar IceCube mission and navigation and radiation tolerance requirements related to lunar and L1/L2 orbits. Potential CubeSat radios and antennas for such missions are investigated and compared. Ground station coverage, link analysis, and ground station solutions are also discussed. This paper will describe modifications in process for the Morehead ground station, as well as further enhancements of the Morehead ground station and NASA Near Earth Network (NEN) that are being considered. The potential NEN enhancements include upgrading current NEN Cortex receiver with Forward Error Correction (FEC) Turbo Code, providing X-band uplink capability, and adding ranging options. The benefits of ground station enhancements for CubeSats flown on NASA Exploration Missions (EM) are presented. This paper also describes how the NEN may support lunar and L1/L2 CubeSats without any enhancements. In addition, NEN is studying other initiatives to better support the CubeSat community
An efficient and stable hybrid extended Lagrangian/self-consistent field scheme for solving classical mutual induction
Albaugh, Alex; Demerdash, Omar; Head-Gordon, Teresa
2015-11-01
We have adapted a hybrid extended Lagrangian self-consistent field (EL/SCF) approach, developed for time reversible Born Oppenheimer molecular dynamics for quantum electronic degrees of freedom, to the problem of classical polarization. In this context, the initial guess for the mutual induction calculation is treated by auxiliary induced dipole variables evolved via a time-reversible velocity Verlet scheme. However, we find numerical instability, which is manifested as an accumulation in the auxiliary velocity variables, that in turn results in an unacceptable increase in the number of SCF cycles to meet even loose convergence tolerances for the real induced dipoles over the course of a 1 ns trajectory of the AMOEBA14 water model. By diagnosing the numerical instability as a problem of resonances that corrupt the dynamics, we introduce a simple thermostating scheme, illustrated using Berendsen weak coupling and Nose-Hoover chain thermostats, applied to the auxiliary dipole velocities. We find that the inertial EL/SCF (iEL/SCF) method provides superior energy conservation with less stringent convergence thresholds and a correspondingly small number of SCF cycles, to reproduce all properties of the polarization model in the NVT and NVE ensembles accurately. Our iEL/SCF approach is a clear improvement over standard SCF approaches to classical mutual induction calculations and would be worth investigating for application to ab initio molecular dynamics as well.
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.)
Lavraud, B.; Liu, Y.; Segura, K.; He, J.; Qin, G.; Temmer, M.; Vial, J.-C.; Xiong, M.; Davies, J. A.; Rouillard, A. P.;
2016-01-01
We present a concept for a small mission to the Sun-Earth Lagrangian L5 point for innovative solar, heliospheric and space weather science. The proposed INvestigation of Solar-Terrestrial Activity aNd Transients (INSTANT) mission is designed to identify how solar coronal magnetic fields drive eruptions, mass transport and particle acceleration that impact the Earth and the heliosphere. INSTANT is the first mission designed to (1) obtain measurements of coronal magnetic fields from space and (2) determine coronal mass ejection (CME) kinematics with unparalleled accuracy. Thanks to innovative instrumentation at a vantage point that provides the most suitable perspective view of the Sun-Earth system, INSTANT would uniquely track the whole chain of fundamental processes driving space weather at Earth. We present the science requirements, payload and mission profile that fulfill ambitious science objectives within small mission programmatic boundary conditions.
Design of four-point SENB specimens with stable crack growth
DEFF Research Database (Denmark)
Jørgensen, Jeppe Bjørn; Kildegaard, Casper; Sørensen, Bent F.
2018-01-01
A four-point single-edge-notch-beam (SENB) test specimen loaded in displacement control (fixed grip) is proposed for studying crack deflection at bi-material interfaces. In order to ensure stable crack growth, a novel analytical model of the four-point SENB specimen in fixed grip is derived...... and compared with numerical models. Model results show that the specimen should be short and thick, and the start-crack length should be deep for the crack to propagate stable towards the bi-material interface. Observations from experimental tests of four-point SENB specimens with different start-crack lengths......, confirmed that the crack grows stable if the start-crack length is deep and unstable if not....
A new method to extract stable feature points based on self-generated simulation images
Long, Fei; Zhou, Bin; Ming, Delie; Tian, Jinwen
2015-10-01
Recently, image processing has got a lot of attention in the field of photogrammetry, medical image processing, etc. Matching two or more images of the same scene taken at different times, by different cameras, or from different viewpoints, is a popular and important problem. Feature extraction plays an important part in image matching. Traditional SIFT detectors reject the unstable points by eliminating the low contrast and edge response points. The disadvantage is the need to set the threshold manually. The main idea of this paper is to get the stable extremums by machine learning algorithm. Firstly we use ASIFT approach coupled with the light changes and blur to generate multi-view simulated images, which make up the set of the simulated images of the original image. According to the way of generating simulated images set, affine transformation of each generated image is also known. Instead of the traditional matching process which contain the unstable RANSAC method to get the affine transformation, this approach is more stable and accurate. Secondly we calculate the stability value of the feature points by the set of image with its affine transformation. Then we get the different feature properties of the feature point, such as DOG features, scales, edge point density, etc. Those two form the training set while stability value is the dependent variable and feature property is the independent variable. At last, a process of training by Rank-SVM is taken. We will get a weight vector. In use, based on the feature properties of each points and weight vector calculated by training, we get the sort value of each feature point which refers to the stability value, then we sort the feature points. In conclusion, we applied our algorithm and the original SIFT detectors to test as a comparison. While in different view changes, blurs, illuminations, it comes as no surprise that experimental results show that our algorithm is more efficient.
Pseudotoric structures: Lagrangian submanifolds and Lagrangian fibrations
Tyurin, N. A.
2017-06-01
This survey presents a generalization of the notion of a toric structure on a compact symplectic manifold: the notion of a pseudotoric structure. The language of these new structures appears to be a convenient and natural tool for describing many non-standard Lagrangian submanifolds and cycles (Chekanov's exotic tori, Mironov's cycles in certain particular cases, and others) as well as for constructing Lagrangian fibrations (for example, special fibrations in the sense of Auroux on Fano varieties). Known properties of pseudotoric structures and constructions based on these properties are discussed, as well as open problems whose solution may be of importance in symplectic geometry and mathematical physics. Bibliography: 28 titles.
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.
McCall, W Vaughn; Batson, Nicolas; Webster, Megan; Joshi, Indu; Derreberry, Todd; McDonough, Adam; Farris, Suzan
2013-07-01
The design of safe clinical trials targeting suicidal ideation requires operational definitions of what degree of suicidal ideation is too excessive to allow safe participation. We examined the Scale for Suicide Ideation (SSI) to develop a psychometric cut-point that would identify patients having a suicidal emergency. The Emergency Department (ED) and the out-patient clinic of a university hospital. We used the SSI to contrast 23 stable, depressed adult out-patients versus 11 depressed adult ED patients awaiting psychiatric admission for a suicidal emergency. The performance of the SSI was examined with nominal logistic regression. ED patients were older than out-patients (Pmodel of SSI score and group yielded a score of 16 (Pmodel was expanded to include SSI along with age, gender, ethnicity, sedative-hypnotic use, and over-the-counter use, only SSI score remained significant as a predictor. A SSI score ≥16 may be useful as an exclusion criterion for out-patients in depression clinical trials.
Ganesh, Shruthi Vatsyayani
With the advent of microfluidic technologies for molecular diagnostics, a lot of emphasis has been placed on developing diagnostic tools for resource poor regions in the form of Extreme Point of Care devices. To ensure commercial viability of such a device there is a need to develop an accurate sample to answer system, which is robust, portable, isolated yet highly sensitive and cost effective. This need has been a driving force for research involving integration of different microsystems like droplet microfluidics, Compact-disc (CD)microfluidics along with sample preparation and detection modules on a single platform. This work attempts to develop a proof of concept prototype of one such device using existing CD microfluidics tools to generate stable droplets used in point of care diagnostics (POC diagnostics). Apart from using a fairly newer technique for droplet generation and stabilization, the work aims to develop this method focused towards diagnostics for rural healthcare. The motivation for this work is first described with an emphasis on the current need for diagnostic testing in rural health-care and the general guidelines prescribed by WHO for such a sample to answer system. Furthermore, a background on CD and droplet microfluidics is presented to understand the merits and de-merits of each system and the need for integrating the two. This phase of the thesis also includes different methods employed/demonstrated to generate droplets on a spinning platform. An overview on the detection platforms is also presented to understand the challenges involved in building an extreme point of care device. In the third phase of the thesis, general manufacturing techniques and materials used to accomplish this work is presented. Lastly, design trials for droplet generation is presented. The shortcomings of these trials are solved by investigating mechanisms pertaining to design modification and use of agarose based droplet generation to ensure a more robust sample
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...
International Nuclear Information System (INIS)
Boyer, Timothy H
2006-01-01
The classical electromagnetic interaction of a point charge and a magnet is discussed by first calculating the interaction of a point charge with a simple model magnetic moment and then suggesting a multiparticle limit. The Darwin-Lagrangian is used to analyse the electromagnetic behaviour of the model magnetic moment (composed of two oppositely charged particles of different masses in an initially circular Coulomb orbit) interacting with a passing point charge. Considerations of force, energy, momentum and centre of energy are treated through second order in 1/c. The changing magnetic moment is found to put a force back on a passing charge; this force is of order 1/c 2 and depends upon the magnitude of the magnetic moment. The limit of a many-particle magnet arranged as a toroid is discussed. It is suggested that in the multiparticle limit, the electric fields of the passing charge are screened out of the body of the magnet while the magnetic fields of the passing charge penetrate into the body of the magnet. This is consistent with our understanding of the penetration of electromagnetic velocity fields into ohmic conductors. The proposed multiparticle limit is consistent with the conservation laws for energy and momentum, as well as constant motion of the centre of energy, and Newton's third law for the net Lorentz forces on the magnet and on the point charge. The work corresponds to a classical electromagnetic analysis of the interaction which is basic to understanding the controversy over the Aharonov-Bohm and Aharonov-Casher phase shifts and represents a refutation of the suggestions of Aharonov, Pearle and Vaidman
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.)
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
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…
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.
Czech Academy of Sciences Publication Activity Database
Axelsson, Owe; Blaheta, Radim; Byczanski, Petr
2012-01-01
Roč. 15, č. 4 (2012), s. 191-207 ISSN 1432-9360 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : poroelasticity * saddle point matrices * preconditioning * stability of discretization Subject RIV: BA - General Mathematics http://link.springer.com/article/10.1007/s00791-013-0209-0
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 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.
Improving Inverse Dynamics Accuracy in a Planar Walking Model Based on Stable Reference Point
Directory of Open Access Journals (Sweden)
Alaa Abdulrahman
2014-01-01
Full Text Available Physiologically and biomechanically, the human body represents a complicated system with an abundance of degrees of freedom (DOF. When developing mathematical representations of the body, a researcher has to decide on how many of those DOF to include in the model. Though accuracy can be enhanced at the cost of complexity by including more DOF, their necessity must be rigorously examined. In this study a planar seven-segment human body walking model with single DOF joints was developed. A reference point was added to the model to track the body’s global position while moving. Due to the kinematic instability of the pelvis, the top of the head was selected as the reference point, which also assimilates the vestibular sensor position. Inverse dynamics methods were used to formulate and solve the equations of motion based on Newton-Euler formulae. The torques and ground reaction forces generated by the planar model during a regular gait cycle were compared with similar results from a more complex three-dimensional OpenSim model with muscles, which resulted in correlation errors in the range of 0.9–0.98. The close comparison between the two torque outputs supports the use of planar models in gait studies.
Caulkins, Jonathan P.; Feichtinger, Gustav; Grass, Dieter; Hartl, Richard F.; Kort, Peter M.; Novak, Andreas J.; Seidl, Andrea
2013-01-01
We present a novel model of corruption dynamics in the form of a nonlinear optimal dynamic control problem. It has a tipping point, but one whose origins and character are distinct from that in the classic Schelling (1978) model. The decision maker choosing a level of corruption is the chief or some other kind of authority figure who presides over a bureaucracy whose state of corruption is influenced by the authority figure’s actions, and whose state in turn influences the pay-off for the authority figure. The policy interpretation is somewhat more optimistic than in other tipping models, and there are some surprising implications, notably that reforming the bureaucracy may be of limited value if the bureaucracy takes its cues from a corrupt leader. PMID:23565027
Caulkins, Jonathan P; Feichtinger, Gustav; Grass, Dieter; Hartl, Richard F; Kort, Peter M; Novak, Andreas J; Seidl, Andrea
2013-03-16
We present a novel model of corruption dynamics in the form of a nonlinear optimal dynamic control problem. It has a tipping point, but one whose origins and character are distinct from that in the classic Schelling (1978) model. The decision maker choosing a level of corruption is the chief or some other kind of authority figure who presides over a bureaucracy whose state of corruption is influenced by the authority figure's actions, and whose state in turn influences the pay-off for the authority figure. The policy interpretation is somewhat more optimistic than in other tipping models, and there are some surprising implications, notably that reforming the bureaucracy may be of limited value if the bureaucracy takes its cues from a corrupt leader.
Toroidal regularization of the guiding center Lagrangian
Burby, J. W.; Ellison, C. L.
2017-11-01
In the Lagrangian theory of guiding center motion, an effective magnetic field B*=B +(m /e )v∥∇× b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. This letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, the Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.
Shah, Neerav
2011-01-01
The Magnetospheric MultiScale Mission (MMS) is scheduled to launch in late 2014. Its primary goal is to discover the fundamental plasma physics processes of reconnection in the Earth's magnetosphere. Each of the four MMS spacecraft is spin-stabilized at a nominal rate of 3 RPM. Traditional spin-stabilized spacecraft have used a number of separate modes to control nutation, spin rate, and precession. To reduce the number of modes and simplify operations, the Delta-H control mode is designed to accomplish nutation control, spin rate control, and precession control simultaneously. A nonlinear design technique, Lyapunov's method, is used to design the Delta-H control mode. A global spin rate controller selected as the baseline controller for MMS, proved to be insufficient due to an ambiguity in the attitude. Lyapunov's design method was used to solve this ambiguity, resulting in a controller that meets the design goals. Simulation results show the advantage of the pointing and rate controller for maneuvers larger than 90 deg and provide insight into the performance of this controller.
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.
Borsten, L; Ferrara, S; Marrani, A
2013-01-01
The global U-dualities of extended supergravity have played a central role in differentiating the distinct classes of extremal black hole solutions. When the U-duality group satisfies certain algebraic conditions, as is the case for a broad class of supergravities, the extremal black holes enjoy a further symmetry known as Freudenthal duality (F-duality), which although distinct from U-duality preserves the Bekenstein-Hawking entropy. Here it is shown that, by adopting the doubled Lagrangian formalism, F-duality, defined on the doubled field strengths, is not only a symmetry of the black hole solutions, but also of the equations of motion themselves. A further role for F-duality is introduced in the context of world-sheet actions. The Nambu-Goto world-sheet action in any (t, s) signature spacetime can be written in terms of the F-dual. The corresponding field equations and Bianchi identities are then related by F-duality allowing for an F-dual formulation of Gaillard-Zumino duality on the world-sheet. An equi...
Stability analysis of Eulerian-Lagrangian methods for the one-dimensional shallow-water equations
Casulli, V.; Cheng, R.T.
1990-01-01
In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined Eulerian-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit Eulerian-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the Eulerian-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses. ?? 1990.
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.
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
The Lagrangian in Quantum Mechanics
Dirac, P. A. M.
Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue, as a result of which the whole of the classical Hamiltonian theory, which is just a structure built up on this notion, could be taken over in all its details into quantum mechanics. Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. In the first place the Lagrangian method allows one to collect together all the equations of motion and express them as the stationary property of a certain action function. (This action function is just the time-integral of the Lagrangian.) There is no corresponding action principle in terms of the coordinates and momenta of the Hamiltonian theory. Secondly the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially non-relativistic in form, since it marks out a particular time variable as the canonical conjugate of the Hamiltonian function. For these reasons it would seem desirable to take up the question of what corresponds in the quantum theory to the Lagrangian method of the classical theory. A little consideration shows, however, that one cannot expect to be able to take over the classical Lagrangian equations in any very direct way. These equations involve partial derivatives of the Lagrangian with respect to the coordinates and velocities and no meaning can be given to such derivatives in quantum mechanics. The only differentiation process that can be carried out with respect to the dynamical variables of
Turbulence Interface Simulation by Lagrangian Blocks
Chu, V. H.
2015-12-01
stable interface in part of the interface and the overturning in another part of the unstable interface. The process is not quantitative known until the compilation of results obtained from the present Lagrangian-block simulation. The development of the interface however is of great significance to many geo-environmental applications.
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.
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
Lagrangian continuum dynamics in ALEGRA.
Energy Technology Data Exchange (ETDEWEB)
Wong, Michael K. W.; Love, Edward
2007-12-01
Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.
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)
Energy Technology Data Exchange (ETDEWEB)
Rogers, Karyne M
2003-07-01
Stable carbon and nitrogen isotopes have been used to assess sewage contamination of a sewage outfall, discharging milli-screened effluent into Moa Point Bay, New Zealand, and monitor the recovery of flora and fauna after the outfall's closure. An initial study characterising the extent of the discharge and the effects on seaweed (Ulva lactuca L.), blue mussels (Mytilus galloprovincialis) and limpets (Cellana denticulata) from the area, showed effects of the sewage discharge on flora and fauna were localised within in the bay. The immediate area surrounding the discharge area was found to contain limited biodiversity, with an abundance of Ulva lactuca, a bright green lettuce-like seaweed, typically found in areas with high nutrient input, limpets and small blue mussels. The nitrogen isotopic signature ({delta}{sup 15}N) is shown to be a good tracer of sewage pollution in seaweed and associated grazers (i.e. limpets) as a result of the increased contribution of urea and ammonia to seawater nitrogen derived from the effluent. The carbon isotopic signature ({delta}{sup 13}C) is suggested as a more appropriate sewage tracer for mussels, which filter feed the effluent's particulate organic matter from the water. Lower carbon:nitrogen ratios were found in Ulva lactuca sampled from around the outfall region compared to uncontaminated control sites. However carbon:nitrogen ratios do not vary significantly amongst shellfish species. After closure, monitoring continued for 9 months and showed that the carbon and nitrogen isotopic signatures of algae (Ulva lactuca L.) returned to similar control site levels within 3 months. Limpet and blue mussels (Cellana denticulata and Mytilus galloprovincialis) showed slower recovery times than the Ulva lactuca, with detectable levels of the sewage-derived carbon and nitrogen remaining in the animal's tissue for up to 9 months.
International Nuclear Information System (INIS)
Rogers, Karyne M.
2003-01-01
Stable carbon and nitrogen isotopes have been used to assess sewage contamination of a sewage outfall, discharging milli-screened effluent into Moa Point Bay, New Zealand, and monitor the recovery of flora and fauna after the outfall's closure. An initial study characterising the extent of the discharge and the effects on seaweed (Ulva lactuca L.), blue mussels (Mytilus galloprovincialis) and limpets (Cellana denticulata) from the area, showed effects of the sewage discharge on flora and fauna were localised within in the bay. The immediate area surrounding the discharge area was found to contain limited biodiversity, with an abundance of Ulva lactuca, a bright green lettuce-like seaweed, typically found in areas with high nutrient input, limpets and small blue mussels. The nitrogen isotopic signature (δ 15 N) is shown to be a good tracer of sewage pollution in seaweed and associated grazers (i.e. limpets) as a result of the increased contribution of urea and ammonia to seawater nitrogen derived from the effluent. The carbon isotopic signature (δ 13 C) is suggested as a more appropriate sewage tracer for mussels, which filter feed the effluent's particulate organic matter from the water. Lower carbon:nitrogen ratios were found in Ulva lactuca sampled from around the outfall region compared to uncontaminated control sites. However carbon:nitrogen ratios do not vary significantly amongst shellfish species. After closure, monitoring continued for 9 months and showed that the carbon and nitrogen isotopic signatures of algae (Ulva lactuca L.) returned to similar control site levels within 3 months. Limpet and blue mussels (Cellana denticulata and Mytilus galloprovincialis) showed slower recovery times than the Ulva lactuca, with detectable levels of the sewage-derived carbon and nitrogen remaining in the animal's tissue for up to 9 months
Lagrangian and Hamiltonian formulation of classical electrodynamics without potentials
Vollick, Dan N.
2017-10-01
In the standard Lagrangian and Hamiltonian approach to Maxwell's theory the potentials A^{μ} are taken as the dynamical variables. In this paper I take the electric field \\overrightarrow{E} and the magnetic field \\overrightarrow{B} as the dynamical variables. I find a Lagrangian that gives the dynamical Maxwell equations and include the constraint equations by using Lagrange multipliers. In passing to the Hamiltonian one finds that the canonical momenta \\overrightarrow{Π}E and \\overrightarrow{Π}B are constrained giving 6 second class constraints at each point in space. Gauss's law and \\overrightarrow{\
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.
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.
Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations
Directory of Open Access Journals (Sweden)
Ning-Bo Tan
2013-01-01
Full Text Available An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.
Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.
Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun
2013-01-01
An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.
Lagrangian Studies of Lateral Mixing
2017-09-19
any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a...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...waves, mixing, stirring 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON Craig
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
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.
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.
Etingof, P.; Henriques, A.G.; Kamnitzer, J.; Rains, E.M.
2010-01-01
We compute the Poincaré polynomial and the cohomology algebra with rational coefficients of the manifold Mn of real points of the moduli space of algebraic curves of genus 0 with n labeled points. This cohomology is a quadratic algebra, and we conjecture that it is Koszul. We also compute the
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....... Based on an analytical result and on a sensitivity analysis, both presented here, we estimate the accuracy for filtered strain, (s) over tilde (2), and enstrophy, (omega) over tilde (2), at around 30%. The accuracy improves with higher tracer seeding density and with smaller filter scale Delta. We...
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)
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,
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
Lagrangian Vortices in Developing Tropical Cyclones
2015-06-25
Meteorological Society Q. J. R. Meteorol. Soc. (2015) Lagrangian Vortices in Developing Tropical Cyclones these vortices through diabatic vortex stretching or...through horizontal mergers. The Lagrangian structures and their role in the merger of these smaller vorticity anomalies and diabatic activation
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
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
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 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)
Directory of Open Access Journals (Sweden)
Carles Comas
2015-04-01
Full Text Available Aim of study: Understanding inter- and intra-specific competition for water is crucial in drought-prone environments. However, little is known about the spatial interdependencies for water uptake among individuals in mixed stands. The aim of this work was to compare water uptake patterns during a drought episode in two common Mediterranean tree species, Quercus ilex L. and Pinus halepensis Mill., using the isotope composition of xylem water (δ18O, δ2H as hydrological marker. Area of study: The study was performed in a mixed stand, sampling a total of 33 oaks and 78 pines (plot area= 888 m2. We tested the hypothesis that both species uptake water differentially along the soil profile, thus showing different levels of tree-to-tree interdependency, depending on whether neighbouring trees belong to one species or the other. Material and Methods: We used pair-correlation functions to study intra-specific point-tree configurations and the bivariate pair correlation function to analyse the inter-specific spatial configuration. Moreover, the isotopic composition of xylem water was analysed as a mark point pattern. Main results: Values for Q. ilex (δ18O = –5.3 ± 0.2‰, δ2H = –54.3 ± 0.7‰ were significantly lower than for P. halepensis (δ18O = –1.2 ± 0.2‰, δ2H = –25.1 ± 0.8‰, pointing to a greater contribution of deeper soil layers for water uptake by Q. ilex. Research highlights: Point-process analyses revealed spatial intra-specific dependencies among neighbouring pines, showing neither oak-oak nor oak-pine interactions. This supports niche segregation for water uptake between the two species.
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...
Ward identities for Lagrangian conformal models
International Nuclear Information System (INIS)
Lazzarini, S.; Stora, R.
1989-01-01
The present period of field theory, well represented at this conference, is actively devoted to the quantization of fields subject to a gauge symmetry. Among the most popular theories are the so-called conformal theories. The present consensus converges towards a geometric quantization scheme on moduli space where representation theory of the Virasoro algebra and extension thereof play a prominent role, but where the notion of field abruptly departs from those previously adopted: analyticity which is of an essentially non local nature replaces locality and the attached smoothness or its dual distribution aspects which allow for the consideration of arbitrary supports. Since many conformal theories are attached to a Lagrangian, it is desirable to understand, at least in these cases, how the two aspects are intermingled. ideally, this ought to be done within the framework of axiomatic and/or constructive field theory, but, this are not being yet well developed in the area of gauge theories, the authors remain at the level of the formal perturbative series. One of the weaknesses of the latter, as compared to the former namely the lost of control on positivity, at the benefit of locality may even turn into an advantage in the present situation where indefinite metric is often needed. This paper illustrates the authors' point on the simplest example which exhibits already most of the problems the authors' want to clear up: the free bosonic string
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 methods in plasma dynamics. II - Construction of Lagrangians for plasmas
Dougherty, J. P.
1974-01-01
Consideration of the construction of suitable Lagrangian functions for the dynamics of a cold plasma in such a way as to retain the relativistically covariant formalism. In one method, this is achieved by the introduction of a set of three variables which label the world lines of the particles. A second method results in a Clebsch-type representation. Sturrock's relativistic Lagrangian and Low's hot plasma Lagrangian are also briefly discussed in the context of the present work. The behavior of the canonical stress tensor is considered. The applicability of many of the general results in part I (Dougherty, 1970) is ensured by establishing the existence of the Lagrangian function.
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
Measurements of Lagrangian atmospheric dispersion statistics over open water
International Nuclear Information System (INIS)
Sheih, C.M.; Frenzen, P.; Hart, R.L.
1980-01-01
Atmospheric dispersion statistics in the Lagrangian frame have been evaluated over open water by using a double-theodolite system to track neutrally buoyant balloons released a few kilometers offshore during onshore winds. Analysis of the trajectories recorded in various atmospheric stabilities finds Lagrangian integral time scales corresponding to Pasquill stability categories C, D and E equal, respectively, to 9.0, 7.3 and 8.1 s for lateral dispersion and 2.3, 5.3 and 6.6 s for vertical dispersion. Normalized standard deviations of component velocity fluctuations (i.e., sigma/sub upsilon//u/sub asterisk/ and sigma/sub ω//u/sub asterisk/) for stability categories C, D and E are found to be 3.7, 1.8 and 2.4 for lateral motion and 2.2, 1.3 and 1.2 for vertical motion. Equivalent dispersion coefficients (sigma/sub y/ and sigma/sub z/) appropriate to flow over water are observed to undergo relatively less variation with stability than do those measured in flow over land. When compared to estimates derived from the Pasquill-Gifford curves for estimating dispersion over flat grassland, the dispersion coefficients over water are, in effect, shifted about two categories toward the stable side for the vertical component and between one and two categories toward the stable side for the lateral component
Stable orbits for lunar landing assistance
Condoleo, Ennio; Cinelli, Marco; Ortore, Emiliano; Circi, Christian
2017-10-01
To improve lunar landing performances in terms of mission costs, trajectory determination and visibility the use of a single probe located over an assistance orbit around the Moon has been taken into consideration. To this end, the properties of two quasi-circular orbits characterised by a stable behaviour of semi-major axis, eccentricity and inclination have been investigated. The analysis has demonstrated the possibility of using an assistance probe, located over one of these orbits, as a relay satellite between lander and Earth, even in the case of landings on the far side of the Moon. A comparison about the accuracy in retrieving the lander's state with respect to the use of a probe located in the Lagrangian point L2 of the Earth-Moon system has also been carried out.
International Nuclear Information System (INIS)
Rogers, K.M.
1999-01-01
Stable carbon and nitrogen isotopes have been used to characterise sewage discharge and effects on seaweed (Ulva lactuca L.), blue mussels (Mytilus galloprovincialis), and limpets (Cellana denticulata) from Moa Point Bay, New Zealand. The nitrogen ( 15 N / 14 N) ratio is shown to be a good tracer of sewage pollution in Ulva lactuca and associated grazers (Cellana denticulata) as a result of the increased contribution of urea and ammonia to the surrounding marine environment from the sewage outfall. The carbon ( 13 C / 12 C) ratio is suggested as a more appropriate sewer tracer for mussels (Mytilus galloprovincialis), which filter feed the particulate organic matter from the effluent. Lower carbon : nitrogen ratios were found in U. lactuca sampled from the outfall region, compared to uncontaminated control sites, however carbon : nitrogen ratios do not vary significantly amongst shellfish species. (author). 18 refs., 4 figs., 2 tabs
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.
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
Forecasting for a Lagrangian aircraft campaign
Directory of Open Access Journals (Sweden)
A. Stohl
2004-01-01
Full Text Available A forecast system has been developed in preparation for an upcoming aircraft measurement campaign, where the same air parcels polluted by emissions over North America shall be sampled repeatedly as they leave the continent, during transport over the Atlantic, and upon their arrival over Europe. This paper describes the model system in advance of the campaign, in order to make the flight planners familiar with the novel model output. The aim of a Lagrangian strategy is to infer changes in the chemical composition and aerosol distribution occurring en route by measured upwind/downwind differences. However, guiding aircraft repeatedly into the same polluted air parcels requires careful forecasting, for which no suitable model system exists to date. This paper describes a procedure using both Eulerian-type (i.e. concentration fields and Lagrangian-type (i.e. trajectories model output from the Lagrangian particle dispersion model FLEXPART to predict the best opportunities for a Lagrangian experiment. The best opportunities are defined as being highly polluted air parcels which receive little or no emission input after the first measurement, which experience relatively little mixing, and which are reachable by as many aircraft as possible. For validation the system was applied to the period of the NARE 97 campaign where approximately the same air masses were sampled on different flights. Measured upwind/downwind differences in carbon monoxide (CO and ozone (O3 decreased significantly as the threshold values used for accepting cases as Lagrangian were tightened. This proves that the model system can successfully identify Lagrangian opportunities.
Euler-Lagrangian computation for estuarine hydrodynamics
Cheng, Ralph T.
1983-01-01
The transport of conservative and suspended matter in fluid flows is a phenomenon of Lagrangian nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an Eulerian formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an Eulerian reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the Eulerian and Lagrangian computational techniques.
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.
Progress in mixed Eulerian-Lagrangian finite element simulation of forming processes
Huetink, Han; Vreede, P.T.; van der Lugt, J.
1990-01-01
A review is given of a mixed Eulerian-Lagrangian finite element method for simulation of forming processes. This method permits incremental adaptation of nodal point locations independently from the actual material displacements. Hence numerical difficulties due to large element distortions, as may
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.
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
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
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
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
Algebraic geometry and effective lagrangians
International Nuclear Information System (INIS)
Martinec, E.J.; Chicago Univ., IL
1989-01-01
N=2 supersymmetric Landau-Ginsburg fixed points describe nonlinear models whose target spaces are algebraic varieties in certain generalized projective spaces; the defining equation is precisely the zero set of the superpotential, considered as a condition in the projective space. The ADE classification of modular invariants arises as the classification of projective descriptions of P 1 ; in general, the hierarchy of fixed points is conjectured to be isomorphic to the classification of quasihomogeneous singularities. The condition of vanishing first Chern class is an integrality condition on the Virasoro central charge; the central charge is determined by the superpotential. The operator algebra is given by the algebra of Wick contractions of perturbations of the superpotential. (orig.)
General form of effective Lagrangian in path integral quantization formalism
Tu Tung Sheng; Yuan Tu Nan
1980-01-01
The general form of the effective lagrangian in path integral formalism is obtained. The effective lagrangian includes the classical lagrangian, the term proportional to delta (0) given by Lee and Yang (see Phys. Rev., vol.128, p.885, 1962) and the additional term which is presented explicitly in the series expansion. The formalism is explicitly covariant. (6 refs).
International Nuclear Information System (INIS)
Drechsler, W.
1977-01-01
A Lagrangian formalism invariant under the gauge group U 1 xUSpsub(2.2) is set up in terms of spinor fields defined on a fiber bundle with Cartan connexion. The fiber of the Cartan bundle over space-time associated with strong interactions is characterized by an elementary length parameter R related to the range of the strong forces, and the structural group USpsub(2.2) of the bundle (being the covering group of the SOsub(4.1) de Sitter group) implies a gauge description of strong interactions based on the noncompact gauge group USpsub(2.2). The U 1 factor in the total gauge group corresponds to the usual gauge formulation for the electromagnetic interactions. The positivity of the energy associated with stable extended one-particle states in this dualistic description of charged hadronic matter immersed in the fiber geometry (this dualism is called strong fiber dynamics (SFD)) requires hadrons to be assigned to representations of the compact subgroup SU 2 xSU 2 of the strong-interaction gauge group USpsub(2.2). A brief discussion of the point-particle limit R→O is given by linking the presented SFD formalism for extended hadrons to an idealized description in terms of operators in a local quantum field theory
Fluid Dynamics Lagrangian Simulation Model
1994-02-08
balance equation for the fluctu- 082 ating enstrophy are contained in Balint , Vukoelavce- where the vorticity is non-dimensionalized by Uo/h, vic and...point statis- According to Tennekes and Lumleys and Balint 4, tics and spectra with from the closed channel calcu- et aL, the eight terms of the...777. [4] Balint , J.-L., Vukoslavcevic, P. and Wallace, [8] Hunt, J.C.R. 1984 Turbulence structure and tur- J.M., 1988 The transport of enstrophy in a
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
Lagrangian perturbation theory for modified gravity
Aviles, Alejandro; Cervantes-Cota, Jorge L.
2017-12-01
We present a formalism to compute Lagrangian displacement fields for a wide range of cosmologies in the context of perturbation theory up to third order. We emphasize the case of theories with scale-dependent gravitational strengths, such as chameleons, but our formalism can be accommodated to other modified gravity theories. In the nonlinear regime, two qualitative features arise. One, as is well known, is that nonlinearities lead to a screening of the force mediated by the scalar field. The second is a consequence of the transformation of the Klein-Gordon equation from Eulerian to Lagrangian coordinates, producing frame lagging terms that are important especially at large scales, and if not considered, the theory does not reduce to the Λ CDM model in that limit. We apply our formalism to compute the one-loop power spectrum and the correlation function in f (R ) gravity by using different resummation schemes. We further discuss the IR divergences of these formalisms.
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.
An ambitwistor Yang-Mills Lagrangian
International Nuclear Information System (INIS)
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
Distributed Control by Lagrangian Steepest Descent
Wolpert, David H.; Bieniawski, Stefan
2004-01-01
Often adaptive, distributed control can be viewed as an iterated game between independent players. The coupling between the players' mixed strategies, arising as the system evolves from one instant to the next, is determined by the system designer. Information theory tells us that the most likely joint strategy of the players, given a value of the expectation of the overall control objective function, is the minimizer of a Lagrangian function of the joint strategy. So the goal of the system d...
Lagrangian for the Majorana-Ahluwalia construct
Dvoeglazov, V. V.
1995-12-01
The equations describing self/anti-self charge conjugate states, recently proposed by Ahluwalia, are re-written to covariant form. The corresponding Lagrangian for the neutral particle theory is proposed. From a group-theoretical viewpoint the construct is an example of the Nigam-Foldy-Bargmann-Wightman-Wigner-type quantum field theory based on the doubled representations of the extended Lorentz group. Relations with the Sachs-Schwebel and Ziino-Barut concepts of relativistic quantum theory are discussed.
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
Floating shock fitting via Lagrangian adaptive meshes
Vanrosendale, John
1995-01-01
In recent work we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.
Lagrangian Observations and Modeling of Marine Larvae
Paris, Claire B.; Irisson, Jean-Olivier
2017-04-01
Just within the past two decades, studies on the early-life history stages of marine organisms have led to new paradigms in population dynamics. Unlike passive plant seeds that are transported by the wind or by animals, marine larvae have motor and sensory capabilities. As a result, marine larvae have a tremendous capacity to actively influence their dispersal. This is continuously revealed as we develop new techniques to observe larvae in their natural environment and begin to understand their ability to detect cues throughout ontogeny, process the information, and use it to ride ocean currents and navigate their way back home, or to a place like home. We present innovative in situ and numerical modeling approaches developed to understand the underlying mechanisms of larval transport in the ocean. We describe a novel concept of a Lagrangian platform, the Drifting In Situ Chamber (DISC), designed to observe and quantify complex larval behaviors and their interactions with the pelagic environment. We give a brief history of larval ecology research with the DISC, showing that swimming is directional in most species, guided by cues as diverse as the position of the sun or the underwater soundscape, and even that (unlike humans!) larvae orient better and swim faster when moving as a group. The observed Lagrangian behavior of individual larvae are directly implemented in the Connectivity Modeling System (CMS), an open source Lagrangian tracking application. Simulations help demonstrate the impact that larval behavior has compared to passive Lagrangian trajectories. These methodologies are already the base of exciting findings and are promising tools for documenting and simulating the behavior of other small pelagic organisms, forecasting their migration in a changing ocean.
Lagrangian 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)
Inverse Variational Problem for Nonstandard Lagrangians
Saha, A.; Talukdar, B.
2014-06-01
In the mathematical physics literature the nonstandard Lagrangians (NSLs) were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of the equation of motion and solve the associated inverse problem to obtain some of the existing results for NSLs. In addition, we provide a number of alternative Lagrangian representations. The case studies envisaged by us include (i) the usual modified Emden-type equation, (ii) Emden-type equation with dissipative term quadratic in velocity, (iii) Lotka-Volterra model and (vi) a number of the generic equations for dissipative-like dynamical systems. Our method works for nonstandard Lagrangians corresponding to the usual action integral of mechanical systems but requires modification for those associated with the modified actions like S =∫abe L(x ,x˙ , t) dt and S =∫abL 1 - γ(x ,x˙ , t) dt because in the latter case one cannot construct expressions for the Jacobi integrals.
Applications the Lagrangian description in aperiodic flows
Mendoza, Carolina; Mancho, Ana Maria
2012-11-01
We use several recently developed Lagrangian tools for describing transport in general aperiodic flows. In our approach the first step is based in a Lagrangian descriptor (the so called function M). It measures the length of particle trajectories on the ocean surface over a given interval of time. We describe its output over satellite altimetry data on the Kuroshio current. The technique is combined with the direct computation of manifolds of Distinguished Hyperbolic trajectories and a very detailed description of transport is achieved across an eddy and a jet on the Kuroshio current,. A second velocity data set is examined with the M function tool. These are obtained from the HYCOM project on the Gulf of Mexico during the time of the oil-spill. We have identified underlying Lagrangian structures and dynamics. We acknowledge to the hospitality of the university of Delaware and the assistance of Bruce Lipphardt and Helga Huntley in accessing the model data sets. We acknowledge to the grants: UPM-AL12-PAC-09, Becas de Movilidad de Caja Madrid 2011, MTM2011-26696 and ILINK-0145.
Zwick, D.; Sakhaee, E.; Balachandar, S.; Entezari, A.
2017-10-01
Multiphase flow simulation serves a vital purpose in applications as diverse as engineering design, natural disaster prediction, and even study of astrophysical phenomena. In these scenarios, it can be very difficult, expensive, or even impossible to fully represent the physical system under consideration. Even still, many such real-world applications can be modeled as a two-phase flow containing both continuous and dispersed phases. Consequentially, the continuous phase is thought of as a fluid and the dispersed phase as particles. The continuous phase is typically treated in the Eulerian frame of reference and represented on a fixed grid, while the dispersed phase is treated in the Lagrangian frame and represented by a sample distribution of Lagrangian particles that approximate a cloud. Coupling between the phases requires interpolation of the continuous phase properties at the locations of the Lagrangian particles. This interpolation step is straightforward and can be performed at higher order accuracy. The reverse process of projecting the Lagrangian particle properties from the sample points to the Eulerian grid is complicated by the time-dependent non-uniform distribution of the Lagrangian particles. In this paper we numerically examine three reconstruction, or projection, methods: (i) direct summation (DS), (ii) least-squares, and (iii) sparse approximation. We choose a continuous representation of the dispersed phase property that is systematically varied from a simple single mode periodic signal to a more complex artificially constructed turbulent signal to see how each method performs in reconstruction. In these experiments, we show that there is a link between the number of dispersed Lagrangian sample points and the number of structured grid points to accurately represent the underlying functional representation to machine accuracy. The least-squares method outperforms the other methods in most cases, while the sparse approximation method is able to
A semi-Lagrangian method for DNS with large time-stepping
Xiu, Dongbin; Karniadakis, George
2000-11-01
An efficient time-step discretization based on semi-Lagrangian methods, often used in metereology, is proposed for direct numerical simulations. It is unconditionally stable and retains high-order accuracy comparable to Eulerian schemes. The structure of the total error is analyzed in detail, and shows a non-monotonic trend with the size of the time-step. Numerical experiments for a variety of flows shows that stable and accurate results are obtained with time steps more than fifty times the CFL-bound time step used in current semi-implicit DNS.
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.
Macroscopic Lagrangian description of warm plasmas. I Formulation of the Lagrangian
Peng, Y.-K. M.; Crawford, F. W.
1983-01-01
A macroscopic Lagrangian is derived which includes a pressure tensor, heat conduction, and elastic collisions. Its Euler-Lagrange equations are shown to be the Maxwell equations and the macroscopic force law. The corresponding Hamiltonian is derived, and Hamilton's canonical equations are also demonstrated to lead to the Maxwell equations and the macroscopic force law. The treatment is facilitated by working in a mixture of Eulerian coordinates (for the fields) and Lagrangian coordinates (for the particle motions), and the introduction of a macroscopic potential expressed in terms of the plasma thermal energy and the energy losses by heat conduction.
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.
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
Analytical solution of the problem of a shock wave in the collapsing gas in Lagrangian coordinates
Kuropatenko, V. F.; Shestakovskaya, E. S.
2016-10-01
It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in Lagrangian coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t0 the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and Lagrangian coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For Lagrangian coordinates the problem is first solved. It is fundamentally different from previously known formulations of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.
Lagrangian transport in a class of three-dimensional buoyancy-driven flows
Contreras, Sebastian; Speetjens, Michel; Clercx, Herman
2017-11-01
The study concerns the Lagrangian dynamics of three-dimensional (3D) buoyancy-driven cavity flows under steady and laminar conditions due to a global temperature gradient imposed via an opposite hot and cold sidewall. This serves as archetypal configuration for natural-convection flows in which gravity is perpendicular to the global temperature gradient. Limited insight into the Lagrangian properties of this class of flows motivates this study. The 3D Lagrangian dynamics are investigated in terms of the generic structure of the Lagrangian flow topology that is described in terms of the Grashof number (Gr) and the Prandtl number (Pr). Gr is the principal control parameter for the flow topology: vanishing Gr yields a state of closed streamlines (integrable state); increasing Gr causes the formation of toroidal coherent structures embedded in chaotic streamlines governed by Hamiltonian mechanisms. Fluid inertia prevails for ``smaller'' Gr. A buoyancy-induced bifurcation of the flow topology occurs for ``larger'' Gr and underlies the emergence of ``secondary rolls'' and secondary tori for ``larger'' Pr. Stagnation points and corresponding manifold interactions are key to the dynamics. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).
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.)
Lagrangians for plasmas in the drift-fluid approximation
Energy Technology Data Exchange (ETDEWEB)
Pfirsch, Dieter; Corres-Restrepo, Dario [Association Euratom-Max-Planck-Institut fuer Plasmaphysik, Garching (Germany)
1997-04-01
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 the 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 multifluid Lagrangian via an iterative approximation procedure which resembles the standard method usually applied to the equations of motion. That method, however, does not guarantee that all the conservation laws hold. (author).
The MHV Lagrangian for a spontaneously broken gauge theory
Buchta, Sebastian; Weinzierl, Stefan
2010-09-01
Starting from the standard Lagrangian for a SU(2) × U(1) gauge theory plus a Higgs field we derive the corresponding "maximal helicity violating" (MHV) Lagrangian. From this MHV Lagrangian one deduces simple diagrammatic rules for the calculation of multi-particle scattering amplitudes. We arrive at the MHV Lagrangian by a canonical change of the field variables in the light-cone gauge. We comment on the modifications which occur in a spontaneously broken gauge theory as compared to a pure (unbroken) Yang-Mills theory.
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
STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY
International Nuclear Information System (INIS)
Wang, Xin; Szalay, Alex
2016-01-01
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field
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.
International Nuclear Information System (INIS)
Bogolyubov, N.N.; Bogolyubov, N.N.; Prykarpatsky, A.K.; Prykarpatsky, A.K.
2009-01-01
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry approach developed in the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. The Dirac-type quantization procedure for the considered alternative electrodynamics models, based on the obtained canonical Hamiltonian formulations, is developed
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.
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)
Parcel Eulerian-Lagrangian fluid dynamics for rotating geophysical flows
Bokhove, Onno; Oliver, M.
2006-01-01
Parcel Eulerian-Lagrangian Hamiltonian formulations have recently been used in structure-preserving numerical schemes, asymptotic calculations and in alternative explanations of fluid parcel (in) stabilities. A parcel formulation describes the dynamics of one fluid parcel with a Lagrangian kinetic
Lagrangian formalism for constrained systems. 2. Gauge symmetries
International Nuclear Information System (INIS)
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
Continuous time random walks for the evolution of Lagrangian velocities
Dentz, Marco; Kang, Peter K.; Comolli, Alessandro; Le Borgne, Tanguy; Lester, Daniel R.
2016-11-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes the persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model the persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space-continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have nonstationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and nonstationary conditions. We provide explicit expressions for the Lagrangian velocity statistics and determine the behaviors of the mean particle velocity, velocity covariance, and particle dispersion. We find strong Lagrangian correlation and anomalous dispersion for velocity distributions that are tailed toward low velocities as well as marked differences depending on the initial conditions. The developed CTRW approach predicts the Lagrangian particle dynamics from an arbitrary initial condition based on the Eulerian velocity distribution and a characteristic correlation scale.
Upper Tolerances and Lagrangian Relaxation for the DCMSTP
DEFF Research Database (Denmark)
Turkensteen, Marcel
of networks. Many efficient solution methods for the DCMSTP rely on Lagrangian relaxation for the tight lower bounds needed to solve instances. Lagrangian procedures for the DCMSTP solve a modified version of the regular Minimum Spanning Tree Problem (MSTP) in which the degree constraint violations...... bounds within their given running times....
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
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.
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.
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.
LAGRANGIAN PARTICLE DISPERSION MODEL (LPDM) TECHNICAL DESCRIPTION
International Nuclear Information System (INIS)
Chen, K
2006-01-01
The Savannah River National Laboratory (SRNL) uses the Lagrangian Particle Dispersion Model (LPDM) in conjunction with the Regional Atmospheric Modeling System as an operational tool for emergency response consequence assessments for the Savannah River Site (SRS). The LPDM is an advanced stochastic atmospheric transport model used to transport and disperse passive tracers subject to the meteorological field generated by RAMS from sources of varying number and shape. The Atmospheric Technologies Group (ATG) of the SRNL is undertaking the task of reviewing documentation and code for LPDM Quality Assurance (QA). The LPDM QA task will include a model technical description, computer coding descriptions, model applications, and configuration control. This report provides a comprehensive technical description of the LPDM model
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.
Distributed Control by Lagrangian Steepest Descent
Wolpert, David H.; Bieniawski, Stefan
2004-01-01
Often adaptive, distributed control can be viewed as an iterated game between independent players. The coupling between the players mixed strategies, arising as the system evolves from one instant to the next, is determined by the system designer. Information theory tells us that the most likely joint strategy of the players, given a value of the expectation of the overall control objective function, is the minimizer of a function o the joint strategy. So the goal of the system designer is to speed evolution of the joint strategy to that Lagrangian mhimbhgpoint,lowerthe expectated value of the control objective function, and repeat Here we elaborate the theory of algorithms that do this using local descent procedures, and that thereby achieve efficient, adaptive, distributed control.
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.
Zhang, Yong; Meerschaert, Mark M.; Baeumer, Boris; LaBolle, Eric M.
2015-08-01
This study develops an explicit two-step Lagrangian scheme based on the renewal-reward process to capture transient anomalous diffusion with mixed retention and early arrivals in multidimensional media. The resulting 3-D anomalous transport simulator provides a flexible platform for modeling transport. The first step explicitly models retention due to mass exchange between one mobile zone and any number of parallel immobile zones. The mobile component of the renewal process can be calculated as either an exponential random variable or a preassigned time step, and the subsequent random immobile time follows a Hyper-exponential distribution for finite immobile zones or a tempered stable distribution for infinite immobile zones with an exponentially tempered power-law memory function. The second step describes well-documented early arrivals which can follow streamlines due to mechanical dispersion using the method of subordination to regional flow. Applicability and implementation of the Lagrangian solver are further checked against transport observed in various media. Results show that, although the time-nonlocal model parameters are predictable for transport with retention in alluvial settings, the standard time-nonlocal model cannot capture early arrivals. Retention and early arrivals observed in porous and fractured media can be efficiently modeled by our Lagrangian solver, allowing anomalous transport to be incorporated into 2-D/3-D models with irregular flow fields. Extensions of the particle-tracking approach are also discussed for transport with parameters conditioned on local aquifer properties, as required by transient flow and nonstationary media.
A Lagrangian View of Spring Phytoplankton Blooms
Kida, Shinichiro; Ito, Takamitsu
2017-11-01
The mechanisms of spring phytoplankton blooms are investigated from a Lagrangian framework by using a Lagrangian NPZD model that can track the movement and transfers of nutrient parcels in a turbulent environment. The model reveals that the onset of spring blooms depends on the cumulative euphotic age, which is the total time that inorganic nutrient is exposed to light before the photosynthetic conversion to phytoplankton biomass. A spring bloom, defined as a tenfold increase of near-surface phytoplankton, occurs when this cumulative euphotic age is approximately μeff-1·ln10, where μeff is the effective growth rate in the euphotic layer, regardless of the underlying mechanism. If the turbulent layer depth is shallower than the critical depth and turbulence is strong, nutrient parcels accumulate enough light exposure through multiple entries to the sun-lit zone near the surface. If turbulence is weak, as that considered in the critical turbulence theory, the accumulation of the light exposure depends on the residence time of the nutrients parcels near the surface. The spectral shape of the cumulative euphotic age can clearly distinguish these two modes of spring blooms. The spectrum shows a peak at the theoretical growth timescale when multiple entries become important, while it shows a maximum near age zero that decays with age when the near-surface residence time becomes important. Mortality increases the cumulative euphotic age necessary for a bloom but does not affect the spectral shape, suggesting that it does not alter the primary mechanism behind the accumulation of cumulative euphotic age.
Stable Orbits in the Didymos Binary Asteroid System - Useful Platforms for Exploration
Damme, Friedrich; Hussmann, Hauke; Wickhusen, Kai; Enrico, Mai; Oberst, Jürgen
2016-04-01
We have analyzed particle motion in binary asteroid systems to search for stable orbits. In particular, we studied the motion of particles near the asteroid 1996 GT (Didymos), proposed as a target for the AIDA mission. The combined gravity fields of the odd-shaped rotating objects moving about each other are complex. In addition, orbiting spacecraft or dust particles are affected by radiation pressure, possibly exceeding the faint gravitational forces. For the numerical integrations, we adopt parameters for size, shape, and rotation from telescopic observations. To simulate the effect of radiation pressure during a spacecraft mission, we apply a spacecraft wing-box shape model. Integrations were carried out beginning in near-circular orbits over 11 days, during which the motion of the particles were examined. Most orbits are unstable with particles escaping quickly or colliding with the asteroid bodies. However, with carefully chosen initial positions, we found stable motion (in the orbiting plane of the secondary) associated with the Lagrangian points (L4 and L5), in addition to horseshoe orbits, where particles move from one of the Lagrangian point to the other. Finally, we examined orbits in 1:2 resonances with the motion of the orbital period of the secondary. Stable conditions depend strongly on season caused by the inclination of the mutual orbit plane with respect to Didymos solar orbit. At larger distance from the asteroid pair, we find the well-known terminator orbits where gravitational attraction is balanced against radiation pressure. Stable orbits and long motion arcs are useful for long tracking runs by radio or Laser instruments and are well-suited for modelling of the ephemerides of the asteroid pair and gravity field mapping. Furthermore, these orbits may be useful as observing posts or as platforms for approach. These orbits may also represent traps for dust particles, an opportunity for dust collection - or possibly a hazard to spacecraft
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017-01-01
The following results are obtained for the Cauchy problem with localized initial data for the crystal lattice vibration equations with continuous and discrete time: (i) the asymptotics of the solution is determined by Lagrangian manifolds with singularities ("punctured" Lagrangian manifolds); (ii) Maslov's canonical operator is defined on such manifolds as a modification of a new representation recently obtained for the canonical operator by the present authors together with A. I. Shafarevich (Dokl. Ross. Akad. Nauk 46 (6), 641-644 (2016)); (iii) the projection of the Lagrangian manifold onto the configuration plane specifies a bounded oscillation region, whose boundary (which is naturally referred to as the leading edge front) is determined by the Hamiltonians corresponding to the limit wave equations; (iv) the leading edge front is a special caustic, which possibly contains stronger focal points. These observations, together with earlier results, lead to efficient formulas for the wave field in a neighborhood of the leading edge front.
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.
Directory of Open Access Journals (Sweden)
Zdenek Dostal
2017-01-01
Full Text Available The classical convergence theory of the augmented Lagrangian method has been developed under the assumption that the solutions satisfy a constraint qualification. The point of this note is to show that the constraint qualification can be limited to the constraints that are not enforced by the Lagrange multipliers. In particular, it follows that if the feasible set is non-empty and the inequality constraints are convex and separable, then the convergence of the algorithm is guaranteed without any additional assumptions. If the feasible set is empty and the projected gradients of the Lagrangians are forced to go to zero, then the iterates are shown to converge to the nearest well posed problem.
The probability density function (PDF) of Lagrangian Turbulence
Birnir, B.
2012-12-01
The statistical theory of Lagrangian turbulence is derived from the stochastic Navier-Stokes equation. Assuming that the noise in fully-developed turbulence is a generic noise determined by the general theorems in probability, the central limit theorem and the large deviation principle, we are able to formulate and solve the Kolmogorov-Hopf equation for the invariant measure of the stochastic Navier-Stokes equations. The intermittency corrections to the scaling exponents of the structure functions require a multiplicative (multipling the fluid velocity) noise in the stochastic Navier-Stokes equation. We let this multiplicative noise, in the equation, consists of a simple (Poisson) jump process and then show how the Feynmann-Kac formula produces the log-Poissonian processes, found by She and Leveque, Waymire and Dubrulle. These log-Poissonian processes give the intermittency corrections that agree with modern direct Navier-Stokes simulations (DNS) and experiments. The probability density function (PDF) plays a key role when direct Navier-Stokes simulations or experimental results are compared to theory. The statistical theory of turbulence is determined, including the scaling of the structure functions of turbulence, by the invariant measure of the Navier-Stokes equation and the PDFs for the various statistics (one-point, two-point, N-point) can be obtained by taking the trace of the corresponding invariant measures. Hopf derived in 1952 a functional equation for the characteristic function (Fourier transform) of the invariant measure. In distinction to the nonlinear Navier-Stokes equation, this is a linear functional differential equation. The PDFs obtained from the invariant measures for the velocity differences (two-point statistics) are shown to be the four parameter generalized hyperbolic distributions, found by Barndorff-Nilsen. These PDF have heavy tails and a convex peak at the origin. A suitable projection of the Kolmogorov-Hopf equations is the
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.
Two-dimensional Lagrangian simulation of suspended sediment
Schoellhamer, David H.
1988-01-01
A two-dimensional laterally averaged model for suspended sediment transport in steady gradually varied flow that is based on the Lagrangian reference frame is presented. The layered Lagrangian transport model (LLTM) for suspended sediment performs laterally averaged concentration. The elevations of nearly horizontal streamlines and the simulation time step are selected to optimize model stability and efficiency. The computational elements are parcels of water that are moved along the streamlines in the Lagrangian sense and are mixed with neighboring parcels. Three applications show that the LLTM can accurately simulate theoretical and empirical nonequilibrium suspended sediment distributions and slug injections of suspended sediment in a laboratory flume.
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.
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
Effective Lagrangian for a light Higgs-like scalar
Contino, Roberto; Grojean, Christophe; Muhlleitner, Margarete; Spira, Michael
2013-01-01
We reconsider the effective Lagrangian that describes a light Higgs-like boson and better clarify a few issues which were not exhaustively addressed in the previous literature. In particular we highlight the strategy to determine whether the dynamics responsible for the electroweak symmetry breaking is weakly or strongly interacting. We also discuss how the effective Lagrangian can be implemented into automatic tools for the calculation of Higgs decay rates and production cross sections. Finally, we present eHDECAY, a modified version of the program HDECAY which includes the full list of leading bosonic operators of the effective Lagrangian and implements two benchmark composite Higgs models.
Directory of Open Access Journals (Sweden)
M. Branicki
2010-03-01
Full Text Available In this work we discuss applications of Lagrangian techniques to study transport properties of flows generated by shallow water models of estuarine flows. We focus on the flow in the Chesapeake Bay generated by Quoddy (see Lynch and Werner, 1991, a finite-element (shallow water model adopted to the bay by Gross et al. (2001. The main goal of this analysis is to outline the potential benefits of using Lagrangian tools for both understanding transport properties of such flows, and for validating the model output and identifying model deficiencies. We argue that the currently available 2-D Lagrangian tools, including the stable and unstable manifolds of hyperbolic trajectories and techniques exploiting 2-D finite-time Lyapunov exponent fields, are of limited use in the case of partially mixed estuarine flows. A further development and efficient implementation of three-dimensional Lagrangian techniques, as well as improvements in the shallow-water modelling of 3-D velocity fields, are required for reliable transport analysis in such flows. Some aspects of the 3-D trajectory structure in the Chesapeake Bay, based on the Quoddy output, are also discussed.
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
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
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-...
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.
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.
A Lagrangian approach to the Loop Current eddy separation
Directory of Open Access Journals (Sweden)
F. Andrade-Canto
2013-01-01
Full Text Available Determining when and how a Loop Current eddy (LCE in the Gulf of Mexico will finally separate is a difficult task, since several detachment re-attachment processes can occur during one of these events. Separation is usually defined based on snapshots of Eulerian fields such as sea surface height (SSH but here we suggest that a Lagrangian view of the LCE separation process is more appropriate and objective. The basic idea is very simple: separation should be defined whenever water particles from the cyclonic side of the Loop Current move swiftly from the Yucatan Peninsula to the Florida Straits instead of penetrating into the NE Gulf of Mexico. The properties of backward-time finite time Lyapunov exponents (FTLE computed from a numerical model of the Gulf of Mexico and Caribbean Sea are used to estimate the "skeleton" of flow and the structures involved in LCE detachment events. An Eulerian metric is defined, based on the slope of the strain direction of the instantaneous hyperbolic point of the Loop Current anticyclone that provides useful information to forecast final LCE detachments. We highlight cases in which an LCE separation metric based on SSH contours (Leben, 2005 suggests there is a separated LCE that later reattaches, whereas the slope method and FTLE structure indicate the eddy remains dynamically connected to the Loop Current during the process.
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.
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.)
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
A Lagrangian for self-dual strings
Niarchos, Vasilis
2015-12-01
We propose a Lagrangian for the low-energy theory that resides at the (1 + 1)-dimensional intersection of N semi-infinite M2-branes ending orthogonally on M M5-branes in {R}^{1,2}× {C}^4/{Z}_k (for arbitrary positive integers N, M, k). We formulate this theory as a 2d boundary theory with explicit N=(1,1) supersymmetry that contains two superfields in the bi-fundamental representation of U( N )×U( M ) interacting with the (2+1)-dimensional U( N ) k × U( N )- k ABJM Chern-Simons-matter theory in the bulk. We postulate that the boundary theory exhibits in the deep infrared supersymmetry enhancement to N=(4,2) , or N=(4,4) depending on the value of k. Arguments in favor of the proposal follow from the study of the open string theory of a U-dual type IIB Hanany-Witten setup. To formulate the bulk-boundary interactions special care is taken to incorporate all the expected boundary effects on gauge symmetry, supersymmetry, and other global symmetries.
A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints
Energy Technology Data Exchange (ETDEWEB)
de Leon, M. [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); de Diego, D.M. [Departamento de Economia Aplicada Cuantitativa, Facultad de Ciencias Economicas y Empresariales, UNED, 28040 Madrid (Spain)
1997-06-01
We construct a constraint algorithm for singular Lagrangian systems subjected to nonholonomic constraints which generalizes that of Dirac for constrained Hamiltonian systems. {copyright} {ital 1997 American Institute of Physics.}
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 lagrangians * global symmetries Subject RIV: BE - Theoretical Physics Impact factor: 6.111, year: 2014
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.)
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
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
Lagrangian analysis of explosive models with simple inner structures
International Nuclear Information System (INIS)
Daneri, A.; Trombetti, G.
1983-01-01
Fast reactor model explosive experiments with inner structures interposed between the explosive energy source and the containment vessel have been analyzed in the paper, with reference to the COVA saries experiments IT/10, IT/11, It/12. Capability and limitations of a Lagrangian fluid dynamics analysis in such expe-rimental conditions have been discussed. The ENEA version of the Lagrangian code ASTARTE-4 has been used in the computations
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
Schwinger's effective Lagrangian from reflection and transmission amplitudes
International Nuclear Information System (INIS)
Warke, C.S.
1992-01-01
The reflection and transmission amplitudes are defined from the asymptotic form of the solution of Dirac equation of a charged fermion in the presence of uniform time independent external electromagnetic field (E, H). Schwinger's effective Lagrangian is derived from the reflection and transmission amplitudes. It is found that both the real and imaginary parts of the effective Lagrangian agree with Schwinger's expressions derived from the elegant method of proper time formalism. (author). 14 refs
BRST Lagrangian construction for spin-2 field in Einstein space
International Nuclear Information System (INIS)
Buchbinder, I.L.; Krykhtin, V.A.; Lavrov, P.M.
2010-01-01
We explore a new possibility of BRST construction in higher spin field theory to obtain a consistent Lagrangian for massive spin-2 field in Einstein space. Such approach automatically leads to gauge invariant Lagrangian with suitable auxiliary and Stueckelberg fields. It is proved that in this case a propagation of spin-2 field is hyperbolic and causal. Also we extend notion of partial masslessness for spin-2 field in the background under consideration.
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
Persistent Lagrangian transport patterns in the northwestern Gulf of Mexico
Gough, M. K.; Beron-Vera, F. J.; Olascoaga, M. J.; Sheinbaum, J.; Juoanno, J.; Duran, R.
2017-01-01
Persistent Lagrangian transport patterns at the ocean surface are revealed from Lagrangian Coherent Structures (LCSs) computed from daily climatological surface current velocities in the northwestern Gulf of Mexico (NWGoM). The velocities are produced by a submesoscale permitting regional ocean model of the Gulf of Mexico. The significance of the climatological LCSs (cLCSs) is supported with ensemble-mean drifter density evolutions from simulated and historical satellite-tracked drifter traje...
Projection operator techniques in Lagrangian mechanics: symmetrically coupled oscillators
J. N. Boyd; P. N. Raychowdhury
1980-01-01
We apply projection operator techniques to the computation of the natural frequencies of oscillation for three symmetrically coupled mechanical systems. In each case, the rotation subgroup of the full symmetry group is used to determine the projection operators with the result that the Lagrangian must be expressed in terms of complex-valued coordinates. In the coordinate system obtained from the action of the projection operators upon the original coordinates, the Lagrangian yields equations ...
A Note on the Equivalence of Post-Newtonian Lagrangian and Hamiltonian Formulations
International Nuclear Information System (INIS)
Chen Rong-Chao; Wu Xin
2016-01-01
Recently, it has been generally claimed that a low order post-Newtonian (PN) Lagrangian formulation, whose Euler-Lagrange equations are up to an infinite PN order, can be identical to a PN Hamiltonian formulation at the infinite order from a theoretical point of view. In general, this result is difficult to check because the detailed expressions of the Euler-Lagrange equations and the equivalent Hamiltonian at the infinite order are clearly unknown. However, there is no difficulty in some cases. In fact, this claim is shown analytically by means of a special first-order post-Newtonian (1PN) Lagrangian formulation of relativistic circular restricted three-body problem, where both the Euler-Lagrange equations and the equivalent Hamiltonian are not only expanded to all PN orders, but have converged functions. It is also shown numerically that both the Euler-Lagrange equations of the low order Lagrangian and the Hamiltonian are equivalent only at high enough finite orders. (paper)
International Nuclear Information System (INIS)
Ettle, James H.; Fu, C.-H.; Fudger, Jonathan P.; Mansfield, Paul R.W.; Morris, Tim R.
2007-01-01
We demonstrate that the canonical change of variables that yields the MHV lagrangian, also provides contributions to scattering amplitudes that evade the equivalence theorem. This 'ET evasion' in particular provides the tree-level (-++) amplitude, which is non-vanishing off shell, or on shell with complex momenta or in (2,2) signature, and is missing from the MHV (/aka CSW) rules. At one loop there are ET-evading diagrammatic contributions to the amplitudes with all positive helicities. We supply the necessary regularisation in order to define these contributions (and quantum MHV methods in general) by starting from the light-cone Yang-Mills lagrangian in D dimensions and making a canonical change of variables for all D-2 transverse degrees of freedom of the gauge field. In this way, we obtain dimensionally regularised three- and four-point MHV amplitudes. Returning to the one-loop (++++) amplitude, we demonstrate that its quadruple cut coincides with the known result, and show how the original light-cone Yang-Mills contributions can in fact be algebraically recovered from the ET-evading contributions. We conclude that the canonical MHV lagrangian, supplemented with the extra terms brought to correlation functions by the non-linear field transformation, provide contributions which are just a rearrangement of those from light-cone Yang-Mills and thus coincide with them both on and off shell
International Nuclear Information System (INIS)
Evans, D.K.
1986-01-01
Seventy-five percent of the world's stable isotope supply comes from one producer, Oak Ridge Nuclear Laboratory (ORNL) in the US. Canadian concern is that foreign needs will be met only after domestic needs, thus creating a shortage of stable isotopes in Canada. This article describes the present situation in Canada (availability and cost) of stable isotopes, the isotope enrichment techniques, and related research programs at Chalk River Nuclear Laboratories (CRNL)
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.
Predicting transport by Lagrangian coherent structures with a high-order method
Salman, Hayder; Hesthaven, Jan S.; Warburton, Tim; Haller, George
2007-01-01
Recent developments in identifying Lagrangian coherent structures from finite-time velocity data have provided a theoretical basis for understanding chaotic transport in general flows with aperiodic dependence on time. As these theoretical developments are extended and applied to more complex flows, an accurate and general numerical method for computing these structures is needed to exploit these ideas for engineering applications. We present an unstructured high-order hp/spectral-element method for solving the two-dimensional compressible form of the Navier-Stokes equations. A corresponding high-order particle tracking method is also developed for extracting the Lagrangian coherent structures from the numerically computed velocity fields. Two different techniques are used; the first computes the direct Lyapunov exponent from an unstructured initial particle distribution, providing easier resolution of structures located close to physical boundaries, whereas the second advects a small material line initialized close to a Lagrangian saddle point to delineate these structures. We demonstrate our algorithm on simulations of a bluff-body flow at a Reynolds number of Re = 150 and a Mach number of M = 0.2 with and without flow forcing. We show that, in the unforced flow, periodic vortex shedding is predicted by our numerical simulations that is in stark contrast to the aperiodic flow field in the case with forcing. An analysis of the Lagrangian structures reveals a transport barrier that inhibits cross-wake transport in the unforced flow. The transport barrier is broken with forcing, producing enhanced transport properties by chaotic advection and consequently improved mixing of advected scalars within the wake.
Mechanisms underlying temperature extremes in Iberia: a Lagrangian perspective
Directory of Open Access Journals (Sweden)
João A. Santos
2015-04-01
Full Text Available The mechanisms underlying the occurrence of temperature extremes in Iberia are analysed considering a Lagrangian perspective of the atmospheric flow, using 6-hourly ERA-Interim reanalysis data for the years 1979–2012. Daily 2-m minimum temperatures below the 1st percentile and 2-m maximum temperatures above the 99th percentile at each grid point over Iberia are selected separately for winter and summer. Four categories of extremes are analysed using 10-d backward trajectories initialized at the extreme temperature grid points close to the surface: winter cold (WCE and warm extremes (WWE, and summer cold (SCE and warm extremes (SWE. Air masses leading to temperature extremes are first transported from the North Atlantic towards Europe for all categories. While there is a clear relation to large-scale circulation patterns in winter, the Iberian thermal low is important in summer. Along the trajectories, air mass characteristics are significantly modified through adiabatic warming (air parcel descent, upper-air radiative cooling and near-surface warming (surface heat fluxes and radiation. High residence times over continental areas, such as over northern-central Europe for WCE and, to a lesser extent, over Iberia for SWE, significantly enhance these air mass modifications. Near-surface diabatic warming is particularly striking for SWE. WCE and SWE are responsible for the most extreme conditions in a given year. For WWE and SCE, strong temperature advection associated with important meridional air mass transports are the main driving mechanisms, accompanied by comparatively minor changes in the air mass properties. These results permit a better understanding of mechanisms leading to temperature extremes in Iberia.
Dark halos and elliptical galaxies as marginally stable dynamical systems
Energy Technology Data Exchange (ETDEWEB)
El Zant, A. A. [Centre for Theoretical Physics, Zewail City of Science and Technology, Sheikh Zayed, 12588 Giza (Egypt); The British University in Egypt, Sherouk City, Cairo 11837 (Egypt)
2013-12-10
The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold of particle positions—a context in which subtle spurious effects originating from the singularity in the two-body potential become particularly clear. We focus on the case of spherical systems, which support only regular orbits in the collisionless limit, despite the persistence of local exponential instability of N-body trajectories in the anomalous case of discrete point particle representation even as N → ∞. When the singularity in the potential is removed, this apparent contradiction disappears. In the absence of fluctuations, equilibrium configurations generally correspond to positive scalar curvature and thus support stable trajectories. A null scalar curvature is associated with an effective, averaged equation of state describing dynamically relaxed equilibria with marginally stable trajectories. The associated configurations are quite similar to those of observed elliptical galaxies and simulated cosmological halos and are necessarily different from the systems dominated by isothermal cores, expected from entropy maximization in the context of the standard theory of violent relaxation. It is suggested that this is the case because a system starting far from equilibrium does not reach a 'most probable state' via violent relaxation, but that this process comes to an end as the system finds and (settles in) a configuration where it can most efficiently wash out perturbations. We explicitly test this interpretation by means of direct simulations.
Chern-Simons topological Lagrangians in odd dimensions and their Kaluza-Klein reduction
International Nuclear Information System (INIS)
Wu, Y.
1984-01-01
Clarifying the behavior of generic Chern-Simons secondary invariants under infinitesimal variation and finite gauge transformation, it is proved that they are eligible to be a candidate term in the Lagrangian in odd dimensions (2k-1 for gauge theories and 4k-1 for gravity). The coefficients in front of these terms may be quantized because of topological reasons. As a possible application, the dimensional reduction of such actions in Kaluza-Klein theory is discussed. The difficulty in defining the Chern-Simons action for topologically nontrivial field configurations is pointed out and resolved
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.
Geometric deviation modeling by kinematic matrix based on Lagrangian coordinate
Liu, Weidong; Hu, Yueming; Liu, Yu; Dai, Wanyi
2015-09-01
Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it's expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.
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.
On frame indifferent Lagrangians of micropolar thermoelastic continuum
Directory of Open Access Journals (Sweden)
Vladimir A. Kovalev
2015-06-01
Full Text Available A non-linear mathematical model of type-II thermoelastic continuum with fine microstructure is developed. The model is described in terms of 4-covariant field theoretical formalism attributed to field theories of continuum mechanics. Fine microstructure is introduced by d-vectors and tensors playing role of extra field variables. A Lagrangian density for type-II thermoelastic continuum with fine microstructure is proposed and the least action principle is formulated. Virtual microstructural inertia is added to the considered action density. It is also valid for the thermal inertia. Corresponding 4-covariant field equations of type-II thermoelasticity are obtained. Constitutive equations of type-II microstructural thermoelasticity are discussed. Following the usual procedure for type-II micropolar thermoelastic Lagrangians functionally independent rotationally invariant arguments are obtained. Those are proved to form a complete set. Objective forms of the Lagrangians satisfying the frame indifference principle are given. Those are derived by using extrastrain vectors and tensors.
An updated Lagrangian particle hydrodynamics (ULPH) for Newtonian fluids
Tu, Qingsong; Li, Shaofan
2017-11-01
In this work, we have developed an updated Lagrangian particle hydrodynamics (ULPH) for Newtonian fluid. Unlike the smoothed particle hydrodynamics, the non-local particle hydrodynamics formulation proposed here is consistent and convergence. Unlike the state-based peridynamics, the discrete particle dynamics proposed here has no internal material bond between particles, and it is not formulated with respect to initial or a fixed referential configuration. In specific, we have shown that (1) the non-local update Lagrangian particle hydrodynamics formulation converges to the conventional local fluid mechanics formulation; (2) the non-local updated Lagrangian particle hydrodynamics can capture arbitrary flow discontinuities without any changes in the formulation, and (3) the proposed non-local particle hydrodynamics is computationally efficient and robust.
Integration over families of Lagrangian submanifolds in BV formalism
Directory of Open Access Journals (Sweden)
Andrei Mikhailov
2018-03-01
Full Text Available 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.
Lagrangian Approach to Dispersionless KdV Hierarchy
Directory of Open Access Journals (Sweden)
Amitava Choudhuri
2007-09-01
Full Text Available We derive a Lagrangian based approach to study the compatible Hamiltonian structure of the dispersionless KdV and supersymmetric KdV hierarchies and claim that our treatment of the problem serves as a very useful supplement of the so-called r-matrix method. We suggest specific ways to construct results for conserved densities and Hamiltonian operators. The Lagrangian formulation, via Noether's theorem, provides a method to make the relation between symmetries and conserved quantities more precise. We have exploited this fact to study the variational symmetries of the dispersionless KdV equation.
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.
Lagrangian dimensionality reduction of convection dominated nonlinear flows
Balajewicz, Maciej; Mojgani, Rambod
2016-11-01
We introduce a new projection-based model reduction approach for convection dominated nonlinear fluid flows. In this method the evolution of the fluid is approximated in the Lagrangian frame of reference. More specifically, global basis functions are utilized for both the state of the system and the positions of the Lagrangian computational domain. In this approach, wave-like solutions exhibit low-rank structure and thus, can be approximated efficiently using a small number of reduced bases. The proposed approach is successfully demonstrated for the reduction of several simple but representative flow problems.
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)
Projection operator techniques in Lagrangian mechanics: symmetrically coupled oscillators
Directory of Open Access Journals (Sweden)
J. N. Boyd
1980-01-01
Full Text Available We apply projection operator techniques to the computation of the natural frequencies of oscillation for three symmetrically coupled mechanical systems. In each case, the rotation subgroup of the full symmetry group is used to determine the projection operators with the result that the Lagrangian must be expressed in terms of complex-valued coordinates. In the coordinate system obtained from the action of the projection operators upon the original coordinates, the Lagrangian yields equations of motion which are separated to the maximum extent made possible by symmetry considerations.
International Nuclear Information System (INIS)
Ishida, T.
1992-01-01
The research has been in four general areas: (1) correlation of isotope effects with molecular forces and molecular structures, (2) correlation of zero-point energy and its isotope effects with molecular structure and molecular forces, (3) vapor pressure isotope effects, and (4) fractionation of stable isotopes. 73 refs, 38 figs, 29 tabs
Mayor, Fernando Sales; Askar, Attila; Rabitz, Herschel A.
1999-08-01
This paper considers the practical utility of quantum fluid dynamics (QFD) whereby the time-dependent Schrödinger's equation is transformed to observing the dynamics of an equivalent "gas continuum." The density and velocity of this equivalent gas continuum are respectively the probability density and the gradient of the phase of the wave function. The numerical implementation of the QFD equations is carried out within the Lagrangian approach, which transforms the solution of Schrödinger's equation into following the trajectories of a set of mass points, i.e., subparticles, obtained by discretization of the continuum equations. The quantum dynamics of the subparticles which arise in the present formalism through numerical discretization are coupled by the density and the quantum potential. Numerical illustrations are performed for photodissociation of NOCl and NO2 treated as two-dimensional models. The dissociation cross sections σ(ω) are evaluated in the dramatically short CPU times of 33 s for NOCl and 40 s for NO2 on a Pentium-200 MHz PC machine. The computational efficiency comes from a combination of (a) the QFD representation dealing with the near monotonic amplitude and phase as dependent variables, (b) the Lagrangian description concentrating the computation effort at all times into regions of highest probability as an optimal adaptive grid, and (c) the use of an explicit time integrator whereby the computational effort grows only linearly with the number of discrete points.
2009-04-16
Mon- teith, 1965; Jones, 1976) is used to partition net radiation absorbed by the leaves into latent heat exchange at each level based upon the...of a coupled photosynthesis- based gas exchange evapotranspiration model (GEM) for mesoscale weather forecasting applications, J. Clim. Appl. Meteorol
The gauge invariant Lagrangian for Seiberg-Witten topological monopoles
International Nuclear Information System (INIS)
Gianvittorio, R.; Martin, I.; Restuccia, A.
1995-04-01
A topological gauge invariant Lagrangian for Seiberg-Witten monopole equations is constructed. The actions is invariant under a huge class of gauge transformations which after BRST fixing leads to the BRST invariant actin associated to Seiberg-Witten monopole topological theory. The supersymmetric transformation of the fields involved in the construction is obtained from the nilpotent BRST algebra. (author). 6 refs
Comparison of Euler-Lagrangian and Fischer's Methods of ...
African Journals Online (AJOL)
This paper is aimed at comparing the prediction of dispersion coefficient of a natural stream using a new Euler-Lagrangian model, Fischer's models and Levenspiel and smith equation. In order to achieve this, stream data were extracted from \\American Stream Tracer Analysis on Humboldt River" and applied to the models.
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.
Multidimensional test assembly based on Lagrangian relaxation techniques
Veldkamp, Bernard P.
1998-01-01
In this paper, a mathematical programming approach is presented for the assembly of ability tests measuring multiple traits. The values of the variance functions of the estimators of the traits are minimized, while test specifications are met. The approach is based on Lagrangian relaxation
String Lagrangian for the Bardakci-Halpern model
International Nuclear Information System (INIS)
Antonov, E.N.; Kudryavtsev, V.A.; Lyakhov, K.B.
1984-01-01
The string Lagrangian is constructed for the Bardakci-Halpern model. The anticommuting operators carrying spin are spinors in n-dimensional space-time, rather than vectors, as in the conventional Neveu-Schwarz-Ramond model. The conservation laws leading to the gauge conditions are found
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
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
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.)
Perturbation analysis of Lagrangian invariant subspaces of symplectic matrices
Ran, A.C.M.; Mehl, Ch.; Mehrmann, V.; Rodman, L.
2009-01-01
Lagrangian invariant subspaces for symplectic matrices play an important role in the numerical solution of discrete time, robust and optimal control problems. The sensitivity (perturbation) analysis of these subspaces, however, is a difficult problem, in particular, when the eigenvalues are on or
Lagrangian approach to weakly nonlinear stability of elliptical flow
International Nuclear Information System (INIS)
Fukumoto, Y; Mie, Y; Hirota, M
2010-01-01
Rotating flows with elliptically strained streamlines suffer from parametric resonance instability between a pair of Kelvin waves whose azimuthal wavenumbers are separated by two. We address the weakly nonlinear amplitude evolution of three-dimensional (3D) Kelvin waves, in resonance, on a flow confined in a cylinder of elliptic cross-section. In a traditional Eulerian approach, derivation of the mean flow induced by nonlinear interaction of Kelvin waves stands as an obstacle. We show how a topological idea, or the Lagrangian approach, facilitates calculation of the wave-induced mean flow. A steady incompressible Euler flow is characterized as a state of the maximum of the total kinetic energy with respect to perturbations constrained to an isovortical sheet, and the isovortical perturbation is handled only in terms of the Lagrangian variables. The criticality in energy of a steady flow allows us to calculate the wave-induced mean flow only from the linear Lagrangian displacement. With the mean flow at hand, the Lagrangian approach provides us with a shortcut to enter into a weakly nonlinear amplitude evolution regime of 3D disturbances. Unlike the Eulerian approach, the amplitude equations are available directly in the Hamiltonian normal form.
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.)
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}(\
Lagrangian Predictive Skill Assessment for the Deepwater Horizon Spill
Lipphardt, B. L.; Huntley, H. S.; Sulman, M.; Kirwan, A. D.
2011-12-01
The explosion and sinking of the Deepwater Horizon drilling platform produced enormous human, ecological, and economic impacts. At the same time this disaster provided an unprecedented amount of Lagrangian information on ocean processes, including a large number of surface and near-surface drifters deployed in the northeastern Gulf of Mexico as well as remotely sensed images of the surface oil slick. In addition several global and regional ocean model predictions were used to forecast the spill movements. These models generally exhibited large variations in the mesoscale flow near the Deepwater Horizon site, even though they all assimilated similar sets of ocean observations. This provides a unique opportunity to thoroughly assess model Lagrangian predictive skill. Here, the predictive skill of one model, a regional implementation of the Hybrid Coordinate Ocean Model (HYCOM), is evaluated using data from more than 80 drifter trajectories in the northern Gulf of Mexico. These trajectories are compared with maps of Lagrangian coherent structures, computed from near-surface model velocities, to determine whether the observations are consistent with the larger scale transport structure predicted by the model. We also discuss new metrics to assess model Lagrangian predictive skill of the plume movement.
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 ...
Effective lagrangian and mass generation in supersymmetric QCD
International Nuclear Information System (INIS)
Lerche, W.; Steger, H.; Luest, D.; Muenchen Univ.
1985-01-01
We calculate the electromagnetic mass shift of composite Goldstone bosons and quasi-Goldstone fermions in supersymmetric QCD for the case where supersymmetry is explicitly broken by a photino mass term. We use an effective lagrangian approach incorporating the analogues of the p and A 1 vector mesons together with vector meson dominance. (orig.)
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
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...
Simulation on the Self-Compacting Concrete by an Enhanced Lagrangian Particle Method
Directory of Open Access Journals (Sweden)
Jun Wu
2016-01-01
Full Text Available The industry has embraced self-compacting concrete (SCC to overcome deficiencies related to consolidation, improve productivity, and enhance safety and quality. Due to the large deformation at the flowing process of SCC, an enhanced Lagrangian particle-based method, Smoothed Particles Hydrodynamics (SPH method, though first developed to study astrophysics problems, with its exceptional advantages in solving problems involving fragmentation, coalescence, and violent free surface deformation, is developed in this study to simulate the flow of SCC as a non-Newtonian fluid to achieve stable results with satisfactory convergence properties. Navier-Stokes equations and incompressible mass conservation equations are solved as basics. Cross rheological model is used to simulate the shear stress and strain relationship of SCC. Mirror particle method is used for wall boundaries. The improved SPH method is tested by a typical 2D slump flow problem and also applied to L-box test. The capability and results obtained from this method are discussed.
Energy Technology Data Exchange (ETDEWEB)
Simpson, J.J.; Gobat, J.I. (Scripps Institution of Oceanography, La Jolla, CA (United States). Digital Image Analysis Lab.)
1994-05-01
The maximum cross-correlation (MCC) method has been used to compute both oceanic and cloud velocity vectors from sequences of satellite data [e.g., advanced very high resolution radiometer (AVHRR), coastal zone color scanner (CZCS), geostationary observing earth satellite (GOES)]. Unfortunately, the two-dimensional cross-correlation functions used in the computation often contain saddlepoints, which can give rise to large magnitude and direction uncertainties in the derived velocity estimates. This paper develops a numerical iterative procedure that combines image analysis methods and dynamical constraints to minimize these difficulties. The resultant velocities are both physically realistic and numerically stable. Thus, it is also possible to compute stream functions and simulated Lagrangian drifters. The validity of these results are confirmed with independent oceanic observations. Finally, the advective-diffusive equation is solved for a few oceanic applications (e.g., prediction of sea-surface temperature, dispersal of anchovy eggs and larvae) using the derived velocities.
Three dimensional Lagrangian structures in the Antarctic Polar Vortex.
Mancho, Ana M.; Garcia-Garrido, Victor J.; Curbelo, Jezabel; Niang, Coumba; Mechoso, Carlos R.; Wiggins, Stephen
2017-04-01
Dynamical systems theory has supported the description of transport processes in fluid dynamics. For understanding trajectory patterns in chaotic advection the geometrical approach by Poincaré seeks for spatial structures that separate regions corresponding to qualitatively different types of trajectories. These structures have been referred to as Lagrangian Coherent Structures (LCS), which typically in geophysical flows are well described under the approach of incompressible 2D flows. Different tools have been used to visualize LCS. In this presentation we use Lagrangian Descriptors [1,2,3,4] (function M) for visualizing 3D Lagrangian structures in the atmosphere, in particular in the Antarctic Polar Vortex. The function M is computed in a fully 3D incompressible flow obtained from data provided by the European Centre for Medium-Range Weather Forecast and it is represented in 2D surfaces. We discuss the findings during the final warming that took place in the spring of 1979 [5]. This research is supported by MINECO grant MTM2014-56392-R. Support is acknowledged also from CSIC grant COOPB20265, U.S. NSF grant AGS-1245069 and ONR grant No. N00014- 01-1-0769. C. Niang acknowledges Fundacion Mujeres por Africa and ICMAT Severo Ochoa project SEV-2011-0087 for financial support. [1] C. Mendoza, A. M. Mancho. The hidden geometry of ocean flows. Physical Review Letters 105 (2010), 3, 038501-1-038501-4. [2] A. M. Mancho, S. Wiggins, J. Curbelo, C. Mendoza. Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems. Communications in Nonlinear Science and Numerical Simulation. 18 (2013) 3530-3557. [3] C. Lopesino, F. Balibrea-Iniesta, S. Wiggins and A. M. Mancho. Lagrangian descriptors for two dimensional, area preserving autonomous and nonautonomous maps. Communications in Nonlinear Science and Numerical Simulations, 27 (2015) (1-3), 40-51. [4] C. Lopesino, F. Balibrea-Iniesta, V. J. García-Garrido, S. Wiggins, and A
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.
International Nuclear Information System (INIS)
Samios, N.P.
1994-01-01
I have been asked to review the subject of stable particles, essentially the particles that eventually comprised the meson and baryon octets, with a few more additions - with an emphasis on the contributions made by experiments utilizing the bubble chamber technique. In this activity, much work had been done by the photographic emulsion technique and cloud chambers - exposed to cosmic rays as well as accelerator based beams. In fact, many if not most of the stable particles were found by these latter two techniques, however, the foree of the bubble chamber (coupled with the newer and more powerful accelerators) was to verify, and reinforce with large statistics, the existence of these states, to find some of the more difficult ones, mainly neutrals and further to elucidate their properties, i.e., spin, parity, lifetimes, decay parameters, etc. (orig.)
International Nuclear Information System (INIS)
Samios, N.P.
1993-01-01
I have been asked to review the subject of stable particles, essentially the particles that eventually comprised the meson and baryon octets. with a few more additions -- with an emphasis on the contributions made by experiments utilizing the bubble chamber technique. In this activity, much work had been done by the photographic emulsion technique and cloud chambers-exposed to cosmic rays as well as accelerator based beams. In fact, many if not most of the stable particles were found by these latter two techniques, however, the forte of the bubble chamber (coupled with the newer and more powerful accelerators) was to verify, and reinforce with large statistics, the existence of these states, to find some of the more difficult ones, mainly neutrals and further to elucidate their properties, i.e., spin, parity, lifetimes, decay parameters, etc
Directory of Open Access Journals (Sweden)
Nikolai N. Bogolubov
2015-04-01
Full Text Available We review new electrodynamics models of interacting charged point particles and related fundamental physical aspects, motivated by the classical A.M. Ampère magnetic and H. Lorentz force laws electromagnetic field expressions. Based on the Feynman proper time paradigm and a recently devised vacuum field theory approach to the Lagrangian and Hamiltonian, the formulations of alternative classical electrodynamics models are analyzed in detail and their Dirac type quantization is suggested. Problems closely related to the radiation reaction force and electron mass inertia are analyzed. The validity of the Abraham-Lorentz electromagnetic electron mass origin hypothesis is argued. The related electromagnetic Dirac–Fock–Podolsky problem and symplectic properties of the Maxwell and Yang–Mills type dynamical systems are analyzed. The crucial importance of the remaining reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized.
Lagrangian Coherent Structures in a Non-Euclidean Global Thermosphere
Wang, N.; Ramirez, U.; Flores, F.; Datta-Barua, S.
2016-12-01
Lagrangian Coherent Structures (LCSs) are manifolds of maximum divergence or convergence in 2D or 3D time-varying flow fields. The study of LCSs has been used to predict material transport in numerous geophysical flows. The most commonly used computational method for finding LCSs is to compute the finite time Lyapunov exponent (FTLE), a scalar field measuring the ratio of stretching after a given interval of time among neighboring particles, relative to their initial separation. LCS ridges are located at the local maxima of the FTLE. The LCS must be objective (frame-invariant for different observers), and the technique for computing the FTLE that determines the LCS typically assumes a Euclidean domain. Previous work showed that LCSs are likely to exist globally at high latitudes using the Euclidean norm. Here we refine that calculation by deriving the FTLE calculation for the Riemannian manifold of a spherical surface, and applying it to the thermospheric layer of the atmosphere globally. The thermosphere is treated as a closed spherical 2D domain on which the fluid flows, assuming negligible vertical flow. The domain is discretized in longitude and latitude, and the Horizontal Wind Model 2014 (HWM14) is used to generate the 2D velocity field at each grid point, each of which is a ground speed in the local east-north-up (ENU) frame. To make the LCS objective, the ground speed in each local ENU frame is converted to angular velocity in the earth-centered earth-fixed (ECEF) coordinates. Using bilinear interpolation and including the rotational velocity of Earth to transform to an inertial frame, we trace the trajectory of each particle to compute the final positions after the integration time. Replacing the Euclidean distance between particles with the great circle distance gives the FTLE scalar field from which the LCSs can be identified. We find and illustrate objective LCSs in the neutral wind flow field at high latitudes by applying this algorithm for the
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.
Simulating NJL-mechanism with realistic vector-type confining Lagrangian
International Nuclear Information System (INIS)
Mitra, A.N.; Delhi Univ.; Mitra, B.
1991-01-01
The concrete possibilities for a realistic simulation of the Nambu-Jona Lasino mechanism of dynamical mass generation are examined from the view-point of a Vector-type confining form of 4-fermion Lagrangian with a natural mass scale which substitutes for the canonical NJL-model of contact interaction, and is designed to keep a conscious link with spectroscopy. Such Lagrangians are known to lead (through the minimality condition on the effective Action) to both the Schwinger-Dyson and Bethe-Salpeter equations for the quark-mass operation Σ(ρ) and the hadron-quark vertex function F H (q,P) respectively. With a choice of the interactions which corresponds to a Lorentz-covariant generalization of the familiar instantaneous approximation, the related Bethe-Salpeter equation already provides a good description of both q bar q and qqq spectra, as well a Lorentz covariant access to different types of transition amplitudes via quark loops, within a common dynamical framework. With this pre-calabration, the model is subjected to the interlinked SDE and BSE for testing some key aspects of the NJL-self consistency mechanism by evaluating some basic constants. The results are: m NJL = 300 Mev, M π 2 ∼ m c ; M σ = 857 Mev; [q bar q] 0 = (219 mev) 3 . From these values two independent estimates of m c are found as 21.8 and 17.8 (Mev)
3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"
Douglass, A.
2005-01-01
The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.
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.
2015-01-01
Stable beams: two simple words that carry so much meaning at CERN. When LHC page one switched from "squeeze" to "stable beams" at 10.40 a.m. on Wednesday, 3 June, it triggered scenes of jubilation in control rooms around the CERN sites, as the LHC experiments started to record physics data for the first time in 27 months. This is what CERN is here for, and it’s great to be back in business after such a long period of preparation for the next stage in the LHC adventure. I’ve said it before, but I’ll say it again. This was a great achievement, and testimony to the hard and dedicated work of so many people in the global CERN community. I could start to list the teams that have contributed, but that would be a mistake. Instead, I’d simply like to say that an achievement as impressive as running the LHC – a machine of superlatives in every respect – takes the combined effort and enthusiasm of everyone ...
Fully Lagrangian Renormalized Approximation theory of fluid turbulence: Progress report
International Nuclear Information System (INIS)
Frieman, E.A.; Hagan, W.K.
1988-01-01
The purpose of this paper is to discuss our refinement and extension of the work of Y. Kaneda on a Lagrangian Renormalized Approximation (LRA) for homogeneous hydrodynamic turbulence. Kaneda's results are important to the development of a consistent theory of turbulence because the LRA theory successfully overcomes the failure of other turbulence theories (namely the Direct Interaction Approximation) to predict the Kolmogorov wavenumber spectrum. It is thought that this success is due to the use of a Lagrangian rather than Eulerian description of the fluid so that convection of the small eddies by the large ones is properly treated. However, some aspects of these results are puzzling and are considered here. For example, the form of the correlation function and the value of the Kolmogorov constant, K, depend on the choice of the form of the correlation function
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.
Yasutake, Nobutoshi; Fujisawa, Kotaro; Yamada, Shoichi
2016-12-01
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.
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
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.
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.
Theoretical study (Lagrangian modeling) of turbulent particulate dispersion
Berlemont, A.; Grancher, M. S.; Desjonqueres, P.
A study aimed at improving the prediction and knowledge of two phase phenomena in a turbomachine is presented. A code to three dimensionally simulate particle dispersion, taking account of turbulent droplet evaporation, and which can be easily integrated into the DIAMANT code, is developed. Lagrangian modeling of particle dispersion is used. The influence of turbulence on evaporation appears to be non-negligible and must therefore be taken into account in droplet turbulent transfer problems.
Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
Montenegro, David; Torrieri, Giorgio
2016-09-01
We rederive relativistic hydrodynamics as a Lagrangian effective theory using the doubled coordinates technique, allowing us to include dissipative terms. We include Navier-Stokes shear and bulk terms, as well as Israel-Stewart relaxation time terms, within this formalism. We show how the inclusion of shear dissipation forces the inclusion of the Israel-Stewart term into the theory, thereby providing an additional justification for the form of this term.
Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds
Yau, S-T
2002-01-01
The collection of articles in this volume are based on lectures presented during the Winter School on Mirror Symmetry held at Harvard University. There are many new directions suggested by mirror symmetry which could potentially have very rich connections in physics and mathematics. This book brings together the latest research in a major area of mathematical physics, including the recent progress in mirror manifolds and Lagrangian submanifolds. In particular, several articles describing homological approach and related topics are included.
Forecasting Future Sea Ice Conditions: A Lagrangian Approach
2015-09-30
Journal of Climate, in revision). The decadal forecasting of the minimum sea ice extent based on the output of 30 ensemble members of the Community...1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Forecasting Future Sea Ice Conditions: A Lagrangian...1- Show from observations whether the dynamics of the multi -year pack ice has a influence on the location of the following summer MIZ. 2
Updated Lagrangian formulation for corrected smooth particle hydrodynamics
Huerta, Antonio; Vidal Seguí, Yolanda; Bonet Carbonell, Javier
2006-01-01
Smooth Particle Hydrodynamics (SPH) are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may be necessary in some problems involving extremely large distortions. If a standard updated formulation is implemented in SPH zero energy modes are activated and spoil the solution. It is important to note that the updated Lagrangian does not present tension instability but only zero energy modes. Here an stabilization techn...
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 Enstrophy Dynamics in Highly Turbulent Premixed Flames
Darragh, Ryan; Towery, Colin; Poludnenko, Alexei; Hamlington, Peter
2017-11-01
Turbulent combustion is a multi-scale and multi-physics problem depending upon both chemical and fluid dynamic processes. These processes are often examined using an Eulerian framework, but recently the Lagrangian framework, a long-time tool in non-reacting flow research, has become increasingly common for the study of turbulent combustion. The two analysis frameworks are in fact equivalent, with the only difference being a change in reference frame. In this study, a Lagrangian fluid parcel tracking algorithm is used to analyze the enstrophy (i.e., vorticity magnitude) dynamics in turbulent premixed reacting flows. The analysis of vorticity dynamics in the premixed flame case is based on data from a three dimensional direct numerical simulation of a premixed stoichiometric hydrogen-air flame in an unconfined domain. Enstrophy budget terms are tracked along Lagrangian trajectories as fluid parcels travel through the flame, with particular focus on understanding the dynamical causes of turbulence variations through the flame preheat and reaction zones with respect to both the fluid parcel and the flame. Additionally, the ability of trajectories to completely sample the flame is discussed.
Lagrangian chaos in three- dimensional steady buoyancy-driven flows
Contreras, Sebastian; Speetjens, Michel; Clercx, Herman
2016-11-01
Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside a cubic cavity differentially-heated from the side. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. The Lagrangian dynamics are controlled by the Péclet number (Pe) and the Prandtl number (Pr). Pe controls the behaviour qualitatively in that growing Pe progressively perturbs the integable state (Pe =0), thus paving the way to chaotic dynamics. Pr plays an entirely quantitative role in that Pr1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).
Lagrangian-based investigation of the transient flow structures around a pitching hydrofoil
Wu, Qin; Huang, Biao; Wang, Guoyu
2016-02-01
The objective of this paper is to address the transient flow structures around a pitching hydrofoil by combining physical and numerical studies. In order to predict the dynamic behavior of the flow structure effectively, the Lagrangian coherent structures (LCS) defined by the ridges of the finite-time Lyapunov exponent (FTLE) are utilized under the framework of Navier-Stokes flow computations. In the numerical simulations, the k-ω shear stress transport (SST) turbulence model, coupled with a two-equation γ {-Re}_θ transition model, is used for the turbulence closure. Results are presented for a NACA66 hydrofoil undergoing slowly and rapidly pitching motions from 0° to 15° then back to 0° at a moderate Reynolds number Re=7.5× 105. The results reveal that the transient flow structures can be observed by the LCS method. For the slowly pitching case, it consists of five stages: quasi-steady and laminar, transition from laminar to turbulent, vortex development, large-scale vortex shedding, and reverting to laminar. The observation of LCS and Lagrangian particle tracers elucidates that the trailing edge vortex is nearly attached and stable during the vortex development stage and the interaction between the leading and trailing edge vortex caused by the adverse pressure gradient forces the vortexes to shed downstream during the large-scale vortex shedding stage, which corresponds to obvious fluctuations of the hydrodynamic response. For the rapidly pitching case, the inflection is hardly to be observed and the stall is delayed. The vortex formation, interaction, and shedding occurred once instead of being repeated three times, which is responsible for just one fluctuation in the hydrodynamic characteristics. The numerical results also show that the FTLE field has the potential to identify the transient flows, and the LCS can represent the divergence extent of infinite neighboring particles and capture the interface of the vortex region.
Technical note: The Lagrangian particle dispersion model FLEXPART version 6.2
Directory of Open Access Journals (Sweden)
A. Stohl
2005-01-01
Full Text Available The Lagrangian particle dispersion model FLEXPART was originally (about 8 years ago designed for calculating the long-range and mesoscale dispersion of air pollutants from point sources, such as after an accident in a nuclear power plant. In the meantime FLEXPART has evolved into a comprehensive tool for atmospheric transport modeling and analysis. Its application fields were extended from air pollution studies to other topics where atmospheric transport plays a role (e.g., exchange between the stratosphere and troposphere, or the global water cycle. It has evolved into a true community model that is now being used by at least 25 groups from 14 different countries and is seeing both operational and research applications. A user manual has been kept actual over the years and was distributed over an internet page along with the model's source code. In this note we provide a citeable technical description of FLEXPART's latest version (6.2.
Photobioreactors for microalgal cultures: A Lagrangian model coupling hydrodynamics and kinetics.
Olivieri, Giuseppe; Gargiulo, Luigi; Lettieri, Paola; Mazzei, Luca; Salatino, Piero; Marzocchella, Antonio
2015-01-01
Closed photobioreactors have to be optimized in terms of light utilization and overall photosynthesis rate. A simple model coupling the hydrodynamics and the photosynthesis kinetics has been proposed to analyze the photosynthesis dynamics due to the continuous shuttle of microalgae between dark and lighted zones of the photobioreactor. Microalgal motion has been described according to a stochastic Lagrangian approach adopting the turbulence model suitable for the photobioreactor configuration (single vs. two-phase flows). Effects of light path, biomass concentration, turbulence level and irradiance have been reported in terms of overall photosynthesis rate. Different irradiation strategies (internal, lateral and rounding) and several photobioreactor configurations (flat, tubular, bubble column, airlift) have been investigated. Photobioreactor configurations and the operating conditions to maximize the photosynthesis rate have been pointed out. Results confirmed and explained the common experimental observation that high concentrated cultures are not photoinhibited at high irradiance level. © 2015 American Institute of Chemical Engineers.
Relativistic Hartree-Fock theory. Part I: density-dependent effective Lagrangians
Energy Technology Data Exchange (ETDEWEB)
LongWen Hui [School of Physics, Peking University, 100871 Beijing (China)]|[CNRS-IN2P3, UMR 8608, F-91406 Orsay Cedex (France)]|[Univ Paris-Sud, F-91405 Orsay (France); Giai, Nguyen Van [CNRS-IN2P3, UMR 8608, F-91406 Orsay Cedex (France)]|[Univ Paris-Sud, F-91405 Orsay (France); Meng, Jie [School of Physics, Peking University, 100871 Beijing (China)]|[Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing (China)]|[Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, 730000 Lanzhou (China)
2006-10-15
Effective Lagrangians suitable for a relativistic Hartree-Fock description of nuclear systems are presented. They include the 4 effective mesons {sigma}, {omega}, {rho} and {pi} with density-dependent meson-nucleon couplings. The criteria for determining the model parameters are the reproduction of the binding energies in a number of selected nuclei, and the bulk properties of nuclear matter (saturation point, compression modulus, symmetry energy). An excellent description of nuclear binding energies and radii is achieved for a range of nuclei encompassing light and heavy systems. The predictions of the present approach compare favorably with those of existing relativistic mean field models, with the advantage of incorporating the effects of pion-nucleon coupling. (authors)
The Lagrangian particle dispersion model FLEXPART-WRF VERSION 3.1
Energy Technology Data Exchange (ETDEWEB)
Brioude, J.; Arnold, D.; Stohl, A.; Cassiani, M.; Morton, Don; Seibert, P.; Angevine, W. M.; Evan, S.; Dingwell, A.; Fast, Jerome D.; Easter, Richard C.; Pisso, I.; Bukhart, J.; Wotawa, G.
2013-11-01
The Lagrangian particle dispersion model FLEXPART was originally designed for cal- culating long-range and mesoscale dispersion of air pollutants from point sources, such as after an accident in a nuclear power plant. In the meantime FLEXPART has evolved into a comprehensive tool for atmospheric transport modeling and analysis at different scales. This multiscale need from the modeler community has encouraged new developments in FLEXPART. In this document, we present a version that works with the Weather Research and Forecasting (WRF) mesoscale meteoro- logical model. Simple procedures on how to run FLEXPART-WRF are presented along with special options and features that differ from its predecessor versions. In addition, test case data, the source code and visualization tools are provided to the reader as supplementary material.
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
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.
Eulerian and Lagrangian approaches to multidimensional condensation and collection
Li, Xiang-Yu; Brandenburg, A.; Haugen, N. E. L.; Svensson, G.
2017-06-01
Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow or just gravitational acceleration without gas flow. Good agreement between the different schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. The Lagrangian superparticle schemes are found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results. For the Eulerian scheme, gravitational collection is rather sensitive to the mass bin resolution, but not so in the case with turbulence.type="synopsis">type="main">Plain Language SummaryThe bottleneck problem of cloud droplet growth is one of the most challenging problems in cloud physics. Cloud droplet growth is neither dominated by condensation nor gravitational collision in the size range of 15 μm ˜ 40 μm [1]. Turbulence-generated collection has been thought to be the mechanism to bridge the size gap, i.e., the bottleneck problem. This study compares the Lagrangian and Eulerian schemes in detail to tackle with the turbulence-generated collection.
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...... select and use tidal currents so that a profiler can autonomously reach a desired destination. After presenting the profiler and possible modifications for a coastal environment, we introduce simple mathematical models for the profiler and its environment. We then present a feedback controller that...
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.)
Application of Newton's method to Lagrangian dynamical systems
International Nuclear Information System (INIS)
Kook, Hyung-tae; Meiss, J.D.
1989-01-01
An algorithm for Newton's method is presented to find periodic orbits for N degree-of-freedom Lagrangian mappings. The computation time of the method is proportional to n, the period of the orbit, and the required storage space is reduced to ο(n). The construction of the algorithm is based upon block-diagonalization of the Hessian matrix of the action function. The index of the action function, which is closely related to orbital stability, is obtained during execution of the algorithm. 12 refs., 1 fig
Lagrangian dynamical geography of the Gulf of Mexico
Miron, P.; Beron-Vera, F. J.; Olascoaga, M. J.; Sheinbaum, J.; P?rez-Brunius, P.; Froyland, G.
2017-01-01
We construct a Markov-chain representation of the surface-ocean Lagrangian dynamics in a region occupied by the Gulf of Mexico (GoM) and adjacent portions of the Caribbean Sea and North Atlantic using satellite-tracked drifter trajectory data, the largest collection so far considered. From the analysis of the eigenvectors of the transition matrix associated with the chain, we identify almost-invariant attracting sets and their basins of attraction. With this information we decompose the GoM's...
Bao, Weizhu
2013-01-01
We propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating Bose-Einstein condensates (BECs) in a rotational frame with or without longrange dipole-dipole interaction (DDI). We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with an angular momentum rotation term and/or long-range DDI, state the twodimensional (2D) GPE obtained from the 3D GPE via dimension reduction under anisotropic external potential, and review some dynamical laws related to the 2D and 3D GPEs. By introducing a rotating Lagrangian coordinate system, the original GPEs are reformulated to GPEs without the angular momentum rotation, which is replaced by a time-dependent potential in the new coordinate system. We then cast the conserved quantities and dynamical laws in the new rotating Lagrangian coordinates. Based on the new formulation of the GPE for rotating BECs in the rotating Lagrangian coordinates, a time-splitting spectral method is presented for computing the dynamics of rotating BECs. The new numerical method is explicit, simple to implement, unconditionally stable, and very efficient in computation. It is spectral-order accurate in space and second-order accurate in time and conserves the mass on the discrete level. We compare our method with some representative methods in the literature to demonstrate its efficiency and accuracy. In addition, the numerical method is applied to test the dynamical laws of rotating BECs such as the dynamics of condensate width, angular momentum expectation, and center of mass, and to investigate numerically the dynamics and interaction of quantized vortex lattices in rotating BECs without or with the long-range DDI.Copyright © by SIAM.
Zehe, Erwin; Jackisch, Conrad; Rodriguez, Nicolas; Klaus, Julian
2017-04-01
Only a minute amount of global fresh water is stored in the unsaturated zone. Yet this tiny compartment controls soil microbial activity and associated trace gas emissions, transport and transformations of contaminants, plant productivity, runoff generation and groundwater recharge. To date, the processes controlling renewal and age of different fractions of the soil water stock are far from being understood. Current theories and process concepts were largely inferred either from over-simplified laboratory experiments, or non-exhaustive point observations and tracer data in the field. Tracer data provide key but yet integrated information about the distribution of travel times of the tracer molecules to a certain depth or on their travel depth distribution within a given time. We hence are able to observe the "effect" of soil structure i.e. partitioning of infiltrating water between fast preferential and slow flow paths and imperfect subsequent mixing between these flow paths in the subsurface and the related plant water uptake. However, we are not able to study the "cause" - because technologies for in-situ observations of flow, flow path topology and exchange processes at relevant interfaces have up to now not been at hand. In the present study we will make use of a Lagrangian model for subsurface water dynamics to explore how subsurface heterogeneity and mixing among different storage fractions affects residence time distribution in the unsaturated zone in a forward approach. Soil water is represented by particles of constant mass, which travel according to the Itô form of the Fokker Planck equation. The model concept builds on established soil physics by estimating the drift velocity and the diffusion term based on the soil water characteristics. The model has been shown to simulate capillary driven soil moisture dynamics in good accordance with a) the Richards equation and b) observed soil moisture data in different soil. The particle model may furthermore
Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches
International Nuclear Information System (INIS)
Antonowicz, M.; Szczyrba, W.
1985-01-01
We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8 = 12 independent degrees of freedom in the phase space
Spinor matter fields in SL(2,C) gauge theories of gravity: Lagrangian and Hamiltonian approaches
Antonowicz, Marek; Szczyrba, Wiktor
1985-06-01
We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariant formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8=12 independent degrees of freedom in the phase space.
Lagrangian transported MDF methods for compressible high speed flows
Gerlinger, Peter
2017-06-01
This paper deals with the application of thermochemical Lagrangian MDF (mass density function) methods for compressible sub- and supersonic RANS (Reynolds Averaged Navier-Stokes) simulations. A new approach to treat molecular transport is presented. This technique on the one hand ensures numerical stability of the particle solver in laminar regions of the flow field (e.g. in the viscous sublayer) and on the other hand takes differential diffusion into account. It is shown in a detailed analysis, that the new method correctly predicts first and second-order moments on the basis of conventional modeling approaches. Moreover, a number of challenges for MDF particle methods in high speed flows is discussed, e.g. high cell aspect ratio grids close to solid walls, wall heat transfer, shock resolution, and problems from statistical noise which may cause artificial shock systems in supersonic flows. A Mach 2 supersonic mixing channel with multiple shock reflection and a model rocket combustor simulation demonstrate the eligibility of this technique to practical applications. Both test cases are simulated successfully for the first time with a hybrid finite-volume (FV)/Lagrangian particle solver (PS).
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.
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.
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
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.
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.
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,
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
Dosio, A.; Vilà-Guerau de Arellano, J.; Holtslag, A.A.M.; Builtjes, P.J.H.
2005-01-01
Eulerian and Lagrangian statistics in the atmospheric convective boundary layer (CBL) are studied by means of large eddy simulation (LES). Spectra analysis is performed in both the Eulerian and Lagrangian frameworks, autocorrelations are calculated, and the integral length and time scales are
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.
Optimisation of production from an oil-reservoir using augmented Lagrangian methods
Energy Technology Data Exchange (ETDEWEB)
Doublet, Daniel Christopher
2007-07-01
This work studies the use of augmented Lagrangian methods for water flooding production optimisation from an oil reservoir. Commonly, water flooding is used as a means to enhance oil recovery, and due to heterogeneous rock properties, water will flow with different velocities throughout the reservoir. Due to this, water breakthrough can occur when great regions of the reservoir are still unflooded so that much of the oil may become 'trapped' in the reservoir. To avoid or reduce this problem, one can control the production so that the oil recovery rate is maximised, or alternatively the net present value (NPV) of the reservoir is maximised. We have considered water flooding, using smart wells. Smart wells with down-hole valves gives us the possibility to control the injection/production at each of the valve openings along the well, so that it is possible to control the flowregime. One can control the injection/production at all valve openings, and the setting of the valves may be changed during the production period, which gives us a great deal of control over the production and we want to control the injection/ production so that the profit obtained from the reservoir is maximised. The problem is regarded as an optimal control problem, and it is formulated as an augmented Lagrangian saddle point problem. We develop a method for optimal control based on solving the Karush-Kuhn-Tucker conditions for the augmented Lagrangian functional, a method, which to my knowledge has not been presented in the literature before. The advantage of this method is that we do not need to solve the forward problem for each new estimate of the control variables, which reduces the computational effort compared to other methods that requires the solution of the forward problem every time we find a new estimate of the control variables, such as the adjoint method. We test this method on several examples, where it is compared to the adjoint method. Our numerical experiments show
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.
An improved Lagrangian relaxation and dual ascent approach to facility location problems
DEFF Research Database (Denmark)
Jörnsten, Kurt; Klose, Andreas
2016-01-01
in finding an optimal solution to a mixed integer program than a “solver” applied to the initial MIP formulation, provided that “small” optimal multiplier values can be found in a few iterations. Recently, a simplification of the semi-Lagrangian relaxation scheme has been suggested in the literature...... 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...
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.
Effective Lagrangian Approach to pion photoproduction from the nucleon
International Nuclear Information System (INIS)
Fernandez-Ramirez, C.; Moya de Guerra, E.; Udias, J.M.
2006-01-01
We present a pion photoproduction model on the free nucleon based on an Effective Lagrangian Approach (ELA) which includes the nucleon resonances (Δ(1232), N(1440), N(1520), N(1535), Δ(1620), N(1650), and Δ(1700)), in addition to Born and vector meson exchange terms. The model incorporates a new theoretical treatment of spin-3/2 resonances, first introduced by Pascalutsa, avoiding pathologies present in previous models. Other main features of the model are chiral symmetry, gauge invariance, and crossing symmetry. We use the model combined with modern optimization techniques to assess the parameters of the nucleon resonances on the basis of world data on electromagnetic multipoles. We present results for electromagnetic multipoles, differential cross-sections, asymmetries, and total cross-sections for all one pion photoproduction processes on free nucleons. We find overall agreement with data from threshold up to 1 GeV in laboratory frame
Phonatory sound sources in terms of Lagrangian Coherent Structures
McPhail, Michael; Krane, Michael
2015-11-01
Lagrangian Coherent Structures (LCS) are used to identify sound sources in phonation. Currently, it is difficult to causally relate changes in airflow topology from voice disorders to changes in voiced sound production. LCS reveals a flow's topology by decomposing the flow into regions of distinct dynamics. The aeroacoustic sources can be written in terms of the motion of these regions in terms of the motion of the boundaries of the distinct regions. Breaking down the flow into constituent parts shows how each distinct region contributes to sound production. This approach provides a framework to connect changes in anatomy from a voice disorder to measurable changes in the resulting sound. This approach is presented for simulations of some canonical cases of vortex sound generation, and a two-dimensional simulation of phonation. Acknowledge NIH grant 2R01 2R01DC005642.
Lagrangian formulation of symmetric space sine-Gordon models
Bakas, Ioannis; Shin, H J; Park, Q Han
1996-01-01
The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim \\sigma-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F \\supset G \\supset H. We show that for every symmetric space F/G, the generalized sine-Gordon models can be derived from the G/H WZW action, plus a potential term that is algebraically specified. Thus, the symmetric space sine-Gordon models describe certain integrable perturbations of coset conformal field theories at the classical level. We also briefly discuss their vacuum structure, Backlund transformations, and soliton solutions.
Alignment of Disks with Lagrangian Stretching in Turbulence
Hunt, Conor; Tierney, Lydia; Kramel, Stefan; Voth, Greg
2015-11-01
We study Lagrangian stretching in isotropic turbulence in order to understand both the rotations of disks and the preferential alignment of vorticity with the intermediate strain rate eigenvector. Using velocity gradient tensors from a numerical simulation of homogeneous isotropic turbulence at Rλ = 180, we calculate the Cauchy-Green strain tensors whose eigenvectors provide a natural basis for studying stretching phenomenon. Previous work has shown that rods preferentially align with the vorticity as a result of both quantities independently aligning with the extensional Cauchy-Green eigenvector. In contrast, disks orient with their symmetry axis perpendicular to vorticity and preferentially align with the compressional Cauchy-Green eigenvector. We also find that the intermediate strain rate eigenvector is aligned with the extensional Cauchy-Green eigenvector. A natural consequence is that the intermediate strain rate eigenvector is aligned with the vorticity vector since conservation of angular momentum aligns vorticity with the direction it has been stretched.
Quantitative evolution of global strings from the Lagrangian viewpoint
International Nuclear Information System (INIS)
Yamaguchi, Masahide; Yokoyama, Jun'ichi
2003-01-01
We clarify the quantitative nature of the cosmological evolution of a global string network, that is, the energy density, peculiar velocity, velocity squared, Lorentz factor, formation rate of loops, and emission rate of Nambu-Goldstone bosons, based on a new type of numerical simulation of scalar fields in Eulerian meshes. We give a detailed explanation of a method to extract the above-mentioned quantities to characterize string evolution by analyzing scalar fields in Eulerian meshes from a Lagrangian viewpoint. We confirm our previous claim that the number of long strings per horizon volume in a global string network is smaller than in the case of a local string network by a factor of ∼10 even under cosmological situations, and its reason is clarified
MESOI: an interactive Lagrangian trajectory puff diffusion model
Energy Technology Data Exchange (ETDEWEB)
Ramsdell, J.V.; Athey, G.F.
1981-12-01
MESOI is an interactive Lagrangian trajectory puff diffusion model based on an earlier model by Start and Wendell at the Air Resources Laboratory Field Office at Idaho Falls, Idaho. Puff trajectories are determined using spatially and temporally varying wind fields. Diffusion in the puffs is computed as a function of distance traveled and atmospheric stability. Exposures are computed at nodes of a 31 by 31 grid. There is also provision for interpolation of short term exposures at off-grid locations. This report discusses: the theoretical bases of the model, the numerical approach used in the model, and the sensitivity and accuracy of the model. It contains a description of the computer program and a listing of the code. MESOI is written in FORTRAN. A companion report (Athey, Allwine and Ramsdell, 1981) contains a user's guide to MESOI and documents utility programs that maintain the data files needed by the model.
Quantization of second-order Lagrangians: Model problem
Moore, R. A.; Scott, T. C.
1991-08-01
Many aspects of a model problem, the Lagrangian of which contains a term depending quadratically on the acceleration, are examined in the regime where the classical solution consists of two independent normal modes. It is shown that the techniques of conversion to a problem of Lagrange, generalized mechanics, and Dirac's method for constrained systems all yield the same canonical form for the Hamiltonian. It is also seen that the resultant canonical equations of motion are equivalent to the Euler-Lagrange equations. In canonical form, all of the standard results apply, quantization follows in the usual way, and the interpretation of the results is straightforward. It is also demonstrated that perturbative methods fail, both classically and quantum mechanically, indicating the need for the nonperturbative techniques applied herein. Finally, it is noted that this result may have fundamental implications for certain relativistic theories.
The 3D Lagrangian Integral Method. Henrik Koblitz Rasmussen
DEFF Research Database (Denmark)
Rasmussen, Henrik Koblitz
2003-01-01
The numerical simulation of 3D time-dependent viscoelastic flow is of interest in connection with plastic moulding operations. In a large range of polymer processing methods, the most important issue is to find the temporal development of the free surface (or interface) of the plastic....... 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...... with a second order Runge-Kutta integration method. In any development of a numerical method for viscoelastic flow it is important to focus on the constitutive equation associated to the method. For instance the K-BKZ model is not adequate to describe both shear and extensional flow using the same constitutive...
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.
On the Number of Mather Measures of Lagrangian Systems
Bernard, Patrick
2010-09-01
In 1996, Ricardo Ricardo Mañé discovered that Mather measures are in fact the minimizers of a “universal” infinite dimensional linear programming problem. This fundamental result has many applications, of which one of the most important is to the estimates of the generic number of Mather measures. Mañé obtained the first estimation of that sort by using finite dimensional approximations. Recently, we were able, with Gonzalo Contreras, to use this method of finite dimensional approximation in order to solve a conjecture of John Mather concerning the generic number of Mather measures for families of Lagrangian systems. In the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem. We use a notion of countably rectifiable sets of finite codimension in Banach (and Frechet) spaces which may deserve independent interest.
Lagrangian dynamical geography of the Gulf of Mexico.
Miron, P; Beron-Vera, F J; Olascoaga, M J; Sheinbaum, J; Pérez-Brunius, P; Froyland, G
2017-08-01
We construct a Markov-chain representation of the surface-ocean Lagrangian dynamics in a region occupied by the Gulf of Mexico (GoM) and adjacent portions of the Caribbean Sea and North Atlantic using satellite-tracked drifter trajectory data, the largest collection so far considered. From the analysis of the eigenvectors of the transition matrix associated with the chain, we identify almost-invariant attracting sets and their basins of attraction. With this information we decompose the GoM's geography into weakly dynamically interacting provinces, which constrain the connectivity between distant locations within the GoM. Offshore oil exploration, oil spill contingency planning, and fish larval connectivity assessment are among the many activities that can benefit from the dynamical information carried in the geography constructed here.
Two stable steady states in the Hodgkin-Huxley axons
Aihara, K.; Matsumoto, G.
1983-01-01
Two stable steady states were found in the numerical solution of the Hodgkin-Huxley equations for the intact squid axon bathed in potassium-rich sea water with an externally applied inward current. Under the conditions the two stable steady-states exist, the Hodgkin-Huxley equations have a complex bifurcation structure including, in addition to the two stable steady-states, a stable limit cycle, two unstable equilibrium points, and one asymptotically stable equilibrium point. It was also conc...
International Nuclear Information System (INIS)
Basit, Abdul; Raza, S Shoaib; Irfan, Naseem
2006-01-01
In this paper a Monte Carlo model for describing the atmospheric dispersion of radionuclides (represented by Lagrangian particles/neutral tracers) continuously released into a stable planetary boundary layer is presented. The effect of variation in release height and wind directional shear on plume dispersion is studied. The resultant plume concentration and dose rate at the ground is also calculated. The turbulent atmospheric parameters, like vertical profiles of fluctuating wind velocity components and eddy lifetime, were calculated using empirical relations for a stable atmosphere. The horizontal and vertical dispersion coefficients calculated by a numerical Lagrangian model are compared with the original and modified Pasquill-Gifford and Briggs empirical σs. The comparison shows that the Monte Carlo model can successfully predict dispersion in a stable atmosphere using the empirical turbulent parameters. The predicted ground concentration and dose rate contours indicate a significant increase in the affected area when wind shear is accounted for in the calculations
The Lagrangian Map and Lie Symmetries in Magnetohydrodynamics and Gas Dynamics
Ko, C. M.; Webb, G. M.; Ratkiewicz, R. E.; Zank, G. P.
2007-12-01
We explore the role of the Lagrangian map for Lie symmetries in magnetohydrodynamics and gas dynamics. By converting the Eulerian Lie point symmetries of the Galilean group to Lagrange label space, in which the Eulerian position is regarded as a function of the Lagrange fluid label and time t, one finds that there is an infinite class of symmetries in Lagrange label space that map onto each Lie point symmetry. This involves the solution of the Lie determining equations for the fluid relabeling symmetries. We also consider a class of scaling symmetries for a gas with a constant adiabatic index. These symmetries map onto a modified form of the fluid relabeling symmetry determining equations with non-zero source terms. We investigate under what conditions the scaling symmetries give rise to conservation laws, and find that the conservation laws depend on the initial entropy, density and magnetic field of the fluid. Lie algebraic structures in Lagrange label space corresponding to the symmetries are investigated.
National Oceanic and Atmospheric Administration, Department of Commerce — Tissue samples (skin, bone, blood, muscle) are analyzed for stable carbon, stable nitrogen, and stable sulfur analysis. Many samples are used in their entirety for...
Parameterizing Urban Canopy Layer transport in an Lagrangian Particle Dispersion Model
Stöckl, Stefan; Rotach, Mathias W.
2016-04-01
The percentage of people living in urban areas is rising worldwide, crossed 50% in 2007 and is even higher in developed countries. High population density and numerous sources of air pollution in close proximity can lead to health issues. Therefore it is important to understand the nature of urban pollutant dispersion. In the last decades this field has experienced considerable progress, however the influence of large roughness elements is complex and has as of yet not been completely described. Hence, this work studied urban particle dispersion close to source and ground. It used an existing, steady state, three-dimensional Lagrangian particle dispersion model, which includes Roughness Sublayer parameterizations of turbulence and flow. The model is valid for convective and neutral to stable conditions and uses the kernel method for concentration calculation. As most Lagrangian models, its lower boundary is the zero-plane displacement, which means that roughly the lower two-thirds of the mean building height are not included in the model. This missing layer roughly coincides with the Urban Canopy Layer. An earlier work "traps" particles hitting the lower model boundary for a recirculation period, which is calculated under the assumption of a vortex in skimming flow, before "releasing" them again. The authors hypothesize that improving the lower boundary condition by including Urban Canopy Layer transport could improve model predictions. This was tested herein by not only trapping the particles, but also advecting them with a mean, parameterized flow in the Urban Canopy Layer. Now the model calculates the trapping period based on either recirculation due to vortex motion in skimming flow regimes or vertical velocity if no vortex forms, depending on incidence angle of the wind on a randomly chosen street canyon. The influence of this modification, as well as the model's sensitivity to parameterization constants, was investigated. To reach this goal, the model was
Directory of Open Access Journals (Sweden)
Debra Lewis
2013-05-01
Full Text Available Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual of the symmetry group. Setting aside the structures – symplectic, Poisson, or variational – generating dynamical systems from such functions highlights the common features of their construction and analysis, and supports the construction of analogous functions in non-Hamiltonian settings. If the symmetry group is nonabelian, the functions are invariant only with respect to the isotropy subgroup of the given parameter value. Replacing the parametrized family of functions with a single function on the product manifold and extending the action using the (coadjoint action on the algebra or its dual yields a fully invariant function. An invariant map can be used to reverse the usual perspective: rather than selecting a parametrized family of functions and finding their critical points, conditions under which functions will be critical on specific orbits, typically distinguished by isotropy class, can be derived. This strategy is illustrated using several well-known mechanical systems – the Lagrange top, the double spherical pendulum, the free rigid body, and the Riemann ellipsoids – and generalizations of these systems.
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
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
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.)
Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdSd space
International Nuclear Information System (INIS)
Buchbinder, I.L.; Krykhtin, V.A.; Ryskina, L.L.
2009-01-01
We apply the BRST approach, developed for higher spin field theories, to Lagrangian construction for totally antisymmetric massive fermionic fields in AdS d space. As well as generic higher spin massive theories, the obtained Lagrangian theory is a reducible gauge model containing, besides the basic field, a number of auxiliary (Stueckelberg) fields and the order of reducibility grows with the value of the rank of the antisymmetric field. However, unlike the generic higher spin theory, for the special case under consideration we show that one can get rid of all the auxiliary fields and the final Lagrangian for fermionic antisymmetric field is formulated only in terms of basic field.
The Lagrangian Ensemble metamodel for simulating plankton ecosystems
Woods, J. D.
2005-10-01
This paper presents a detailed account of the Lagrangian Ensemble (LE) metamodel for simulating plankton ecosystems. It uses agent-based modelling to describe the life histories of many thousands of individual plankters. The demography of each plankton population is computed from those life histories. So too is bio-optical and biochemical feedback to the environment. The resulting “virtual ecosystem” is a comprehensive simulation of the plankton ecosystem. It is based on phenotypic equations for individual micro-organisms. LE modelling differs significantly from population-based modelling. The latter uses prognostic equations to compute demography and biofeedback directly. LE modelling diagnoses them from the properties of individual micro-organisms, whose behaviour is computed from prognostic equations. That indirect approach permits the ecosystem to adjust gracefully to changes in exogenous forcing. The paper starts with theory: it defines the Lagrangian Ensemble metamodel and explains how LE code performs a number of computations “behind the curtain”. They include budgeting chemicals, and deriving biofeedback and demography from individuals. The next section describes the practice of LE modelling. It starts with designing a model that complies with the LE metamodel. Then it describes the scenario for exogenous properties that provide the computation with initial and boundary conditions. These procedures differ significantly from those used in population-based modelling. The next section shows how LE modelling is used in research, teaching and planning. The practice depends largely on hindcasting to overcome the limits to predictability of weather forecasting. The scientific method explains observable ecosystem phenomena in terms of finer-grained processes that cannot be observed, but which are controlled by the basic laws of physics, chemistry and biology. What-If? Prediction ( WIP), used for planning, extends hindcasting by adding events that describe
Movement and collision of Lagrangian particles in hydro-turbine intakes: a case study
Energy Technology Data Exchange (ETDEWEB)
Romero-Gomez, Pedro [Research Engineer, Hydrology Group, Pacific Northwest National Laboratory, Richland, WA 99354, USA; Richmond, Marshall C. [(IAHR Member), Chief Engineer, Hydrology Group, Pacific Northwest National Laboratory, Richland, WA 99354, USA
2017-03-03
Studies of the stress/survival of migratory fish during downstream passage through operating hydro-turbines are normally conducted to determine the fish-friendliness of units. One field approach consisting of recording extreme hydraulics with autonomous sensors is largely sensitive to the conditions of sensor release and the initial trajectories at the turbine intake. This study applies a modelling strategy based on flow simulations using computational fluid dynamics and Lagrangian particle tracking to represent the travel of live fish and autonomous sensor devices through hydro-turbine intakes. For the flow field calculation, the simulations were conducted with both a time-averaging turbulence model and an eddy-resolving technique. For the particle tracking calculation, different modelling assumptions for turbulence forcing, mass formulation, buoyancy, and release condition were tested. The modelling assumptions are evaluated with respect to data sets collected using a laboratory physical model and an autonomous sensor device deployed at Ice Harbor Dam (Snake River, State of Washington, U.S.A.) at the same discharge and release point as in the present computer simulations. We found an acceptable agreement between the simulated results and observed data and discuss relevant features of Lagrangian particle movement that are critical in turbine design and in the experimental design of field studies.
Directory of Open Access Journals (Sweden)
M. Dütsch
2018-02-01
Full Text Available Stable water isotopes are naturally available tracers of moisture in the atmosphere. Due to isotopic fractionation, they record information about condensation and evaporation processes during the transport of air parcels, and therefore present a valuable means for studying the global water cycle. However, the meteorological processes driving isotopic variations are complex and not very well understood so far, in particular on short (hourly to daily timescales. This study presents a Lagrangian method for attributing the isotopic composition of air parcels to meteorological processes, which provides new insight into the isotopic history of air parcels. It is based on the temporal evolution of the isotope ratios, the humidity, the temperature, and the location of the air parcels. Here these values are extracted along 7-day backward trajectories started every 6 hours from near the surface in a 30-year regional climate simulation over Europe with the isotope-enabled version of the model of the Consortium for Small-Scale Modelling (COSMOiso. The COSMOiso simulation has a horizontal resolution of 0.25° and is driven at the lateral boundaries by a T106 global climate simulation with the isotope-enabled version of the European Centre Hamburg model (ECHAMwiso. Both simulations are validated against measurements from the Global Network of Isotopes in Precipitation (GNIP, which shows that nesting COSMOiso within ECHAMwiso improves the representation of δ2H and deuterium excess in monthly accumulated precipitation. The method considers all isotopic changes that occur inside the COSMOiso model domain, which, on average, correspond to more than half of the mean and variability in both δ2H and deuterium excess at the air parcels' arrival points. Along every trajectory, the variations in the isotope values are quantitatively decomposed into eight process categories (evaporation from the ocean, evapotranspiration from land, mixing with moister air, mixing
Dütsch, Marina; Pfahl, Stephan; Meyer, Miro; Wernli, Heini
2018-02-01
Stable water isotopes are naturally available tracers of moisture in the atmosphere. Due to isotopic fractionation, they record information about condensation and evaporation processes during the transport of air parcels, and therefore present a valuable means for studying the global water cycle. However, the meteorological processes driving isotopic variations are complex and not very well understood so far, in particular on short (hourly to daily) timescales. This study presents a Lagrangian method for attributing the isotopic composition of air parcels to meteorological processes, which provides new insight into the isotopic history of air parcels. It is based on the temporal evolution of the isotope ratios, the humidity, the temperature, and the location of the air parcels. Here these values are extracted along 7-day backward trajectories started every 6 hours from near the surface in a 30-year regional climate simulation over Europe with the isotope-enabled version of the model of the Consortium for Small-Scale Modelling (COSMOiso). The COSMOiso simulation has a horizontal resolution of 0.25° and is driven at the lateral boundaries by a T106 global climate simulation with the isotope-enabled version of the European Centre Hamburg model (ECHAMwiso). Both simulations are validated against measurements from the Global Network of Isotopes in Precipitation (GNIP), which shows that nesting COSMOiso within ECHAMwiso improves the representation of δ2H and deuterium excess in monthly accumulated precipitation. The method considers all isotopic changes that occur inside the COSMOiso model domain, which, on average, correspond to more than half of the mean and variability in both δ2H and deuterium excess at the air parcels' arrival points. Along every trajectory, the variations in the isotope values are quantitatively decomposed into eight process categories (evaporation from the ocean, evapotranspiration from land, mixing with moister air, mixing with drier air
Stability properties of nonlinear dynamical systems and evolutionary stable states
Energy Technology Data Exchange (ETDEWEB)
Gleria, Iram, E-mail: iram@fis.ufal.br [Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL (Brazil); Brenig, Leon [Faculté des Sciences, Université Libre de Bruxelles, 1050 Brussels (Belgium); Rocha Filho, Tarcísio M.; Figueiredo, Annibal [Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília-DF (Brazil)
2017-03-18
Highlights: • We address the problem of equilibrium stability in a general class of non-linear systems. • We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems. • We show that an interior ES point may be related to stable interior fixed points of QP systems. - Abstract: In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.
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
Stable convergence and stable limit theorems
Häusler, Erich
2015-01-01
The authors present a concise but complete exposition of the mathematical theory of stable convergence and give various applications in different areas of probability theory and mathematical statistics to illustrate the usefulness of this concept. Stable convergence holds in many limit theorems of probability theory and statistics – such as the classical central limit theorem – which are usually formulated in terms of convergence in distribution. Originated by Alfred Rényi, the notion of stable convergence is stronger than the classical weak convergence of probability measures. A variety of methods is described which can be used to establish this stronger stable convergence in many limit theorems which were originally formulated only in terms of weak convergence. Naturally, these stronger limit theorems have new and stronger consequences which should not be missed by neglecting the notion of stable convergence. The presentation will be accessible to researchers and advanced students at the master's level...
International Nuclear Information System (INIS)
Ramsdell, J.V.; Athey, G.F.; Glantz, C.S.
1983-11-01
MESOI Version 2.0 is an interactive Lagrangian puff model for estimating the transport, diffusion, deposition and decay of effluents released to the atmosphere. The model is capable of treating simultaneous releases from as many as four release points, which may be elevated or at ground-level. The puffs are advected by a horizontal wind field that is defined in three dimensions. The wind field may be adjusted for expected topographic effects. The concentration distribution within the puffs is initially assumed to be Gaussian in the horizontal and vertical. However, the vertical concentration distribution is modified by assuming reflection at the ground and the top of the atmospheric mixing layer. Material is deposited on the surface using a source depletion, dry deposition model and a washout coefficient model. The model also treats the decay of a primary effluent species and the ingrowth and decay of a single daughter species using a first order decay process. This report is divided into two parts. The first part discusses the theoretical and mathematical bases upon which MESOI Version 2.0 is based. The second part contains the MESOI computer code. The programs were written in the ANSI standard FORTRAN 77 and were developed on a VAX 11/780 computer. 43 references, 14 figures, 13 tables
Phenomenology of the Higgs effective Lagrangian via F eynR ules
Alloul, Adam; Fuks, Benjamin; Sanz, Verónica
2014-04-01
The Higgs discovery and the lack of any other hint for new physics favor a description of non-standard Higgs physics in terms of an effective field theory. We present an implementation of a general Higgs effective Lagrangian containing operators up to dimension six in the framework of F eynR ules and provide details on the translation between the mass and interaction bases, in particular for three- and four-point interaction vertices involving Higgs and gauge bosons. We illustrate the strengths of this implementation by using the UFO interface of F eynR ules capable to generate model files that can be understood by the M adG raph 5 event generator and that have the specificity to contain all interaction vertices, without any restriction on the number of external legs or on the complexity of the Lorentz structures. We then investigate several new physics effects in total rates and differential distributions for different Higgs production modes, including gluon fusion, associated production with a gauge boson and di-Higgs production. We finally study contact interactions of gauge and Higgs bosons to fermions.
Energy Technology Data Exchange (ETDEWEB)
Ramsdell, J.V.; Athey, G.F.; Glantz, C.S.
1983-11-01
MESOI Version 2.0 is an interactive Lagrangian puff model for estimating the transport, diffusion, deposition and decay of effluents released to the atmosphere. The model is capable of treating simultaneous releases from as many as four release points, which may be elevated or at ground-level. The puffs are advected by a horizontal wind field that is defined in three dimensions. The wind field may be adjusted for expected topographic effects. The concentration distribution within the puffs is initially assumed to be Gaussian in the horizontal and vertical. However, the vertical concentration distribution is modified by assuming reflection at the ground and the top of the atmospheric mixing layer. Material is deposited on the surface using a source depletion, dry deposition model and a washout coefficient model. The model also treats the decay of a primary effluent species and the ingrowth and decay of a single daughter species using a first order decay process. This report is divided into two parts. The first part discusses the theoretical and mathematical bases upon which MESOI Version 2.0 is based. The second part contains the MESOI computer code. The programs were written in the ANSI standard FORTRAN 77 and were developed on a VAX 11/780 computer. 43 references, 14 figures, 13 tables.
Codis, Sandrine; Gavazzi, Raphaël; Pichon, Christophe; Gouin, Céline
2017-09-01
Aims: Gravitational lensing allows us to quantify the angular distribution of the convergence field around clusters of galaxies to constrain their connectivity to the cosmic web. We describe the corresponding theory in Lagrangian space in which analytical results can be obtained by identifying clusters to peaks in the initial field. Methods: We derived the three-point Gaussian statistics of a two-dimensional (2D) field and its first and second derivatives. The formalism allowed us to study the statistics of the field in a shell around a central peak, in particular its multipolar decomposition. Results: The peak condition is shown to significantly remove power from the dipolar contribution and to modify the monopole and quadrupole. As expected, higher order multipoles are not significantly modified by the constraint. Analytical predictions are successfully checked against measurements in Gaussian random fields. The effect of substructures and radial weighting is shown to be small and does not change the qualitative picture.The non-linear evolution is shown to induce a non-linear bias of all multipoles proportional to the cluster mass. Conclusions: We predict the Gaussian and weakly non-Gaussian statistics of multipolar moments of a 2D field around a peak as a proxy for the azimuthal distribution of the convergence field around a cluster of galaxies. A quantitative estimate of this multipolar decomposition of the convergence field around clusters in numerical simulations of structure formation and in observations will be presented in two forthcoming papers.
GPU acceleration of Eulerian-Lagrangian particle-laden turbulent flow simulations
Richter, David; Sweet, James; Thain, Douglas
2017-11-01
The Lagrangian point-particle approximation is a popular numerical technique for representing dispersed phases whose properties can substantially deviate from the local fluid. In many cases, particularly in the limit of one-way coupled systems, large numbers of particles are desired; this may be either because many physical particles are present (e.g. LES of an entire cloud), or because the use of many particles increases statistical convergence (e.g. high-order statistics). Solving the trajectories of very large numbers of particles can be problematic in traditional MPI implementations, however, and this study reports the benefits of using graphical processing units (GPUs) to integrate the particle equations of motion while preserving the original MPI version of the Eulerian flow solver. It is found that GPU acceleration becomes cost effective around one million particles, and performance enhancements of up to 15x can be achieved when O(108) particles are computed on the GPU rather than the CPU cluster. Optimizations and limitations will be discussed, as will prospects for expanding to two- and four-way coupled systems. ONR Grant No. N00014-16-1-2472.
Toroidal Lagrangian Flow Structues in highly viscous fluids by moving bent rods
Chtcheprov, Pavel; Camassa, Roberto; Holz, David; Marron, David; Martindale, James; McLaughlin, Richard; Vicci, Leandra; Zhao, Longhua
2010-11-01
Motile cilia play a large role in fluid motion across the surface of ciliates. Flows caused by the cilia move debris and mucus through mass beat patterns controlled by the motor proteins while rotating about the basal body that attaches the cilium to the cell surface. This study approximates the cilium as a slender body rotating about a point of contact of one of its ends in a viscous fluid. The bent rod sweeps out a virtual cone with a chord connecting both ends. The bend of the rod, the cone angle, the angle between the central axis to the normal plane, and the angle of rotation of the bent rod about its chord affect the flow patterns in a Stokes fluid. The slender body theory allows for an asymptotic solution of the Lagrangian trajectories and flow patterns caused by the precessing rod, which can be directly compared to experimental data. Altering the above parameters produces different toroidal flow structures. Using 3D stereo calibration, accurate quantified comparisons of epicyclic particle trajectories in short and long time are made against the model predictions.
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.
A perturbation-theoretic approach to Lagrangian flow networks
Fujiwara, Naoya; Kirchen, Kathrin; Donges, Jonathan F.; Donner, Reik V.
2017-03-01
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway, or airline infrastructures over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (as arising if the background flow is perturbed itself). Our results demonstrate that in all three cases, changes to the steady state solution can be analytically expressed in terms of the eigensystem of the unperturbed flow and the perturbation itself. These results are potentially relevant for developing more efficient strategies for coping with contaminations of fluid or gaseous media such as ocean and atmosphere by oil spills, radioactive substances, non-reactive chemicals, or volcanic aerosols.
Leaving Flatland: 3-D Aspects of Lagrangian Coherent Structures
Kirwan, A. D.; Huntley, H. S.; Lipphardt, B. L.; Sulman, M.
2011-12-01
Methodologies arising from dynamical systems theory are widely used in oceanography to describe flow properties and quantify stirring processes. Of particular interest are special material curves that delineate transport pathways in transient mesoscale eddy fields. To date oceanographic applications have been almost entirely restricted to considerations of the near surface, with the tacit assumption of zero vertical velocity. Even in two dimensions, these material curves are tedious to calculate, and many scientists rely on surrogates such as finite time/space Lyapunov exponents to define Lagrangian Coherent Structures (LCS). Extending such dynamical systems concepts to include depth dependence in a realistic setting presents difficult computational and theoretical challenges. We discuss several of these here. Specifically, we use a range of models, from toy problems to regional data assimilating ocean models, to answer such questions as: Can 3D transport pathways in ocean general circulation models be adequately delineated by material surfaces derived from 2D curves at many levels and stitched together -- or are 3D trajectories, which rely on small and noisy vertical velocity estimates, necessary? How representative are near-surface LCS of LCS below 200 m? What is the shape of LCS around an individual eddy, especially near the bottom of the eddy?
GR angular momentum in the quadratic spinor Lagrangian formulation
Li, Siao-Jing
2016-08-01
We inquire into the question of whether the quadratic spinor Lagrangian (QSL) formulation can describe the angular momentum for a general-relativistic system. The QSL Hamiltonian has previously been shown to be able to yield an energy-momentum quasilocalization which brings a proof of the positive gravitational energy when the spinor satisfies the conformal Witten equation. After inspection, we find that, under the constraint that the spinor on the asymptotic boundary is a constant, the QSL Hamiltonian is successful in giving an angular momentum quasilocalization. We also make certain the spinor in the Hamiltonian plays the role of a gauge field, a warrant of our permission to impose constraints on the spinor. Then, by some adjustment of the QSL Hamiltonian, we gain a covariant center-of-mass moment quasilocalization only under the condition that the displacement on the asymptotic boundary is a Killing boost vector. We expect the spinor expression will bring a proof of some connection between the gravitational energy and angular momentum.
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.
A Lagrangian particle model for marginally heavy gas dispersion
Gopalakrishnan, S. G.; Sharan, Maithili
A simple approach within the framework of Lagrangian particle models was formulated to deal with gas vapours which are marginally affected by gravity and are also subjected to entrainment. For the model discussed in this study, a plume particle represents a small parcel of air and the pollutant. This parcel is subjected to the downward acceleration due to its excess of density over the surrounding. The mean downward motion of each particle was accounted by considering the Langevin equation with buoyancy correction term (Van Dop, 1992, Atmospheric Environment26A, 1335-1346). Further, the effect of entrainment was considered in a simple statistical way similar to the method considered by Cogan (1985, Atmospheric Environment21, 867-878). As an example, the formulation was used to study the dispersion of methyl isocyanate (MIC) that was accidentally released from the Union Carbide pesticide plant (Bhopal). A series of computer runs suggests that the particle model with the new formulation that accounts for heaviness and entrainment mechanisms simulates the transport and diffusion of marginally heavy gas vapours realistically.
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 two-phase coupled Eulerian-Lagrangian FEM for offshore spudcan analysis
Yi, Jiang Tao; Lee, Fook Hou; Li, Yu Ping; Zhang, Xi Ying; Goh, Siang Huat
2013-10-01
This paper reports a development of a two-phase coupled Eulerian-Lagrangian FEM for analyzing the short-and long-term response of offshore spudcan footing. The proposed method is composed of three integral components which are effective stress Eulerian analysis for the shrot-term installation behavior of spudcan, mesh-to-mesh solution variable mapping and coupled-flow Lagrangian analysis for the post-installation, long-term working behaviour of spudcan. By combining the advantages of Eulerian and Lagrangian finite element methods, this coupled Eulerian-Lagrangian FEM is tailored to solve offshore foundation problems which often see rapid and large-scale undrained soil flow during installation followed by much longer periods of embedment in the ground during operation.
Formal Killing fields for minimal Lagrangian surfaces in complex space forms
Wang, Joe S.
2017-04-01
The differential system for minimal Lagrangian surfaces in a 2C-dimensional, non-flat, complex space form is an elliptic integrable system defined on the Grassmann bundle of oriented Lagrangian 2-planes. This is a 6-symmetric space associated with the Lie group SL(3 , C) , and the minimal Lagrangian surfaces arise as the primitive maps. Utilizing this property, we derive the inductive differential algebraic formulas for a pair of the formal loop algebra sl(3 , C) [ [ λ ] ] -valued canonical formal Killing fields. For applications, (a) we give a complete classification of the (pseudo) Jacobi fields for the minimal Lagrangian system, (b) we obtain an infinite sequence of conservation laws from the components of the canonical formal Killing fields.
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...
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.
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.
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
The representation of the Heisenberg-Euler Lagrangian by means of special functions
International Nuclear Information System (INIS)
Mielniczuk, W.J.
1982-01-01
A representation of the real part of the Heisenberg-Euler Lagrangian density in quantum electrodynamics is obtained by means of special functions. It is shown that this representation is very convenient for numerical calculations of the real part of the Heisenberg-Euler Lagrangian density and its use for calculations of a quantum electrodynamical field energy density in the absence of real charges and for calculations of polarisation and magnetisation of the vacuum, is examined. (author)
National Aeronautics and Space Administration — The code in the stableGP package implements Gaussian process calculations using efficient and numerically stable algorithms. Description of the algorithms is in the...
International Nuclear Information System (INIS)
Davidson, R.M.
1992-01-01
The author investigates theoretical uncertainties and model dependence in the extraction of the nucleon-delta(1232) electromagnetic transition amplitudes from the multipole data base. The starting point is an effective Lagrangian incorporating chiral symmetry, which includes at the tree level the pseudovector Born terms, leading t-channel vector meson exchanges, and s and u channel delta exchanges. The nucleon-delta magnetic dipole (M1) and electric quadrupole (E2) transition amplitudes are expressed in terms of two independent gauge couplings at the γNΔ vertex. After unitarizing the tree level amplitude, the gauge couplings are fitted to various multipole data sets, thus determining E2 and M1. Although there is much sensitivity to the method used to unitarize the amplitude, the author extracts the E2/M1 ratio to be negative, with a magnitude around 1.5%. 11 refs., 3 figs
Phase-space Lagrangian dynamics of incompressible thermofluids
Tessarotto, Marco; Cremaschini, Claudio; Tessarotto, Massimo
2009-09-01
Phase-space Lagrangian dynamics in ideal fluids (i.e., continua) is usually related to the so-called ideal tracer particles. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves. An unsolved theoretical problem is the correct definition of their dynamics in ideal fluids. The issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system, underlying a prescribed fluid system, which uniquely generates its time-evolution. The goal of this paper is to show that the tracer-particle dynamics can be exactly established for an arbitrary incompressible fluid uniquely based on the construction of an inverse kinetic theory (IKT) [M. Tessarotto, M. Ellero, Bull. Am. Phys. Soc. 45 (9) (2000) 40; M. Tessarotto, M. Ellero, AIP Conf. Proc. 762 (2005) 108. RGD24, Italy, July 10-16, 2004; M. Ellero, M. Tessarotto, Physica A 355 (2005) 233; M. Tessarotto, M. Ellero, Physica A 373 (2007) 142, arXiv: physics/0602140; M. Tessarotto, M. Ellero, in: M.S. Ivanov, A.K. Rebrov (Eds.), Proc. 25th RGD, International Symposium on Rarefied gas Dynamics, St. Petersburg, Russia, July 21-28, 2006, Novosibirsk Publ. House of the Siberian Branch of the Russian Academy of Sciences, 2007, p. 1001, arXiv:physics/0611113; M. Tessarotto, C. Cremaschini, Strong solutions of the incompressible Navier-Stokes equations in external domains: Local existence and uniqueness, arXiv:0809.5164v1 [math-ph], 2008]. As an example, the case of an incompressible Newtonian thermofluid is considered here.
Full Text Available ... en español Blog About OnSafety CPSC Stands for Safety The Tipping Point Home > 60 Seconds of Safety (Videos) > The Tipping Point The Tipping Point by ... danger death electrical fall furniture head injury product safety television tipover tv Watch the video in Adobe ...
Directory of Open Access Journals (Sweden)
B. Rutherford
2012-12-01
Full Text Available The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation.
Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance.
The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.
MEDSLIK-II, a Lagrangian marine surface oil spill model for short-term forecasting – Part 1: Theory
Dominicis, M.; Pinardi, N.; Zodiatis, G.; Lardner, R.
2013-01-01
The processes of transport, diffusion and transformation of surface oil in seawater can be simulated using a Lagrangian model formalism coupled with Eulerian circulation models. This paper describes the formalism and the conceptual assumptions of a Lagrangian marine surface oil slick numerical model and rewrites the constitutive equations in a modern mathematical framework. The Lagrangian numerical representation of the oil slick requires three different state variables: the...
Hittmeir, Sabine; Philipp, Anne; Seibert, Petra
2017-04-01
In discretised form, an extensive variable usually represents an integral over a 3-dimensional (x,y,z) grid cell. In the case of vertical fluxes, gridded values represent integrals over a horizontal (x,y) grid face. In meteorological models, fluxes (precipitation, turbulent fluxes, etc.) are usually written out as temporally integrated values, thus effectively forming 3D (x,y,t) integrals. Lagrangian transport models require interpolation of all relevant variables towards the location in 4D space of each of the computational particles. Trivial interpolation algorithms usually implicitly assume the integral value to be a point value valid at the grid centre. If the integral value would be reconstructed from the interpolated point values, it would in general not be correct. If nonlinear interpolation methods are used, non-negativity cannot easily be ensured. This problem became obvious with respect to the interpolation of precipitation for the calculation of wet deposition FLEXPART (http://flexpart.eu) which uses ECMWF model output or other gridded input data. The presently implemented method consists of a special preprocessing in the input preparation software and subsequent linear interpolation in the model. The interpolated values are positive but the criterion of cell-wise conservation of the integral property is violated; it is also not very accurate as it smoothes the field. A new interpolation algorithm was developed which introduces additional supporting grid points in each time interval with linear interpolation to be applied in FLEXPART later between them. It preserves the integral precipitation in each time interval, guarantees the continuity of the time series, and maintains non-negativity. The function values of the remapping algorithm at these subgrid points constitute the degrees of freedom which can be prescribed in various ways. Combining the advantages of different approaches leads to a final algorithm respecting all the required conditions. To
Lagrangian Displacement Ensembles for Aerosol Data Assimilation (Invited)
da Silva, A.; Colarco, P. R.; Govindaraju, R. C.
2010-12-01
A challenge common to many constituent data assimilation applications is the fact that one observes a much smaller fraction of the phase space that one wishes to estimate. For example, remotely-sensed estimates of the column average concentrations are available, while one is faced with the problem of estimating 3D concentractions for initializing a prognostic model. This problem is exarcebated in the the case of aerosols because the observable Aerosol Optical Depth (AOD) is not only a column integrated quantity, but it also sums over a large number of species (dust, sea-salt, carbonaceous and sulfate aerosols). An aerosol transport model when driven by high-resolution, state-of-the-art analysis of meterorological fields and realistc emissions can produce skillful forecasts even when no aerosol data is assimilated. The main task of aerosol data assimilation is to address the bias arising from innacurate emissions, and the Lagrangian misplacement of plumes induced by errors in the driving meterorological fields. As long as one decouples the meteorological and aerosol assimilation as we do here, the classic baroclinic growth of errors is no longer the main order of business. We will describe and aerosol data assimilation scheme in which the anaysis update step is conducted in observation space, using an adaptive maximum-likelihood scheme for estimating background errors in AOD space. This scheme includes explicit sequential bias estimation as in Dee and da Silva (1998). Unlikely existing aerosol data assimiltion schemes we do not obtain analysis increments of the 3D concentrations by scalling the background profiles. Instead, we explore the Langrangian characteristics of the problem for generating local displacement ensembles. These high-resolution, state-dependent ensembles are then used to parameterize the background errors and generate 3D aerosol increments. The algorithm has computational complexity comparable to the forecasting step by the aerosol transport model
One-loop effective Lagrangian for a standard model with a heavy charged scalar singlet
Bilenky, S M; Bilenky, Mikhail; Santamaria, Arcadi
1994-01-01
We study several problems related to the construction and the use of effective Lagrangians by considering an extension of the standard model that includes a heavy scalar singlet coupled to the leptonic doublet. Starting from the full renormalizable model, we build an effective field theory by integrating out the heavy scalar. A local effective Lagrangian (up to operators of dimension six) is obtained by expanding the one-loop effective action in inverse powers of the heavy mass. This is done by matching some Green functions calculated with both the full and the effective theories. Using this simple example we study the renormalization of effective Lagrangians in general and discuss how they can be used to bound new physics. We also discuss the effective Lagrangian after spontaneous symmetry breaking, and the use of the standard model classical equations of motion to rewrite it in different forms. The final effective Lagrangian in the physical basis is well suited to the study of the phenomenology of the model...
Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex
Directory of Open Access Journals (Sweden)
J. Curbelo
2017-07-01
Full Text Available 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.
Dual domain material point method for multiphase flows
Zhang, Duan
2017-11-01
Although the particle-in-cell method was first invented in the 60's for fluid computations, one of its later versions, the material point method, is mostly used for solid calculations. Recent development of the multi-velocity formulations for multiphase flows and fluid-structure interactions requires the Lagrangian capability of the method be combined with Eulerian calculations for fluids. Because of different numerical representations of the materials, additional numerical schemes are needed to ensure continuity of the materials. New applications of the method to compute fluid motions have revealed numerical difficulties in various versions of the method. To resolve these difficulties, the dual domain material point method is introduced and improved. Unlike other particle based methods, the material point method uses both Lagrangian particles and Eulerian mesh, therefore it avoids direct communication between particles. With this unique property and the Lagrangian capability of the method, it is shown that a multiscale numerical scheme can be efficiently built based on the dual domain material point method. In this talk, the theoretical foundation of the method will be introduced. Numerical examples will be shown. Work sponsored by the next generation code project of LANL.
Full Text Available ... OnSafety CPSC Stands for Safety The Tipping Point Home > 60 Seconds of Safety (Videos) > The Tipping Point ... 24 hours a day. For young children whose home is a playground, it’s the best way to ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 5; Issue 5. Fixed Points - From Russia with Love - A Primer of Fixed Point Theory. A K Vijaykumar. Book Review Volume 5 Issue 5 May 2000 pp 101-102. Fulltext. Click here to view fulltext PDF. Permanent link:
The tempered one-sided stable density: a universal model for hydrological transport?
International Nuclear Information System (INIS)
Cvetkovic, Vladimir
2011-01-01
A generalized distribution for the water residence time in hydrological transport is proposed in the form of the tempered one-sided stable (TOSS) density. It is shown that limiting cases of the TOSS distribution recover virtually all distributions that have been considered in the literature for hydrological transport, from plug flow to flow reactor, the advection-dispersion model, and the gamma and Levy densities. The stable property of TOSS is particularly important, enabling a seamless transition between a time-domain random walk, and the Lagrangian (trajectory) approach along hydrological transport pathways.
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
Lagrangian duality applied to the vehicle routing problem with time windows
DEFF Research Database (Denmark)
Kallehauge, Brian; Larsen, Jesper; Madsen, Oli B.G.
2006-01-01
multiplier convergence due to a stabilization of the dual variables. We have embedded the stabilized cutting-plane algorithm in a branch-and-bound search and introduce strong valid inequalities at the master problem level by Lagrangian relaxation. The result is a Lagrangian branch-and-cut-and-price (LBCP...... shortest path subproblem. We present a stabilized cutting-plane algorithm within the framework of linear programming for solving the associated Lagrangian dual problem. This algorithm creates easier constrained shortest path subproblems because less negative cycles are introduced and it leads to faster......) algorithm for the VRPTW. Making use of this acceleration strategy at the master problem level gives a significant speed-up compared to algorithms in the literature based on traditional column generation. We have solved two test problems introduced in 2001 by Gehring and Homberger with 400 and 1000 customers...
A manifestly MHV Lagrangian for mathcal{N} = 4 Yang-Mills
Ananth, Sudarshan; Kovacs, Stefano; Parikh, Sarthak
2011-05-01
We derive a manifestly MHV Lagrangian for the {N} = 4 supersymmetric Yang-Mills theory in light-cone superspace. This is achieved by constructing a canonical redefinition which maps the {N} = 4 superfield, ϕ, and its conjugate, bar{φ } , to a new pair of superfields, χ and tilde{χ } . In terms of these new superfields the {N} = 4 Lagrangian takes a (non-polynomial) manifestly MHV form, containing vertices involving two superfields of negative helicity and an arbitrary number of superfields of positive helicity. We also discuss constraints satisfied by the new superfields, which ensure that they describe the correct degrees of freedom in the {N} = 4 supermultiplet. We test our derivation by showing that an expansion of our superspace Lagrangian in component fields reproduces the correct gluon MHV vertices.
Lagrangian descriptors and the assessment of the predictive capacity of oceanic data sets
Mendoza, C.; Mancho, A. M.; Wiggins, S.
2014-06-01
We use a recently developed Lagrangian transport tool, Lagrangian descriptors, to compare the transport properties of data distributed by AVISO and numerical simulations obtained from the HYCOM model in the Yucatán-Florida current system. Our data correspond to the months from June through August 2010. Structures obtained from HYCOM are noisier than those from AVISO; however, both AVISO and HYCOM succeed in identifying Lagrangian structures that influence the paths of drifters, such as eddies, currents, lobes, etc. We find evidence in which AVISO gives the positions of important hyperbolic trajectories in a manner that is inconsistent with the trajectories of the drifters, while for the same examples HYCOM succeeds to this end.
Electroweak chiral Lagrangian from a natural topcolor-assisted technicolor model
International Nuclear Information System (INIS)
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.
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,...
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.
Finite-size Lagrangian coherent particle structures in thermocapillary liquid bridges
Romano, Francesco; Kuhlmann, Hendrik
2017-11-01
A surprisingly rapid accumulation of small but finite-size particles taking curious shapes is observed in travelling hydrothermal waves in liquid bridges. The phenomenon has been termed particle accumulation structure (PAS) and belongs to the wider class of Lagrangian coherent structures. In PAS, particles are transferred from chaotic to regular regions of the flow by way of collision with the boundaries. Lubrication forces cause a dissipation of kinetic energy of the particle and give rise to particle motion attractors in the incompressible flow. Since the mechanism relies solely on the particle size, PAS is nothing but a finite-size Lagrangian coherent structure. Different theoretical models are investigated to find a minimum model for the simulation of Lagrangian finite-size coherent structures. Corresponding numerical simulations compare very well with experiments on SL-I and SL-II PAS.
Quantum information metric and Berry curvature from a Lagrangian approach
Alvarez-Jimenez, Javier; Dector, Aldo; Vergara, J. David
2017-03-01
We take as a starting point an expression for the quantum geometric tensor recently derived in the context of the gauge/gravity duality. We proceed to generalize this formalism in such way it is possible to compute the geometrical phases of quantum systems. Our scheme provides a conceptually complete description and introduces a different point of view of earlier works. Using our formalism, we show how this expression can be applied to well-known quantum mechanical systems.
Quantum information metric and Berry curvature from a Lagrangian approach
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Jimenez, Javier [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,Circuito Exterior, C.University, Ciudad de México 04510 (Mexico); Dector, Aldo [Instituto de Física Teórica IFT UAM/CSIC,Calle Nicolás Cabrera 13. UAM, Cantoblanco 28049, Madrid (Spain); Vergara, J. David [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,Circuito Exterior, C.University, Ciudad de México 04510 (Mexico)
2017-03-08
We take as a starting point an expression for the quantum geometric tensor recently derived in the context of the gauge/gravity duality. We proceed to generalize this formalism in such way it is possible to compute the geometrical phases of quantum systems. Our scheme provides a conceptually complete description and introduces a different point of view of earlier works. Using our formalism, we show how this expression can be applied to well-known quantum mechanical systems.
Fredj, Erick; Kohut, Josh; Roarty, Hugh; Lai, Jian-Wu
2017-04-01
The Lagrangian separation distance between the endpoints of simulated and observed drifter trajectories is often used to assess the performance of numerical particle trajectory models. However, the separation distance fails to indicate relative model performance in weak and strong current regions, such as over continental shelves and the adjacent deep ocean. A skill score described in detail by (Lui et.al. 2011) was applied to estimate the cumulative Lagrangian separation distances normalized by the associated cumulative trajectory lengths. In contrast, the Lagrangian separation distance alone gives a misleading result. The proposed dimensionless skill score is particularly useful when the number of drifter trajectories is limited and neither a conventional Eulerian-based velocity nor a Lagrangian based probability density function may be estimated. The skill score assesses The Taiwan Ocean Radar Observing System (TOROS) performance. TOROS consists of 17 SeaSonde type radars around the Taiwan Island. The currents off Taiwan are significantly influenced by the nearby Kuroshio current. The main stream of the Kuroshio flows along the east coast of Taiwan to the north throughout the year. Sometimes its branch current also bypasses the south end of Taiwan and goes north along the west coast of Taiwan. The Kuroshio is also prone to seasonal change in its speed of flow, current capacity, distribution width, and depth. The evaluations of HF-Radar National Taiwanese network performance using Lagrangian drifter records demonstrated the high quality and robustness of TOROS HF-Radar data using a purely trajectory-based non-dimensional index. Yonggang Liu and Robert H. Weisberg, "Evaluation of trajectory modeling in different dynamic regions using normalized cumulative Lagrangian separation", Journal of Geophysical Research, Vol. 116, C09013, doi:10.1029/2010JC006837, 2011
Directory of Open Access Journals (Sweden)
François Van Dorpe
2007-01-01
Full Text Available The results of four gas tracer experiments of atmospheric dispersion on a regional scale are used for the benchmarking of two atmospheric dispersion modeling codes, MINERVE-SPRAY (CEA, and NOSTRADAMUS (IBRAE. The main topic of this comparison is to estimate the Lagrangian code capability to predict the radionuclide atmospheric transfer on a large field, in the case of risk assessment of nuclear power plant for example. For the four experiments, the results of calculations show a rather good agreement between the two codes, and the order of magnitude of the concentrations measured on the soil is predicted. Simulation is best for sampling points located ten kilometers from the source, while we note a divergence for more distant points results (difference in concentrations by a factor 2 to 5. This divergence may be explained by the fact that, for these four experiments, only one weather station (near the point source was used on a field of 10 000 km2, generating the simulation of a uniform wind field throughout the calculation domain.
Stable isotopes labelled compounds
International Nuclear Information System (INIS)
1982-09-01
The catalogue on stable isotopes labelled compounds offers deuterium, nitrogen-15, and multiply labelled compounds. It includes: (1) conditions of sale and delivery, (2) the application of stable isotopes, (3) technical information, (4) product specifications, and (5) the complete delivery programme
Steeneveld, G.J.
2012-01-01
Understanding and prediction of the stable atmospheric boundary layer is a challenging task. Many physical processes are relevant in the stable boundary layer, i.e. turbulence, radiation, land surface coupling, orographic turbulent and gravity wave drag, and land surface heterogeneity. The
Indian Academy of Sciences (India)
IAS Admin
After Maynard-Smith and Price [1] mathematically derived why a given behaviour or strategy was adopted by a certain proportion of the population at a given time, it was shown that a strategy which is currently stable in a population need not be stable in evolutionary time (across generations). Additionally it was sug-.
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.
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
Prants, Sergey V.; Budyansky, Maxim V.; Uleysky, Michael Y.
2017-06-01
A Lagrangian methodology is developed to simulate, track, document and analyze the origin and history of water masses in ocean mesoscale features. It aims to distinguish whether water masses inside the mesoscale eddies originated from the main currents in the Kuroshio-Oyashio confluence zone. By computing trajectories for a large number of synthetic Lagrangian particles advected by the AVISO velocity field after the Fukushima accident, we identify and track the mesoscale eddies which were sampled in the cruises in 2011 and 2012 and estimate their risk of being contaminated by Fukushima-derived radionuclides. The simulated results are compared with in situ measurements, showing a good qualitative correspondence.
A Lagrangian Slug Capturing Scheme for Gas-Liquid Flows in Pipes
Energy Technology Data Exchange (ETDEWEB)
Renault, Fabien
2007-06-15
In this thesis a new Lagrangian numerical scheme for the simulation of gas-liquid flows in pipelines is presented. Based on an approximate two-fluid model, this new scheme, called LASSI (Lagrangian Approximate Scheme for Slug Initiation) is dedicated to the modelling of the transition between stratified and slug flow. It is able to capture directly the slug initiation process and to track the motion of every single slug in the pipe without numerical diffusion. It can thus be qualified as a slug capturing and slug tracking scheme
Gravitational Lagrangians, Mach’s Principle, and the Equivalence Principle in an Expanding Universe
Directory of Open Access Journals (Sweden)
Hanno Essén
2014-01-01
Full Text Available Gravitational Lagrangians as derived by Fock for the Einstein-Infeld-Hoffmann approach, and by Kennedy assuming only a fourth rank tensor interaction, contain long range interactions. Here we investigate how these affect the local dynamics when integrated over an expanding universe out to the Hubble radius. Taking the cosmic expansion velocity into account in a heuristic manner it is found that these long range interactions imply Mach’s principle, provided the universe has the critical density, and that mass is renormalized. Suitable higher order additions to the Lagrangians make the formalism consistent with the equivalence principle.
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
Directory of Open Access Journals (Sweden)
S. V. Prants
2017-06-01
Full Text Available A Lagrangian methodology is developed to simulate, track, document and analyze the origin and history of water masses in ocean mesoscale features. It aims to distinguish whether water masses inside the mesoscale eddies originated from the main currents in the Kuroshio–Oyashio confluence zone. By computing trajectories for a large number of synthetic Lagrangian particles advected by the AVISO velocity field after the Fukushima accident, we identify and track the mesoscale eddies which were sampled in the cruises in 2011 and 2012 and estimate their risk of being contaminated by Fukushima-derived radionuclides. The simulated results are compared with in situ measurements, showing a good qualitative correspondence.
Full Text Available ... Point by CPSC Blogger September 22, 2009 appliance child Childproofing CPSC danger death electrical fall furniture head ... see news reports about horrible accidents involving young children and furniture, appliance and tv tip-overs. The ...
Kurt Symanzik-a stable fixed point beyond triviality
International Nuclear Information System (INIS)
Kleefeld, Frieder
2006-01-01
In 1970 Kurt Symanzik proposed a 'precarious' Φ 4 -theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions. Symanzik's deep insight into the non-trivial properties of this theory has been overruled since then by the Hermitian intuition of generations of scientists, who considered or consider this actually non-Hermitian highly important theory to be unstable. This short-certainly controversial-communication tries to shed some light on the historical and formalistic context of Symanzik's theory in order to sharpen our (quantum) intuition about non-perturbative theoretical physics between (non-)triviality and asymptotic freedom. (letter to the editor)
Mohrmann, J.; Albrecht, B. A.; Bretherton, C. S.; Ghate, V. P.; Zuidema, P.; Wood, R.
2015-12-01
The Cloud System Evolution in the Trades (CSET) field campaign took place during July/August 2015 with the purpose of characterizing the cloud, aerosol and thermodynamic properties of the northeast Pacific marine boundary layer. One major science goal of the campaign was to observe a Lagrangian transition from thin stratocumulus (Sc) upwind near California to trade cumulus (Cu) nearer to Hawaii. Cloud properties were observed from the NSF/NCAR Gulfstream V research plane (GV) using the HIAPER Cloud Radar (HCR) and the HIAPER Spectral Resolution Lidar (HSRL), among other instrumentation. Aircraft observations were complemented by a suite of satellite-derived products. To observe a the evolution of airmasses over the course of two days, upwind regions were sampled on an outbound flight to from Sacramento, CA, to Kona, HI. The sampled airmasses were then tracked using HYSPLIT trajectories based on GFS model forecasts, and the return flight to California was planned to intercept those airmasses, using satellite observation to track cloud evolution in the interim. This approach required that trajectories were reasonably stable up to 3 days prior to final sampling, and also that forecast trajectories were in agreement with post-flight analysis and visual cloud feature tracking. The extent to which this was realised, and hence the validity of this new approach to Lagrangian airmass observation, is assessed here. We also present results showing that a Sc-Cu airmass transition was consistently observed during the CSET study using measurements from research flights and satellite.
Kaufman, Allan N.
1987-01-01
The covariant coupled equations for plasma dynamics and the Maxwell field are expressed as a phase-space-Lagrangian action principle. The linear interaction is transformed to the bilinear beat Hamiltonian by a gauge-invariant Lagrangian Lie transform. The result yields the generalized linear susceptibility directly.
Rashid, M.
2011-01-01
Considering the Lagrangian density of the electromagnetic field, a 4 × 4 transformation matrix is found which can be used to include two of the symmetrized Maxwell’s equations as one of the Euler-Lagrange equations of the complete Lagrangian density. The 4 × 4 transformation matrix introduces newly
Normal modified stable processes
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Shephard, N.
2002-01-01
This paper discusses two classes of distributions, and stochastic processes derived from them: modified stable (MS) laws and normal modified stable (NMS) laws. This extends corresponding results for the generalised inverse Gaussian (GIG) and generalised hyperbolic (GH) or normal generalised inverse...... Gaussian (NGIG) laws. The wider framework thus established provides, in particular, for added flexibility in the modelling of the dynamics of financial time series, of importance especially as regards OU based stochastic volatility models for equities. In the special case of the tempered stable OU process...
Applications of stable isotopes
International Nuclear Information System (INIS)
Letolle, R.; Mariotti, A.; Bariac, T.
1991-06-01
This report reviews the historical background and the properties of stable isotopes, the methods used for their measurement (mass spectrometry and others), the present technics for isotope enrichment and separation, and at last the various present and foreseeable application (in nuclear energy, physical and chemical research, materials industry and research; tracing in industrial, medical and agronomical tests; the use of natural isotope variations for environmental studies, agronomy, natural resources appraising: water, minerals, energy). Some new possibilities in the use of stable isotope are offered. A last chapter gives the present state and forecast development of stable isotope uses in France and Europe
Stronger Lagrangian bounds by use of slack variables: applications to machine scheduling problems
J.A. Hoogeveen (Han); S.L. van de Velde (Steef)
1995-01-01
textabstractLagrangian relaxation is a powerful bounding technique that has been applied successfully to manyNP-hard combinatorial optimization problems. The basic idea is to see anNP-hard problem as an easy-to-solve problem complicated by a number of nasty side constraints. We show that
On the Hamiltonian and Lagrangian formulation of classical dynamics for particles with spin
Ruijgrok, Th.W.; Vlist, H. van der
The classical mechanics of nonrelativistic particles is generalized by also considering the spin components as canonical variables. Poisson-brackets and canonical transformations are discussed. The Lagrangian equations of motion are given and it is shown how rotational invariance leads to well known
International Nuclear Information System (INIS)
Caratu, G.; Marmo, G.; Simoni, A.; Vitale, B.; Zaccaria, F.
1976-01-01
The notion of dynamical system in classical mechanics is built starting from the trajectories on the configuration space. Classes of equivalent vector fields on tangent and cotangent bundles are obtained. This leads to a re-examination in detail of the meaning of the Hamiltonian and Lagrangian functions
Equivalence of two independent calculations of the higher order guiding center Lagrangian
International Nuclear Information System (INIS)
Parra, F. I.; Calvo, I.; Burby, J. W.; Squire, J.; Qin, H.
2014-01-01
The difference between the guiding center phase-space Lagrangians derived in J. W. Burby et al. [Phys. Plasmas 20, 072105 (2013)] and F. I. Parra and I. Calvo [Plasma Phys. Controlled Fusion 53, 045001 (2011)] is due to a different definition of the guiding center coordinates. In this brief communication, the difference between the guiding center coordinates is calculated explicitly
Fast Lagrangian relaxation for constrained generation scheduling in a centralized electricity market
International Nuclear Information System (INIS)
Ongsakul, Weerakorn; Petcharaks, Nit
2008-01-01
This paper proposes a fast Lagrangian relaxation (FLR) for constrained generation scheduling (CGS) problem in a centralized electricity market. FLR minimizes the consumer payment rather than the total supply cost subject to the power balance, spinning reserve, transmission line, and generator operating constraints. FLR algorithm is improved by new initialization of Lagrangian multipliers and adaptive adjustment of Lagrangian multipliers. The adaptive subgradient method using high quality initial feasible multipliers requires much less number of iterations to converge, leading to a faster computational time. If congestion exists, the alleviating congestion index is proposed for congestion management. Finally, the unit decommitment is performed to prevent excessive spinning reserve. The FLR for CGS is tested on the 4 unit and the IEEE 24 bus reliability test systems. The proposed uniform electricity price results in a lower consumer payment than system marginal price based on uniformly fixed cost amortized allocation, non-uniform price, and electricity price incorporating side payment, leading to a lower electricity price. In addition, observations on objective functions, pricing scheme comparison and interpretation of Lagrangian multipliers are provided. (author)
Chiral weak lagrangian for vector mesons and K → 3π decay amplitudes
International Nuclear Information System (INIS)
Isidori, G.; Pugliese, A.
1992-01-01
We determine the next-order corrrections to weak chiral lagrangian induced by vector-meson exchange, and we analyze their effects in K → 3π decay amplitudes. The result is a substantial improvement of the lowest-order predictions. (orig.)
Attili, Antonio
2013-09-01
A Lagrangian particle scheme is applied to the solution of soot dynamics in turbulent nonpremixed flames. Soot particulate is described using a method of moments and the resulting set of continuum advection-reaction equations is solved using the Lagrangian particle scheme. The key property of the approach is the independence between advection, described by the movement of Lagrangian notional particles along pathlines, and internal aerosol processes, evolving on each notional particle via source terms. Consequently, the method overcomes the issues in Eulerian grid-based schemes for the advection of moments: errors in the advective fluxes pollute the moments compromising their realizability and the stiffness of source terms weakens the stability of the method. The proposed scheme exhibits superior properties with respect to conventional Eulerian schemes in terms of stability, accuracy, and grid convergence. Taking into account the quality of the solution, the Lagrangian approach can be computationally more economical than commonly used Eulerian schemes as it allows the resolution requirements dictated by the different physical phenomena to be independently optimized. Finally, the scheme posseses excellent scalability on massively parallel computers. © 2013 Elsevier Ltd.
Helm, P.N.; van der Helm, P.N.; Huetink, Han; Akkerman, Remko
1998-01-01
A comparison is made between Arbitrary Lagrangian-Eulerian (ALE) finite element formulations for simulation of forming processes based on an artificial dissipation scheme and a limited flux scheme. The first ALE algorithm is based on an averaging procedure used in post-processing of finite element
Do Assimilated Drifter Velocities Improve Lagrangian Predictability in an Operational Ocean Model?
2015-05-01
Lagrangian information into ocean models. Toner et al. (2001) used a normal mode analysis method with constrained optimization to mini- mize changes...drifter trajectories on the inner Scotian Shelf. J. Geophys. Res., 108, 3287, doi:10.1029/ 2001JC001119. Toner , M., A. D. Kirwan Jr., L. H. Kantha, and
Avelino, P. P.; Azevedo, R. P. L.
2018-03-01
In this paper we show that the on-shell Lagrangian of a perfect fluid depends on microscopic properties of the fluid, giving specific examples of perfect fluids with different on-shell Lagrangians but with the same energy-momentum tensor. We demonstrate that if the fluid is constituted by localized concentrations of energy with fixed rest mass and structure (solitons) then the average on-shell Lagrangian of a perfect fluid is given by Lm=T , where T is the trace of the energy-momentum tensor. We show that our results have profound implications for theories of gravity where the matter Lagrangian appears explicitly in the equations of motion of the gravitational and matter fields, potentially leading to observable deviations from a nearly perfect cosmic microwave background black body spectrum: n -type spectral distortions, affecting the normalization of the spectral energy density. Finally, we put stringent constraints on f (R ,Lm) theories of gravity using the COBE-FIRAS measurement of the spectral radiance of the cosmic microwave background.
Determination of the electroweak chiral-lagrangian parameters at the LHC
Energy Technology Data Exchange (ETDEWEB)
Dobado, A. [Universidad Complutense de Madrid (Spain). Dept. de Fisica Teorica; Urdiales, M.T. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
1996-08-01
In this work we report on the results obtained in a detailed and systematical study of the possibility to measure the parameters appearing in the electroweak chiral lagrangian. The main novelty of our approach is that we do not use the equivalence theorem and therefore we work explicitly with all the gauge boson degrees of freedom. (orig.). With 16 figs., 5 tabs.
Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform
Huang, Y.; Biferale, L.; Calzavarini, E.; Sun, Chao; Toschi, F.
2013-01-01
The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C i (t) and of their instantaneous frequency ω i (t) . On the basis of
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
Laboratory experiment on the 3D tide-induced Lagrangian residual current using the PIV technique
Chen, Yang; Jiang, Wensheng; Chen, Xu; Wang, Tao; Bian, Changwei
2017-12-01
The 3D structure of the tide-induced Lagrangian residual current was studied using the particle image velocimetry (PIV) technique in a long shallow narrow tank in the laboratory. At the mouth of the tank, a wave generator was used to make periodic wave which represents the tide movement, and at the head of the tank, a laterally sloping topography with the length of one fifth of the water tank was installed, above which the tide-induced Lagrangian residual current was studied. Under the weakly nonlinear condition in the present experiment setup, the results show that the Lagrangian residual velocity (LRV) field has a three-layer structure. The residual current flows inwards (towards the head) in the bottom layer and flows outwards in the middle layer, while in the surface layer, it flows inwards along the shallow side of the sloping topography and outwards along the deep side. The depth-averaged and breadth-averaged LRV are also analyzed based on the 3D LRV observations. Our results are in good agreement with the previous experiment studies, the analytical solutions with similar conditions and the observational results in real bays. Moreover, the volume flux comparison between the Lagrangian and Eulerian residual currents shows that the Eulerian residual velocity violates the mass conservation law while the LRV truly represents the inter-tidal water transport. This work enriches the laboratory studies of the LRV and offers valuable references for the LRV studies in real bays.
eHDECAY: an Implementation of the Higgs Effective Lagrangian into HDECAY
Contino, Roberto; Grojean, Christophe; Muhlleitner, Margarete; Spira, Michael
2014-01-01
We present eHDECAY, a modified version of the program HDECAY which includes the full list of leading bosonic operators of the Higgs effective Lagrangian with a linear or non-linear realization of the electroweak symmetry and implements two benchmark composite Higgs models.
Parcels v0.9: prototyping a Lagrangian Ocean Analysis framework for the petascale age
Lange, Michael; Sebille, Erik van
2017-01-01
As Ocean General Circulation Models (OGCMs) move into the petascale age, where the output from global high-resolution model runs can be of the order of hundreds of terabytes in size, tools to analyse the output of these models will need to scale up too. Lagrangian Ocean Analysis, where virtual
This study evaluates the accuracy of measuring trace gas emission from treatment lagoons using backward Lagrangian stochastic (bLs) technique. The bLs technique was originally developed for relatively homogeneous terrains without any obstacles causing significant windflow disturbance. The errors ass...
Liu, Y.; Weisberg, R. H.
2017-12-01
The Lagrangian separation distance between the endpoints of simulated and observed drifter trajectories is often used to assess the performance of numerical particle trajectory models. However, the separation distance fails to indicate relative model performance in weak and strong current regions, such as a continental shelf and its adjacent deep ocean. A skill score is proposed based on the cumulative Lagrangian separation distances normalized by the associated cumulative trajectory lengths. The new metrics correctly indicates the relative performance of the Global HYCOM in simulating the strong currents of the Gulf of Mexico Loop Current and the weaker currents of the West Florida Shelf in the eastern Gulf of Mexico. In contrast, the Lagrangian separation distance alone gives a misleading result. Also, the observed drifter position series can be used to reinitialize the trajectory model and evaluate its performance along the observed trajectory, not just at the drifter end position. The proposed dimensionless skill score is particularly useful when the number of drifter trajectories is limited and neither a conventional Eulerian-based velocity nor a Lagrangian-based probability density function may be estimated.
Complete one-loop renormalization of the Higgs-electroweak chiral Lagrangian
Buchalla, G.; Catà, O.; Celis, A.; Knecht, M.; Krause, C.
2018-03-01
Employing background-field method and super-heat-kernel expansion, we compute the complete one-loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson. Earlier results from purely scalar fluctuations are confirmed as a special case. We also recover the one-loop renormalization of the conventional Standard Model in the appropriate limit.
Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Campoamor-Stursberg, Rutwig, E-mail: rutwig@ucm.es [Faculted de Ciencias Matematicas Universidad Complutense, Instituto de Matemática Interdisciplinar and Departamento Geometría y Topología (Spain)
2017-03-15
Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.
A Primal-Dual Augmented Lagrangian Method for Optimal Control of ...
African Journals Online (AJOL)
Numerical experiments verify the efficiency of the proposed method. Keywords: Optimal control,primal-dual methods, augmented Lagrangian methods, conjugate gradient method, sequential quadratic programming. Journal of the Nigerian Association of Mathematical Physics, Volume 20 (March, 2012), pp 165 – 174 ...
Effective Lagrangians and parity-conserving time-reversal violation at low energies
International Nuclear Information System (INIS)
Engel, J.; Frampton, P.H.; Springer, R.P.
1996-01-01
Using effective Lagrangians, we argue that any time-reversal-violating but parity-conserving effects are too small to be observed in flavor-conserving nuclear processes without dramatic improvement in experimental accuracy. In the process we discuss other arguments that have appeared in the literature. copyright 1996 The American Physical Society
Anomalous chiral lagrangians and e+e- annihilation into three pions
Bramon, A.; Pallante, E.; Petronzio, R.
1991-01-01
We investigate the reaction e+e-â†’3Ï€ that can be described by the anomalous part of an effective chiral lagrangian. We calculate the next-to-leading corrections to the process and make an estimate of all-order correction within a specific chiral model of pseudoscalars and vector resonances. Our
Higher order point and continuum mechanics from phase-space action
Energy Technology Data Exchange (ETDEWEB)
Shamanna, J.; Talukdar, B.; Das, U
2002-12-02
It is pointed out that use of phase-space action provides an elegant method to study the canonical structure of problems in mechanics. Higher order Lagrangian systems are Hamiltonized by employing the variational principle in phase space. Studies are envisaged for both particle dynamics and field theory. Hamilton's equations are expressed in terms of appropriate Poisson brackets.
National Research Council Canada - National Science Library
Adler, Robert
1997-01-01
We describe how to take a stable, ARMA, time series through the various stages of model identification, parameter estimation, and diagnostic checking, and accompany the discussion with a goodly number...
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Energy Technology Data Exchange (ETDEWEB)
Rieben, R N; White, D A; Wallin, B K; Solberg, J M
2006-06-12
We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.
Do planetary seasons play a role in attaining stable climates?
Olsen, Kasper Wibeck; Bohr, Jakob
2018-02-01
A simple phenomenological account for planetary climate instabilities is presented. The description is based on the standard model where the balance of incoming stellar radiation and outward thermal radiation is described by the effective planet temperature. Often, it is found to have three different points, or temperatures, where the influx of radiation is balanced with the out-flux, even with conserved boundary conditions. Two of these points are relatively long-term stable, namely the point corresponding to a cold climate and the point corresponding to a hot climate. In a classical sense these points are equilibrium balance points. The hypothesis promoted in this paper is the possibility that the intermediate third point can become long-term stable by being driven dynamically. The initially unstable point is made relatively stable over a long period by the presence of seasonal climate variations.
Sandler, U.
2017-11-01
In this paper, we extend our generalized Lagrangian dynamics (i.e., S-Lagrangian dynamics, which can be applied equally to physical and non-physical systems as per Sandler (2014)) to many-body systems. Unlike common Lagrangian dynamics, this is not a trivial task. For many-body systems with S-dependent Lagrangians, the Lagrangian and the corresponding Hamiltonian or energy become vector functions, conjugated momenta become second-order tensors, and the system inevitably develops a hierarchical structure, even if all bodies initially have similar status and Lagrangians. As an application of our theory, we consider dominance and hierarchy formation, which is present in almost all communities of living species. As a biological basis for this application, we assume that the primary motivation of a groups activity is to attempt to cope with stress arising as pressure from the environment and from intrinsic unmet needs of individuals. It has been shown that the S-Lagrangian approach to a group's evolution naturally leads to formation of linear or despotic dominance hierarchies, depending on differences between individuals in coping with stress. That is, individuals that cope more readily with stress take leadership roles during the evolution. Experimental results in animal groups which support our assumption and findings are considered.
Directory of Open Access Journals (Sweden)
Héctor Torres-Silva
2008-11-01
Full Text Available This work deals with the problem of the construction of the Lagrange functional for an electromagnetic field. The generalised Maxwell equations for an electromagnetic field in free space are introduced. The main idea relies on the change of Lagrange function under the integral action. Usually, the Lagrange functional which describes the electromagnetic field is built with the quadrate of the electromagnetic field tensor . Such a quadrate term is the reason, from a mathematical point of view, for the linear form of the Maxwell equations in free space. The author does not make this assumption and nonlinear Maxwell equations are obtained. New material parameters of free space are established. The equations obtained are quite similar to the well-known Maxwell equations. The energy tensor of the electromagnetic field from a chiral approach to the Born Infeld Lagrangian is discussed in connection with the cosmological constant.Se aborda el problema de la construcción de la funcional de Lagrange de un campo electromagnético. Se introducen las ecuaciones generalizadas de Maxwell de un campo electromagnético en el espacio libre. La idea principal se basa en el cambio de función de Lagrange en virtud de la acción integral. Por lo general, la funcional de lagrange, que describe el campo electromagnético, se construye con el cuadrado del tensor de campo electromagnético. Ese término cuadrático es la razón, desde un punto de vista matemático, de la forma lineal de las ecuaciones de Maxwell en el espacio libre. Se obtienen las ecuaciones no lineales de Maxwell sin considerar esta suposición. Las ecuaciones de Maxwell obtenidas son bastante similares a las conocidas ecuaciones de Maxwell. Se analiza el tensor de energía del campo electromagnético en un enfoque quiral de la Lagrangiana de Born Infeld en relación con la constante cosmológica.
Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi
1986-01-01
of intertidal transport processes is illustrated by an analytical solution for an amphidromic system and by a numerical application in South San Francisco Bay, California. The present formulation reveals that the mechanism for long-term transport of solutes is mainly convection due to the Lagrangian residual current in the interior of a tidal estuary. This result also points out the weakness in the tidal dispersion formulation, and explains the large variability of the observed values for tidal dispersion coefficients. Further research on properties of the dispersion boundary layer is needed.
Puyguiraud, Alexandre; Dentz, Marco; Gouze, Philippe
2017-04-01
For the past several years a lot of attention has been given to pore-scale flow in order to understand and model transport, mixing and reaction in porous media. Nevertheless we believe that an accurate study of spatial and temporal evolution of velocities could bring important additional information for the upscaling from pore to higher scales. To gather these pieces of information, we perform Stokes flow simulations on pore-scale digitized images of a Berea sandstone core. First, micro-tomography (XRMT) imaging and segmentation processes allow us to obtain 3D black and white images of the sample [1]. Then we used an OpenFoam solver to perform the Stokes flow simulations mentioned above, which gives us the velocities at the interfaces of a cubic mesh. Subsequently, we use a particle streamline reconstruction technique which uses the Eulerian velocity field previously obtained. This technique, based on a modified Pollock algorithm [2], enables us to make particle tracking simulations on the digitized sample. In order to build a stochastic pore-scale transport model, we analyze the Lagrangian velocity series in two different ways. First we investigate the velocity evolution by sampling isochronically (t-Lagrangian), and by studying its statistical properties in terms of one- and two-points statistics. Intermittent patterns can be observed. These are due to the persistance of low velocities over a characteristic space length. Other results are investigated, such as correlation functions and velocity PDFs, which permit us to study more deeply this persistence in the velocities and to compute the correlation times. However, with the second approach, doing these same analysis in space by computing the velocities equidistantly, enables us to remove the intermittency shown in the temporal evolution and to model these velocity series as a Markov process. This renders the stochastic particle dynamics into a CTRW [3]. [1] Gjetvaj, F., A. Russian, P. Gouze, and M. Dentz (2015
Calcium stable isotope geochemistry
Energy Technology Data Exchange (ETDEWEB)
Gausonne, Nikolaus [Muenster Univ. (Germany). Inst. fuer Mineralogie; Schmitt, Anne-Desiree [Strasbourg Univ. (France). LHyGeS/EOST; Heuser, Alexander [Bonn Univ. (Germany). Steinmann-Inst. fuer Geologie, Mineralogie und Palaeontologie; Wombacher, Frank [Koeln Univ. (Germany). Inst. fuer Geologie und Mineralogie; Dietzel, Martin [Technische Univ. Graz (Austria). Inst. fuer Angewandte Geowissenschaften; Tipper, Edward [Cambridge Univ. (United Kingdom). Dept. of Earth Sciences; Schiller, Martin [Copenhagen Univ. (Denmark). Natural History Museum of Denmark
2016-08-01
This book provides an overview of the fundamentals and reference values for Ca stable isotope research, as well as current analytical methodologies including detailed instructions for sample preparation and isotope analysis. As such, it introduces readers to the different fields of application, including low-temperature mineral precipitation and biomineralisation, Earth surface processes and global cycling, high-temperature processes and cosmochemistry, and lastly human studies and biomedical applications. The current state of the art in these major areas is discussed, and open questions and possible future directions are identified. In terms of its depth and coverage, the current work extends and complements the previous reviews of Ca stable isotope geochemistry, addressing the needs of graduate students and advanced researchers who want to familiarize themselves with Ca stable isotope research.
Eckhardt, Sabine; Cassiani, Massimo; Evangeliou, Nikolaos; Sollum, Espen; Pisso, Ignacio; Stohl, Andreas
2017-12-01
Existing Lagrangian particle dispersion models are capable of establishing source-receptor relationships by running either forward or backward in time. For receptor-oriented studies such as interpretation of "point" measurement data, backward simulations can be computationally more efficient by several orders of magnitude. However, to date, the backward modelling capabilities have been limited to atmospheric concentrations or mixing ratios. In this paper, we extend the backward modelling technique to substances deposited at the Earth's surface by wet scavenging and dry deposition. This facilitates efficient calculation of emission sensitivities for deposition quantities at individual sites, which opens new application fields such as the comprehensive analysis of measured deposition quantities, or of deposition recorded in snow samples or ice cores. This could also include inverse modelling of emission sources based on such measurements. We have tested the new scheme as implemented in the Lagrangian particle dispersion model FLEXPART v10.2 by comparing results from forward and backward calculations. We also present an example application for black carbon concentrations recorded in Arctic snow.
The impact of nonlinearity in Lagrangian data assimilation
Directory of Open Access Journals (Sweden)
A. Apte
2013-05-01
Full Text Available The focus of this paper is on how two main manifestations of nonlinearity in low-dimensional systems – shear around a center fixed point (nonlinear center and the differential divergence of trajectories passing by a saddle (nonlinear saddle – strongly affect data assimilation. The impact is felt through their leading to non-Gaussian distribution functions. The major factors that control the strength of these effects is time between observations, and covariance of the prior relative to covariance of the observational noise. Both these factors – less frequent observations and larger prior covariance – allow the nonlinearity to take hold. To expose these nonlinear effects, we use the comparison between exact posterior distributions conditioned on observations and the ensemble Kalman filter (EnKF approximation of these posteriors. We discuss the serious limitations of the EnKF in handling these effects.
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... Home; Journals; Resonance – Journal of Science Education; Volume 21; Issue 9. Evolutionary Stable Strategy: Application of Nash Equilibrium in Biology. General ... Using some examples of classical games, we show how evolutionary game theory can help understand behavioural decisions of animals.
Kearney, M. Kate
2013-01-01
The concordance genus of a knot is the least genus of any knot in its concordance class. Although difficult to compute, it is a useful invariant that highlights the distinction between the three-genus and four-genus. In this paper we define and discuss the stable concordance genus of a knot, which describes the behavior of the concordance genus under connected sum.
Manifolds admitting stable forms
Czech Academy of Sciences Publication Activity Database
Le, Hong-Van; Panák, Martin; Vanžura, Jiří
2008-01-01
Roč. 49, č. 1 (2008), s. 101-11 ISSN 0010-2628 R&D Projects: GA ČR(CZ) GP201/05/P088 Institutional research plan: CEZ:AV0Z10190503 Keywords : stable forms * automorphism groups Subject RIV: BA - General Mathematics
Interactive Stable Ray Tracing
DEFF Research Database (Denmark)
Dal Corso, Alessandro; Salvi, Marco; Kolb, Craig
2017-01-01
Interactive ray tracing applications running on commodity hardware can suffer from objectionable temporal artifacts due to a low sample count. We introduce stable ray tracing, a technique that improves temporal stability without the over-blurring and ghosting artifacts typical of temporal post-pr...
Directory of Open Access Journals (Sweden)
Behnaz Tolue
2018-07-01
Full Text Available In this paper we introduce stable subgroup graph associated to the group $G$. It is a graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1\\cap H_2\
Semi-implicit semi-Lagrangian modelling of the atmosphere: a Met Office perspective
Directory of Open Access Journals (Sweden)
Benacchio Tommaso
2016-09-01
Full Text Available The semi-Lagrangian numerical method, in conjunction with semi-implicit time integration, provides numerical weather prediction models with numerical stability for large time steps, accurate modes of interest, and good representation of hydrostatic and geostrophic balance. Drawing on the legacy of dynamical cores at the Met Office, the use of the semi-implicit semi-Lagrangian method in an operational numerical weather prediction context is surveyed, together with details of the solution approach and associated issues and challenges. The numerical properties and performance of the current operational version of the Met Office’s numerical model are then investigated in a simplified setting along with the impact of different modelling choices.
International Nuclear Information System (INIS)
Lyubovitskij, V.E.; Gutsche, Th.; Faessler, Amand; Mau, R. Vinh
2002-01-01
We apply the perturbative chiral quark model to the study of the low-energy πN interaction. Using an effective chiral Lagrangian we reproduce the Weinberg-Tomozawa result for the S-wave πN scattering lengths. After inclusion of the photon field we give predictions for the electromagnetic O(p 2 ) low-energy couplings of the chiral perturbation theory effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e 2 ) radiative corrections to the πN scattering amplitude. Finally, we estimate the leading isospin-breaking correction to the strong energy shift of the π - p atom in the 1s state, which is relevant for the experiment 'pionic hydrogen' at PSI
Lagrangian velocity statistics of directed launch strategies in a Gulf of Mexico model
Directory of Open Access Journals (Sweden)
M. Toner
2004-01-01
Full Text Available The spatial dependence of Lagrangian displacement and velocity statistics is studied in the context of a data assimilating numerical model of the Gulf Mexico. In the active eddy region of the Western Gulf, a combination of Eulerian and Lagrangian measures are used to locate strongly hyperbolic regions of the flow. The statistics of the velocity field sampled by sets of drifters launched specifically in these hyperbolic regions are compared to those produced by randomly chosen launch sites. The results show that particle trajectories initialized in hyperbolic regions preferentially sample a broader range of Eulerian velocities than do members of ensembles of randomly launched drifters. The velocity density functions produced by the directed launches compare well with Eulerian velocity pdfs. Implications for the development of launch strategies to improve Eulerian velocity field reconstruction from drifter data are discussed.
International Nuclear Information System (INIS)
Tyurin, A N
2000-01-01
The special geometry of calibrated cycles, which is closely related to the mirror symmetry among Calabi-Yau 3-manifolds, is in fact only a specialization of a more general geometry, which may naturally be called slightly deformed algebraic geometry or phase geometry. On the other hand, both of these geometries are parallel to classical gauge theory and its complexification. This article explains this parallelism. Hence the appearance of new invariants in complexified gauge theory is accompanied by the appearance of analogous invariants in the theory of special Lagrangian cycles, whose development is at present much more modest. Algebraic geometry is transformed into special Lagrangian geometry by the geometric Fourier transform (GFT). Roughly speaking, this construction coincides with the well-known 'spectral curve' constructions plus phase geometry
Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry
Energy Technology Data Exchange (ETDEWEB)
Parra, Felix I [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3NP (United Kingdom); Calvo, Ivan, E-mail: f.parradiaz1@physics.ox.ac.uk, E-mail: ivan.calvo@ciemat.es [Isaac Newton Institute for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0EH (United Kingdom)
2011-04-15
Gyrokinetic theory is based on an asymptotic expansion in the small parameter {epsilon}, defined as the ratio of the gyroradius and the characteristic length of variation of the magnetic field. In this paper, this ordering is strictly implemented to compute the electrostatic gyrokinetic phase-space Lagrangian in general magnetic geometry to order {epsilon}{sup 2}. In particular, a new expression for the complete second-order gyrokinetic Hamiltonian is provided, showing that in a rigorous treatment of gyrokinetic theory magnetic geometry and turbulence cannot be dealt with independently. The new phase-space gyrokinetic Lagrangian gives a Vlasov equation accurate to order {epsilon}{sup 2} and a Poisson equation accurate to order {epsilon}. The final expressions are explicit and can be implemented into any simulation without further computations.
Marom, Gil; Bluestein, Danny
2016-01-01
This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using Lagrangian methods with Eulerian computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and time averaging. This study demonstrated that the implementation assumptions can significantly affect the resulting stress accumulation, i.e., the blood damage model predictions. Careful considerations should be taken in the use of Lagrangian models. Ultimately, the appropriate assumptions should be considered based the physics of the specific case and sensitivity analysis, similar to the ones presented here, should be employed.
A Lagrangian particle method with remeshing for tracer transport on the sphere
Bosler, Peter A.; Kent, James; Krasny, Robert; Jablonowski, Christiane
2017-07-01
A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracer integral, and preservation of nonlinear correlation in a pair of tracers. We compare results obtained using LPM and the Lin-Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.
In-medium effective chiral lagrangians and the pion mass in nuclear matter
International Nuclear Information System (INIS)
Wirzba, A.
1995-01-01
We argue that the effective pion mass in nuclear matter obtained from chiral effective lagrangians is unique and does not depend on off-mass-shell extensions of the pion fields as e.g. the PCAC choice. The effective pion mass in isospin symmetric nuclear matter is predicted to increase slightly with increasing nuclear density, whereas the effective time-like pion decay constant and the magnitude of the density-dependent quark condensate decrease appreciably. The in-medium Gell-Mann-Oakes-Renner relation as well as other in-medium identities are studied in addition. Finally, several constraints on effective lagrangians for the description of the pion propagation in isospin symmetric, isotropic and homogeneous nuclear matter are discussed. (orig.)
Lagrangian neoclassical transport theory applied to the region near the magnetic axis
Energy Technology Data Exchange (ETDEWEB)
Satake, Shinsuke [The Graduate Univ. for Advanced Studies, Dept. of Fusion Science, Toki, Gifu (Japan); Okamoto, Masao; Sugama, Hideo [National Inst. for Fusion Science, Toki, Gifu (Japan)
2002-06-01
Neoclassical transport theory around the magnetic axis of a tokamak is studied, in which relatively wide ''potato'' orbits play an important role in transport. Lagrangian formulation of transport theory, which has been investigated to reflect finiteness of guiding-center orbit widths to transport equations, is developed in order to analyze neoclassical transport near the axis for a low-collisionality plasma. The treatment of self-collision term in Lagrangian formulation is revised to retain momentum conservation property of it. With directly reflecting the orbital properties of all the types of orbits in calculation, the ion thermal conductivity around the axis is found to decrease than from that predicted by conventional neoclassical theory. This result supports recent numerical simulations which show the reduction of thermal conductivity near the magnetic axis. (author)
International Nuclear Information System (INIS)
Lo, D.C.; Young, D.L.
2004-01-01
This paper describes the application of velocity-vorticity formulation of the Navier-Stokes equations for two-dimensional free surface flow using an arbitrary Lagrangian-Eulerian method. The velocity Poisson equations and the vorticity transport equations are solved using a finite element method to obtain the velocity and the vorticity fields in the interior region of the computational domain. The boundary-fitted coordinates system is adopted to solve the boundary equations for kinematic and dynamic conditions at the free surface using a finite difference method. The numerical model for the velocity-vorticity formulation is validated for a square cavity flow at Re=400 and 1000. The solitary wave reflected from a vertical wall is chosen as a test case for comparison and validation of the free surface flow model. Then the proposed numerical model is used to obtain flow results for the following free surface flow cases: (i) interaction between two opposite solitary waves, (ii) seiche phenomenon in a rectangular reservoir, and (iii) solitary wave through a submerged rectangular structure in a viscous fluid. The efficiency of the present numerical model for numerical treatment of free surface flows is discussed. Furthermore the advantage of this formulation with respect to primitive variables formulation is addressed from the computational point of view
Photoproduction of the eta prime meson in the effective Lagrangian approach
Energy Technology Data Exchange (ETDEWEB)
Mukhopadhyay, N.C.; Zhang, J.F. [Rensselaer Polytechnic Inst., Troy, NY (United States); Benmerrouche, M. [Univ. of Saskatchewan, Saskaton (Canada)
1994-04-01
In the framework of the effective Lagrangian approach, the authors study the {eta}{prime} photoproduction off protons, of great interest at CEBAF I and II. They calculate the contributions from the leading nucleon Born terms, vector meson exchanges, and estimate the resonance contributions, using the transition amplitudes from the recent quark model estimates by Capstick and Roberts. They discuss implications for the CEBAF experiments.
Detonation of high explosives in Lagrangian hydrodynamic codes using the programmed burn technique
International Nuclear Information System (INIS)
Berger, M.E.
1975-09-01
Two initiation methods were developed for improving the programmed burn technique for detonation of high explosives in smeared-shock Lagrangian hydrodynamic codes. The methods are verified by comparing the improved programmed burn with existing solutions in one-dimensional plane, converging, and diverging geometries. Deficiencies in the standard programmed burn are described. One of the initiation methods has been determined to be better for inclusion in production hydrodynamic codes
A 3D fast algorithm for computing Lagrangian coherent structures via ridge tracking
Lipinski, Doug; Mohseni, Kamran
2012-01-01
Lagrangian coherent structures (LCS) in fluid flows appear as co-dimension one ridges of the finite time Lyapunov exponent (FTLE) field. In three- dimensions this means two-dimensional ridges. A fast algorithm is presented here to locate and extract such ridge surfaces while avoiding unnecessary computations away from the LCS. This algorithm reduces the order of the computational complexity from O(1/dx^3) to about O(1/dx^2) by eliminating computations over most of the three dimensional domain...
A Lagrangian framework for deriving triples and quadruples corrections to the CCSD energy
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Kristensen, Kasper; Kjærgaard, Thomas
2014-01-01
Using the coupled cluster Lagrangian technique, we have determined perturbative corrections to the coupled cluster singles and doubles (CCSD) energy that converge towards the coupled cluster singles, doubles, and triples (CCSDT) and coupled cluster singles, doubles, triples, and quadruples (CCSDT...... some deficiencies of the latter related to the target energy of the series and its lack of size extensivity. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4862501]...
Lagrangian study of temporal changes of a surface flow through the Kamchatka Strait
Prants, S. V.; Andreev, A. G.; Uleysky, M. Yu.; Budyansky, M. V.
2014-01-01
Using Lagrangian methods we analyze a 20-year-long estimate of water flux through the Kamchatka Strait in the northern North Pacific based on AVISO velocity field. It sheds new light on the flux pattern and its variability on annual and monthly time scales. Strong seasonality in surface outflow through the strait could be explained by temporal changes in the wind stress over the northern and western Bering Sea slopes. Interannual changes in a surface outflow through the Kamchatka Strait corre...
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
An Effective Chiral Meson Lagrangian at O(p6) from the NJL Model
International Nuclear Information System (INIS)
Bel'kov, A.A.; Lanev, A.V.; Schaale, A.; Scherer, S.; Mainz Univ.
1994-01-01
In this work we present a strong chiral meson Lagrangian up to and including O(p 6 ) in the momentum expansion. It is derived from the Nambu-Jona-Lasinio (NJL) model using the heat-kernel method. Identities related to the properties of covariant derivatives of the chiral matrix U as well as field transformations have been used to predict the chiral coefficients of a minimal set of linearly independent terms. 16 refs
Prompt form of relativistic equations of motion in a model of singular lagrangian formalism
International Nuclear Information System (INIS)
Gajda, R.P.; Duviryak, A.A.; Klyuchkovskij, Yu.B.
1983-01-01
The purpose of the paper is to develope the way of transition from equations of motion in singular lagrangian formalism to three-dimensional equations of Newton type in the prompt form of dynamics in the framework of c -2 parameter expansion (s. c. quasireltativistic approaches), as well as to find corresponding integrals of motion. The first quasirelativistifc approach for Dominici, Gomis, Longhi model was obtained and investigated
Collective motions and non-polynomial lagrangians in Fokker-Planck dynamics
International Nuclear Information System (INIS)
Spina, A.; Vucetich, H.
1986-04-01
A method based on the ideas of collective motion is applied to Fokker-Planck dynamics. The usual diagramatic techniques used in stochastic dynamics are enlarged in order to deal with the non-polynomial Lagrangians that appear in the theory. The technique is tested and applied to the case of a self-sustained sinusoidal oscillator whose statistical behaviour is well understood: the Poincare oscillator. (author)
Slob, E.C.; Weiss, C.J.
2011-01-01
We distinguish between trivial and nontrivial differences in retrieving the real or imaginary parts of the Green's function. Trivial differences come from different Green's function definitions. The energy and Lagrangian forms constitute nontrivial differences. Magnetic noise sources suffice to
A Lagrangian Approach to Study the Gulf of Mexicoâs Deep Circulation (NCEI Accession 0159562)
National Oceanic and Atmospheric Administration, Department of Commerce — The data acquisition had two main elements: 1) a deep drifter study employing RAFOS floats and sound sources, which provided Lagrangian drifter tracks at 1500 and...
Hamiltonian and Lagrangian dynamics of charged particles including the effects of radiation damping
Qin, Hong; Burby, Joshua; Davidson, Ronald; Fisch, Nathaniel; Chung, Moses
2015-11-01
The effects of radiation damping (radiation reaction) on accelerating charged particles in modern high-intensity accelerators and high-intensity laser beams have becoming increasingly important. Especially for electron accelerators and storage rings, radiation damping is an effective mechanism and technique to achieve high beam luminosity. We develop Hamiltonian and Lagrangian descriptions of the classical dynamics of a charged particle including the effects of radiation damping in the general electromagnetic focusing channels encountered in accelerators. The direct connection between the classical Hamiltonian and Lagrangian theories and the more fundamental QED description of the synchrotron radiation process is also addressed. In addition to their theoretical importance, the classical Hamiltonian and Lagrangian theories of the radiation damping also enable us to numerically integrate the dynamics using advanced structure-preserving geometric algorithms. These theoretical developments can also be applied to runaway electrons and positrons generated during the disruption or startup of tokamak discharges. This research was supported by the U.S. Department of Energy (DE-AC02-09CH11466).
Rodríguez, Pablo Alonso; Carbajal, Noel; Rodríguez, Juan Heberto Gaviño
2017-07-01
Considering a semi-implicit approximation of the Coriolis terms, a numerical solution of the vertically integrated equations of motion is proposed. To test the two-dimensional numerical model, several experiments for the calculation of Euler, Stokes and Lagrange residual currents in the Gulf of California were carried out. To estimate the Lagrangian residual current, trajectories of particles were also simulated. The applied tidal constituents were M2, S2, K2, N2, K1, P1 and O1. At spring tides, strong tidal velocities occur in the northern half of the gulf. In this region of complex geometry, depths change from a few meter in the northern shelf zone to more than 3000 m in the southern part. In the archipelago region, the presence of islands alters amplitude and direction of tidal currents producing a rectification process which is reflected in a clockwise circulation around Tiburón Island in the Lagrangian residual current. The rectification process is explained by the superposition of the Euler and Stokes residual currents. Residual current patterns show several cyclonic and anticyclonic gyres in the Northern Gulf of California. Numerical experiments for individual and combinations of several tidal constituents revealed a large variability of Lagrangian trajectories.
Salibindla, Ashwanth; Masuk, Ashik Ullah Mohammad; Ni, Rui
2017-11-01
We have designed and constructed a new vertical water tunnel, V-ONSET, to investigate interfacial mass, momentum and energy transfer between two phases in a Lagrangian frame. This system features an independent control of mean flow and turbulence level. The mean flow opposes the rising/falling velocity of the second phase, ``suspending'' the particles and increasing tracking time in the view area. Strong turbulence is generated by shooting 88 digitally-controlled water jets into the test section. The second phase, either bubbles or oil droplets, can be introduced into the test section through a capillary island. In addition to this flow control system, V-ONSET comes with a 3D two-phase visualization system, consisting of high-speed cameras, two-colored LED system, and in-house Lagrangian particle tracking algorithm. This enables us to acquire the Lagrangian evolution of both phases and the interfacial transfer dynamics in between, paving the way for new closure models for two-phase simulations. Financial support for this project was provided by National Science Foundation under Grant Number: 1653389 and 1705246.
Lagrangian stochastic modelling in Large-Eddy Simulation of turbulent particle-laden flows
Chibbaro, Sergio; Innocenti, Alessio; Marchioli, Cristian
2017-11-01
Large-Eddy Simulation (LES) in Eulerian-Lagrangian studies of particle-laden flows is one of the most promising and viable approaches when Direct Numerical Simulation (DNS) is not affordable. However applicability of LES to particle-laden flows is limited by the modeling of the Sub-Grid Scale (SGS) turbulence effects on particle dynamics. These effects may be taken into account through a stochastic SGS model for the Equations of Particle Motion (EPM) that extends the Velocity Filtered Density Function method originally developed for reactive flows, to two-phase flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure, where a set of Stochastic Differential Equations (SDE) is solved along the trajectory of a particle. The resulting Lagrangian stochastic model has been tested for the reference case of turbulent channel flow. Tests with inertial particles have been performed focusing on particle preferential concentration and segregation in the near-wall region: upon comparison with DNS-based statistics, our results show improved accuracy with respect to LES with no SGS model in the EPM for different Stokes numbers. Furthermore, statistics of the particle velocity recover well DNS levels.
An Augmented Lagrangian Method for a Class of Inverse Quadratic Programming Problems
International Nuclear Information System (INIS)
Zhang Jianzhong; Zhang Liwei
2010-01-01
We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semidefinite cone constraint and its dual is a linearly constrained semismoothly differentiable (SC 1 ) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/r, and the rate of multiplier iterates is proportional to 1/√r, where r is the penalty parameter in the augmented Lagrangian. As the objective function of the dual problem is a SC 1 function involving the projection operator onto the cone of symmetrically semi-definite matrices, the analysis requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and properties of the projection operator in the symmetric-matrix space. Furthermore, the semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Finally numerical results, implemented by the augmented Lagrangian method, are reported.
Lagrangian and ALE Formulations For Soil Structure Coupling with Explosive Detonation
Directory of Open Access Journals (Sweden)
M Souli
2017-03-01
Full Text Available Simulation of Soil-Structure Interaction becomes more and more the focus of computational engineering in civil and mechanical engineering, where FEM (Finite element Methods for structural and soil mechanics and Finite Volume for CFD are dominant. New formulations have been developed for FSI applications using ALE (Arbitrary Lagrangian Eulerian and mesh free methods as SPH method, (Smooth Particle Hydrodynamic. In defence industry, engineers have been developing protection systems for many years to reduce the vulnerability of light armoured vehicles (LAV against mine blast using classical Lagrangian FEM methods. To improve simulations and assist in the development of these protections, experimental tests, and new numerical techniques are performed. To carry out these numerical calculations, initial conditions such as the loading prescribed by a mine on a structure need to be simulated adequately. The effects of blast on structures depend often on how these initial conditions are estimated and applied. In this report, two methods were used to simulate a mine blast: the classical Lagrangian and the ALE formulations. The comparative study was done for a simple and a more complex target. Particle methods as SPH method can also be used for soil structure interaction.
The Hamiltonian formulation of regular rth-order Lagrangian field theories
International Nuclear Information System (INIS)
Shadwick, W.F.
1982-01-01
A Hamiltonian formulation of regular rth-order Lagrangian field theories over an m-dimensional manifold is presented in terms of the Hamilton-Cartan formalism. It is demonstrated that a uniquely determined Cartan m-form may be associated to an rth-order Lagrangian by imposing conditions of congruence modulo a suitably defined system of contact m-forms. A geometric regularity condition is given and it is shown that, for a regular Lagrangian, the momenta defined by the Hamilton-Cartan formalism, together with the coordinates on the (r-1)st-order jet bundle, are a minimal set of local coordinates needed to express the Euler-Lagrange equations. When r is greater than one, the number of variables required is strictly less than the dimension of the (2r-1)st order jet bundle. It is shown that, in these coordinates, the Euler-Lagrange equations take the first-order Hamiltonian form given by de Donder. It is also shown that the geometrically natural generalization of the Hamilton-Jacobi procedure for finding extremals is equivalent to de Donder's Hamilton-Jacobi equation. (orig.)
Lagrangian predictability of high-resolution regional models: the special case of the Gulf of Mexico
Directory of Open Access Journals (Sweden)
P. C. Chu
2004-01-01
Full Text Available The Lagrangian prediction skill (model ability to reproduce Lagrangian drifter trajectories of the nowcast/forecast system developed for the Gulf of Mexico at the University of Colorado at Boulder is examined through comparison with real drifter observations. Model prediction error (MPE, singular values (SVs and irreversible-skill time (IT are used as quantitative measures of the examination. Divergent (poloidal and nondivergent (toroidal components of the circulation attractor at 50m depth are analyzed and compared with the Lagrangian drifter buoy data using the empirical orthogonal function (EOF decomposition and the measures, respectively. Irregular (probably, chaotic dynamics of the circulation attractor reproduced by the nowcast/forecast system is analyzed through Lyapunov dimension, global entropies, toroidal and poloidal kinetic energies. The results allow assuming exponential growth of prediction error on the attractor. On the other hand, the q-th moment of MPE grows by the power law with exponent of 3q/4. The probability density function (PDF of MPE has a symmetrical but non-Gaussian shape for both the short and long prediction times and for spatial scales ranging from 20km to 300km. The phenomenological model of MPE based on a diffusion-like equation is developed. The PDF of IT is non-symmetric with a long tail stretched towards large ITs. The power decay of the tail was faster than 2 for long prediction times.
Kuhn, Alexander
2013-12-05
Lagrangian coherent structures (LCSs) have become a widespread and powerful method to describe dynamic motion patterns in time-dependent flow fields. The standard way to extract LCS is to compute height ridges in the finite-time Lyapunov exponent field. In this work, we present an alternative method to approximate Lagrangian features for 2D unsteady flow fields that achieve subgrid accuracy without additional particle sampling. We obtain this by a geometric reconstruction of the flow map using additional material constraints for the available samples. In comparison to the standard method, this allows for a more accurate global approximation of LCS on sparse grids and for long integration intervals. The proposed algorithm works directly on a set 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. © 2013 The Authors Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd.
Palatella, Luigi; Bignami, Francesco; Falcini, Federico; Lacorata, Guglielmo; Lanotte, Alessandra S.; Santoleri, Rosalia
2014-02-01
The interannual variability in the transport of anchovy eggs and larvae in the Sicily Channel, relatively to the period 1999-2012, is studied by means of numerical simulations of the Mediterranean Forecasting System (MFS) circulation model provided by INGV. Subgrid-scale dynamics not resolved by the MFS model is parameterized in terms of kinematic fields. The latter affect small-scale tracer relative dispersion, while leaving the mean large-scale advection substantially unchanged. A Lagrangian Transport Index (LTI) can be defined to characterize the efficiency of the main currents, e.g., the Atlantic Ionian Stream, in connecting spawning and nursery areas to each other. In our case, this indicator comes from the first arrival time statistics of tracers traveling from a spawning area near Sciacca to a nursery area in proximity of Cape Passero. We observe, on the basis of LTI values, that there are years when the Lagrangian connectivity is very efficient (2004, 2008, 2012) and years when it is weak (2000, 2001, 2003, 2010). Lagrangian indicators like the LTI concur to explain observed fluctuations of larval density and, also, can be employed, more in general, in multivariate models of population dynamics.
Slob, Evert; Weiss, Chester J
2011-08-01
We distinguish between trivial and nontrivial differences in retrieving the real or imaginary parts of the Green's function. Trivial differences come from different Green's function definitions. The energy and lagrangian forms constitute nontrivial differences. Magnetic noise sources suffice to extract the quasistatic electromagnetic-field Earth impulse response in the lagrangian form. This is of interest for Earth subsurface imaging. A numerical example demonstrates that all source vector components are necessary to extract a single-field vector component.
Energy Technology Data Exchange (ETDEWEB)
Van Roekel, Luke [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2018-01-30
We have conducted a suite of Large Eddy Simulation (LES) to form the basis of a multi-model comparison (left). The results have led to proposed model improvements. We have verified that Eulerian-Lagrangian effective diffusivity estimates of mesoscale mixing are consistent with traditional particle statistics metrics (right). LES and Lagrangian particles will be utilized to better represent the movement of water into and out of the mixed layer.
Sakurai, Takayoshi; Kusano, Takashi; Saito, Yutaka; Hirato, Kota; Kato, Masakazu; Murai, Masahiko; Nagata, Junichi
This paper presents an effective and practical method based on the Lagrangian relaxation method for solving hydro-thermal unit commitment problem in which operational constraints involve spinning reserve requirements for thermal units and prohibition of simultaneous unit start-up/shut-down at the same plant. This method is processed in each iteration step of LRM that enables a direct solution. To improve convergence, this method applies an augmented Lagrangian relaxation method. Its effectiveness demonstrated for a real power system.
International Nuclear Information System (INIS)
Tibari, Elghali; Taous, Fouad; Marah, Hamid
2014-01-01
This report presents results related to stable isotopes analysis carried out at the CNESTEN DASTE in Rabat (Morocco), on behalf of Senegal. These analyzes cover 127 samples. These results demonstrate that Oxygen-18 and Deuterium in water analysis were performed by infrared Laser spectroscopy using a LGR / DLT-100 with Autosampler. Also, the results are expressed in δ values (‰) relative to V-SMOW to ± 0.3 ‰ for oxygen-18 and ± 1 ‰ for deuterium.
Dentz, M.; Kang, P. K.; Comolli, A.; Le Borgne, T.; Lester, D. R.
2016-12-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steadyheterogeneous porous and fractured media flows based on a stochastic relaxation process.This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods,which model persistence over a characteristic time scale.We first establish the relations between Eulerian and Lagrangian velocities for both equidistant and isochronal sampling along streamlines,under transient and stationary conditions. Based on this, we develop the CTRW approach for the spatial and temporaldynamics of Lagrangian velocities. Unlike classical CTRW formulations, the proposed approach quantifies both stationaryand non-stationary Lagrangian velocity statistics, and their evolution from arbitraryinitial velocity distributions. We provide explicit expressions for the Lagrangian velocity distributions,and determine the behaviors of the mean particle velocity, velocity covariance andparticle dispersion. We find strong correlation and anomalous dispersion for velocity distributions which are tailedtoward low velocities. The developed CTRW approach and thus the Lagrangian particle dynamics are fully determined by the Eulerian velocitydistribution and the characteristic correlation scale. The developed framework is applied to particle transport in two-dimensionalrandom fracture networks.
Forensic Stable Isotope Biogeochemistry
Cerling, Thure E.; Barnette, Janet E.; Bowen, Gabriel J.; Chesson, Lesley A.; Ehleringer, James R.; Remien, Christopher H.; Shea, Patrick; Tipple, Brett J.; West, Jason B.
2016-06-01
Stable isotopes are being used for forensic science studies, with applications to both natural and manufactured products. In this review we discuss how scientific evidence can be used in the legal context and where the scientific progress of hypothesis revisions can be in tension with the legal expectations of widely used methods for measurements. Although this review is written in the context of US law, many of the considerations of scientific reproducibility and acceptance of relevant scientific data span other legal systems that might apply different legal principles and therefore reach different conclusions. Stable isotopes are used in legal situations for comparing samples for authenticity or evidentiary considerations, in understanding trade patterns of illegal materials, and in understanding the origins of unknown decedents. Isotope evidence is particularly useful when considered in the broad framework of physiochemical processes and in recognizing regional to global patterns found in many materials, including foods and food products, drugs, and humans. Stable isotopes considered in the larger spatial context add an important dimension to forensic science.
Water-mass transformation in the Atlantic Ocean in a Lagrangian frame work
Berglund, Sara; Döös, Kristofer; Nycander, Jonas
2017-04-01
The world ocean is constantly moving, mostly due to density differences and atmospheric winds. This circulation is commonly refereed to as the Conveyor Belt circulation. In the Southern parts of the Atlantic, around the tip of South Africa, warm and saline water is entering. The water travels northward towards the equator where it increases in salinity. After passing the equator and reaching the North Atlantic, the water becomes cold and fresh, due to heat release to the atmosphere. Previous studies has introduced and computed the thermohaline stream function to connect water-mass transformations to the Conveyor Belt circulation in a temperature and salinity space. It has been suggested that the northward flowing water mass in the Atlantic Ocean can be shown in the stream function as water that converts from warm and saline to cold and fresh, and that the conversion is due to air-sea interactions. In the present study, Lagrangian trajectories are used to quantify the northward flowing water masses in the Atlantic Oceans contribution to the Conveyor Belt circulation in TS-space by introducing the Lagrangian thermohaline stream function. The stream function shows the Atlantic water-mass transformation, where warm and saline water is converted to cold and fresh, as the water flows from 17°S to 58°N. This conversion is found to be both isopycnal and diapycnal. To connect the water-mass transformation to a geographical position in the Atlantic Ocean, the Lagrangian divergence of heat and salt flux is introduced. Conversions of temperature and salinity shown by the Lagrangian thermohaline stream function are found to occur in the same region of the domain, however, with a different spread. The conversion of temperature is found to take place in the Gulf Stream, the upper flank of the North Atlantic subtropical gyre, and in the North Atlantic Drift, whereas the conversion of salinity occurs over a narrower band in the same regions. To be able to study the processes
Fitted-Stable Finite Difference Method for Singularly Perturbed Two ...
African Journals Online (AJOL)
A fitted-stable central difference method is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right) of the interval. A fitting factor is introduced in second order stable central difference scheme (SCD Method) and its value is obtained using the theory of ...
Stöckl, Stefan; Rotach, Mathias W.; Kljun, Natascha
2018-01-01
We discuss the results of Gibson and Sailor (Boundary-Layer Meteorol 145:399-406, 2012) who suggest several corrections to the mathematical formulation of the Lagrangian particle dispersion model of Rotach et al. (Q J R Meteorol Soc 122:367-389, 1996). While most of the suggested corrections had already been implemented in the 1990s, one suggested correction raises a valid point, but results in a violation of the well-mixed criterion. Here we improve their idea and test the impact on model results using a well-mixed test and a comparison with wind-tunnel experimental data. The new approach results in similar dispersion patterns as the original approach, while the approach suggested by Gibson and Sailor leads to erroneously reduced concentrations near the ground in convective and especially forced convective conditions.
Philipp, Anne; Hittmeir, Sabine; Seibert, Petra
2017-04-01
The distribution of wet deposition as calculated with Lagrangian particle transport models, e.g. FLEXPART (http://flexpart.eu) is governed by the intensity distribution of precipitation. Usually, meteorological input is taken from Eulerian weather forecast models, e.g. ECWMF (European Centre for Medium-Range Weather Forecasts), providing precipitation data as integrated over the time between two output times and over a grid cell. Simple linear interpolation would implicitly assume the integral value to be a point value valid at the grid centre and in the middle of the time interval, and thus underestimate peaks and overestimate local minima. In FLEXPART, a separate pre-processor is used to extract the meteorological input data from the ECMWF archive and prepare them for use in the model. Currently, a relatively simple method prepares the precipitation fields in a way that is consistent with the linear interpolation as applied in FLEXPART. This method is designed to conserve the original amount of precipitation. However, this leads to undesired temporal smoothing of the precipitation time series which even produces nonzero precipitation in dry intervals bordering a precipitation period. A new interpolation algorithm (currently in one dimension) was developed which introduces additional supporting grid points in each time interval (see companion contribution by Hittmeir, Philipp and Seibert). The quality of the algorithm is being tested at first by comparing 1-hourly values derived with the new algorithm from 3- (or 6-)hourly precipitation with the 1-hourly ECMWF model output. As ECWMF provides large-scale and convective precipitation data, the evaluation will be carried out separately as well as for different seasons and climatic zones.
International Nuclear Information System (INIS)
Cushman, Richard; Zhilinskii, Boris
2002-01-01
This letter deals with the global monodromy of singular Lagrangian toral fibrations defined by two degrees of freedom Liouville integrable systems with only focus-focus singular points. We show that any global monodromy matrix in Sl(2,Ζ ) is realizable by such a system. (author). Letter-to-the-editor
Influence of horse stable environment on human airways
Directory of Open Access Journals (Sweden)
Pringle John
2009-05-01
Full Text Available Abstract Background Many people spend considerable amount of time each day in equine stable environments either as employees in the care and training of horses or in leisure activity. However, there are few studies available on how the stable environment affects human airways. This study examined in one horse stable qualitative differences in indoor air during winter and late summer conditions and assessed whether air quality was associated with clinically detectable respiratory signs or alterations to selected biomarkers of inflammation and lung function in stable personnel. Methods The horse stable environment and stable-workers (n = 13 in one stable were investigated three times; first in the winter, second in the interjacent late summer and the third time in the following winter stabling period. The stable measurements included levels of ammonia, hydrogen sulphide, total and respirable dust, airborne horse allergen, microorganisms, endotoxin and glucan. The stable-workers completed a questionnaire on respiratory symptoms, underwent nasal lavage with subsequent analysis of inflammation markers, and performed repeated measurements of pulmonary function. Results Measurements in the horse stable showed low organic dust levels and high horse allergen levels. Increased viable level of fungi in the air indicated a growing source in the stable. Air particle load as well as 1,3-β-glucan was higher at the two winter time-points, whereas endotoxin levels were higher at the summer time-point. Two stable-workers showed signs of bronchial obstruction with increased PEF-variability, increased inflammation biomarkers relating to reported allergy, cold or smoking and reported partly work-related symptoms. Furthermore, two other stable-workers reported work-related airway symptoms, of which one had doctor's diagnosed asthma which was well treated. Conclusion Biomarkers involved in the development of airway diseases have been studied in relation to
On the space of solutions of the Hořava theory at the kinetic-conformal point
Bellorín, Jorge; Restuccia, Alvaro
2017-10-01
The nonprojectable Hořava theory at the kinetic-conformal point is defined by setting a specific value of the coupling constant of the kinetic term of the Lagrangian. This formulation has two additional second class-constraints that eliminate the extra mode. We show that the space of solutions of this theory in the Hamiltonian formalism is bigger than the space of solutions in the original Lagrangian formalism. In the Hamiltonian formalism there are certain configurations for the Lagrange multipliers that lead to solutions that cannot be found in the original Lagrangian formulation. We show specific examples in vacuum and with a source. The solution with the source has homogeneous and isotropic spatial hypersurfaces. The enhancement of the space of solutions leaves the possibility that new solutions applicable to cosmology, or to other physical systems, can be found in the Hamiltonian formalism.
Point-splitting as a regularization method for {lambda}{phi}{sup 4}-type vertices: Abelian case
Energy Technology Data Exchange (ETDEWEB)
Moura-Melo, Winder A.; Helayel Neto, J.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1998-11-01
We obtained regularized Abelian Lagrangians containing {lambda}{phi}{sup 4} -type vertices by means of a suitable point-splitting procedure. The calculation is developed in details for a general Lagrangian, whose fields (gauge and matter ones) satisfy certain conditions. We illustrates our results by considering some special cases, such as the Abelian Higgs, the ({psi}-bar{psi}){sup 2} and the Avdeev-Chizov (real rank-2 antisymmetric tensor as matter fields) models. We also discuss some features of the obtained Lagrangian such as the regularity and non-locality of its new integrating terms. Moreover, the resolution of the Abelian case may teach us some useful technical aspects when dealing with the non-Abelian one. (author)
Marginally Stable Nuclear Burning
Strohmayer, Tod E.; Altamirano, D.
2012-01-01
Thermonuclear X-ray bursts result from unstable nuclear burning of the material accreted on neutron stars in some low mass X-ray binaries (LMXBs). Theory predicts that close to the boundary of stability oscillatory burning can occur. This marginally stable regime has so far been identified in only a small number of sources. We present Rossi X-ray Timing Explorer (RXTE) observations of the bursting, high- inclination LMXB 4U 1323-619 that reveal for the first time in this source the signature of marginally stable burning. The source was observed during two successive RXTE orbits for approximately 5 ksec beginning at 10:14:01 UTC on March 28, 2011. Significant mHz quasi- periodic oscillations (QPO) at a frequency of 8.1 mHz are detected for approximately 1600 s from the beginning of the observation until the occurrence of a thermonuclear X-ray burst at 10:42:22 UTC. The mHz oscillations are not detected following the X-ray burst. The average fractional rms amplitude of the mHz QPOs is 6.4% (3 - 20 keV), and the amplitude increases to about 8% below 10 keV.This phenomenology is strikingly similar to that seen in the LMXB 4U 1636-53. Indeed, the frequency of the mHz QPOs in 4U 1323-619 prior to the X-ray burst is very similar to the transition frequency between mHz QPO and bursts found in 4U 1636-53 by Altamirano et al. (2008). These results strongly suggest that the observed QPOs in 4U 1323-619 are, like those in 4U 1636-53, due to marginally stable nuclear burning. We also explore the dependence of the energy spectrum on the oscillation phase, and we place the present observations within the context of the spectral evolution of the accretion-powered flux from the source.
A contribution to the theory of the extended Lagrangian formalism for rheonomic systems
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Mušicki Đorđe
2009-01-01
Full Text Available In this paper the generalization of the notion of variation in the extended Lagrangian formalism for the rheonomic mechanical systems (Đ. Mušicki, 2004 is formulated and analyzed in details. This formalism is based on the extension of a set of generalized coordinates by new quantities, which determine the position of the frame of reference to which the chosen generalized coordinates refer. In the process of varying, the notion of variation is extended so that these introduced quantities, being additional generalized coordinates, must also to be varied, since the position of each particle of this system is completely determined only by all these generalized coordinates. With the consistent utilization of this notion of variation, the main results of this extended Lagrangian formalism are systematically presented, with the emphasis on the corresponding energy laws, first examined by V. Vujičić (1987, where there are two types of the energy change laws dE/dt and the corresponding conservation laws. Furthermore, the generalized Noether's theorem for the nonconservative systems with the associated Killing's equations (B. Vujanović, 1978 is extended to this formulation of mechanics, and applied for obtaining the corresponding energy laws. It is demonstrated that these energy laws, which are more general and more natural than the usual ones, are in full accordance with the corresponding ones in the vector formulation of mechanics, if they are expressed in terms of quantities introduced in this extended Lagrangian formalism. Finally, the obtained results are illustrated by an example: the motion of a damped linear harmonious oscillator on an inclined plane, which moves along a horizontal axis, where it is demonstrated that there is valid an energy-like conservation law of Vujanović's type.
Emery, B. M.; Washburn, L.; Mezic, I.; Loire, S.; Arbabi, H.; Ohlmann, C.; Harlan, J.
2016-02-01
We apply several analysis methods to HF radar ocean surface current maps to investigate improvements in trajectory modeling. Results from a Lagrangian Stochastic Model (LSM) are compared with methods based on dynamical systems theory: hypergraphs and Koopman mode analysis. The LSM produces trajectories by integrating Eulerian fields from the HF radar, and accounts for sub-grid scale velocity variability by including a random component based on the Lagrangian decorrelation time. Hypergraphs also integrate the HF radar maps in time, showing areas of strain, strain-rotation, and mixing, by plotting the relative strengths of the eigenvalues of the gradient of the time-averaged Lagrangian velocity. Koopman mode analysis decomposes the velocity field into modes of variability, similarly to EOF or a Fourier analysis, though each Koopman mode varies in time with a distinct frequency. Each method simulates oil drift from a the oil spill of May, 2015 that occurred within the coverage area of the HF radars, in the Santa Barbara Channel near Refugio Beach, CA. Preliminary results indicate some skill in determining the transport of oil when compare to publicly available observations of oil in the Santa Barbara Channel. These simulations have not shown a connection between the Refugio spill site and oil observations in the Santa Monica Bay, near Los Angeles CA, though accumulation zones shown by the hypergraphs correlate in time and space with these observations. Improvements in the HF radar coverage and accuracy were observed during the spill by the deployment of an additional HF radar site near Gaviota, CA. Presently we are collecting observations of oil on beaches and in the ocean, determining the role of winds in the oil movement, and refining the methods. Some HF radar data is being post-processed to incorporate recent antenna calibrations for sites in Santa Monica Bay. We will evaluate effects of the newly processed data on analysis results.
Hoffmann, Lars; Rößler, Thomas; Griessbach, Sabine; Heng, Yi; Stein, Olaf
2017-04-01
Sulfur dioxide (SO2) emissions from strong volcanic eruptions are an important natural cause for climate variations. We applied our new Lagrangian transport model Massive-Parallel Trajectory Calculations (MPTRAC) to perform simulations for three case studies of volcanic eruption events. The case studies cover the eruptions of Grímsvötn, Iceland, Puyehue-Cordón Caulle, Chile, and Nabro, Eritrea, in May and June 2011. We used SO2 observations of the Atmospheric Infrared Sounder (AIRS/Aqua) and a backward trajectory approach to initialize the simulations. Besides validation of the new model, the main goal of our study was a comparison of simulations with different meteorological data products. We considered three reanalyses (ERA-Interim, MERRA, and NCAR/NCEP) and the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analysis. Qualitatively, the SO2 distributions from the simulations compare well with the AIRS data, but also with Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) aerosol observations. Transport deviations and the critical success index (CSI) are analyzed to evaluate the simulations quantitatively. During the first 5 or 10 days after the eruptions we found the best performance for the ECMWF analysis (CSI range of 0.25 - 0.31), followed by ERA-Interim (0.25 - 0.29), MERRA (0.23 - 0.27), and NCAR/NCEP (0.21 - 0.23). High temporal and spatial resolution of the meteorological data does lead to improved performance of Lagrangian transport simulations of volcanic emissions in the upper troposphere and lower stratosphere. Reference: Hoffmann L., Rößler, T., Griessbach, S., Heng, Y., and Stein, O., Lagrangian transport simulations of volcanic sulfur dioxide emissions: impact of meteorological data products, J. Geophys. Res., 121(9), 4651-4673, doi:10.1002/2015JD023749, 2016.
SALE-3D, 3-D Fluid Flow, Navier Stokes Equation Using Lagrangian or Eulerian Method
International Nuclear Information System (INIS)
Amsden, A.A.; Ruppel, H.M.
1991-01-01
1 - Description of problem or function: SALE-3D calculates three- dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a three-dimensional network of arbitrarily shaped, six-sided deformable cells, and a variety of user-selectable boundary conditions are provided in the program. 2 - Method of solution: SALE3D uses an ICED-ALE technique, which combines the ICE method of treating flow speeds and the ALE mesh treatment to calculate three-dimensional fluid flow. The finite- difference approximations to the conservation of mass, momentum, and specific internal energy differential equations are solved in a sequence of time steps on a network of deformable computational cells. The basic hydrodynamic part of each cycle is divided into three phases: (1) an explicit solution of the Lagrangian equations of motion updating the velocity field by the effects of all forces, (2) an implicit calculation using Newton-Raphson iterative scheme that provides time-advanced pressures and velocities, and (3) the addition of advective contributions for runs that are Eulerian or contain some relative motion of grid and fluid. A powerful feature of this three-phases approach is the ease with which
Directory of Open Access Journals (Sweden)
P. M. James
Full Text Available An ozone mini-hole is a synoptic-scale area of strongly reduced column total ozone, which undergoes a growth-decay cycle in association with baroclinic weather systems. The tracks of mini-hole events recorded during the TOMS observation period over the Northern Hemisphere provide a database for building anomaly fields of various meteorological parameters, following each mini-hole center in a Lagrangian sense. The resulting fields provide, for the first time, a complete mean Lagrangian picture of the three-dimensional structure of typical ozone mini-holes in the Northern Hemisphere. Mini-holes are shown to be associated with anomalous warm anticyclonic flow in the upper troposphere and cold cyclonic anomalies in the middle stratosphere. Ascending air columns occur upstream and descent downstream of the mini-hole centers. Band-pass filtering is used to reveal the transient synoptic nature of mini-holes embedded within larger scale circulation anomalies. Significant correlations between ozone and Ertel’s potential vorticity on isentropes (IPV both near the tropopause and in the middle stratosphere are shown and then utilized by reconstructing the Lagrangian analysis to follow local IPV anomalies instead of ozone minima. By using IPV as a proxy for ozone, the geopotential anomaly dipolar structure in the vertical characteristic of mini-holes is shown to result from a superposition of two largely independent dynamical components, stratospheric and tropospheric, typically operating on different time scales. Hence, ozone mini-holes may be viewed primarily as phenomena of coincidence.
Key words. Meteorology and atmospheric dynamics (middle atmosphere dynamics; synoptic-scale meteorology
Directory of Open Access Journals (Sweden)
P. M. James
2002-06-01
Full Text Available An ozone mini-hole is a synoptic-scale area of strongly reduced column total ozone, which undergoes a growth-decay cycle in association with baroclinic weather systems. The tracks of mini-hole events recorded during the TOMS observation period over the Northern Hemisphere provide a database for building anomaly fields of various meteorological parameters, following each mini-hole center in a Lagrangian sense. The resulting fields provide, for the first time, a complete mean Lagrangian picture of the three-dimensional structure of typical ozone mini-holes in the Northern Hemisphere. Mini-holes are shown to be associated with anomalous warm anticyclonic flow in the upper troposphere and cold cyclonic anomalies in the middle stratosphere. Ascending air columns occur upstream and descent downstream of the mini-hole centers. Band-pass filtering is used to reveal the transient synoptic nature of mini-holes embedded within larger scale circulation anomalies. Significant correlations between ozone and Ertel’s potential vorticity on isentropes (IPV both near the tropopause and in the middle stratosphere are shown and then utilized by reconstructing the Lagrangian analysis to follow local IPV anomalies instead of ozone minima. By using IPV as a proxy for ozone, the geopotential anomaly dipolar structure in the vertical characteristic of mini-holes is shown to result from a superposition of two largely independent dynamical components, stratospheric and tropospheric, typically operating on different time scales. Hence, ozone mini-holes may be viewed primarily as phenomena of coincidence.Key words. Meteorology and atmospheric dynamics (middle atmosphere dynamics; synoptic-scale meteorology
An airborne perfluorocarbon tracer system and its first application for a Lagrangian experiment
Ren, Y.; Baumann, R.; Schlager, H.
2015-01-01
A perfluorocarbon tracer system (PERTRAS), specifically designed for Lagrangian aircraft experiments, has been developed by the Deutsches Zentrum für Luft- und Raumfahrt (German Aerospace Center, DLR). It consists of three main parts: a tracer release unit (RU), an adsorption tube sampler (ATS), and a tracer analytical system. The RU was designed for airborne tracer release experiments; meanwhile, it can be used on various platforms for different experimental purposes (here research vessel). PERTRAS was for the first time applied in the field campaign Stratospheric ozone: Halogen Impacts in a Varying Atmosphere (SHIVA) in November 2011. An amount of 8.8 kg perfluoromethylcyclopentane (PMCP) was released aboard the research vessel Sonne (RV Sonne) near the operational site of this campaign, Miri, Malaysia, on 21 November. The tracer samples collected using the ATS onboard the DLR research aircraft Falcon were analyzed in the laboratory using a thermal desorber-gas chromatography-mass spectrometry (TD-GC-MS) system. Guided by forecasts calculated with the Lagrangian model Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT), 64 tracer samples were collected onboard the Falcon approximately 5 and 25 h after the release, mostly with a time resolution of 1 min. Enhanced PMCP concentrations relative to ambient PMCP background values (mean: 6.62 fmol mol-1) were detected during three intersects of the fresh tracer plume (age 5 h), with a maximum value of 301.33 fmol mol-1. This indicates that the fresh tracer plume was successfully intercepted at the forecast position. During the second flight, 25 h after the release, the center of tracer plume was not detected by the sampling system due to a faster advection of the plume than forecast. The newly developed PERTRAS system has been successfully deployed for the first time. The instrumental setup and comparisons between the measurements and HYSPLIT simulations are presented in this study.
Eastman, R. M.; Wood, R.
2017-12-01
This study observes the 24-hour Lagrangian evolution of stratocumulus cloud amount and PBL depth in four eastern subtropical ocean basins: the NE Pacific, SE Pacific, SE Atlantic, and E Indian. Nearly 170,000 trajectories are computed using the 2-D wind field at 925mb and cloud properties are sampled along these trajectories twice daily as the A-Train satellite constellation passes overhead. Concurrent measurements of the overlying humidity and temperature profiles are interpolated from the ERA-Interim reanalysis grids. Cloud properties are sampled by MODIS and a measure of planetary boundary layer (PBL) depth is calculated using MODIS cloud top temperatures, CALIPSO lidar observations of cloud top heights, and ERA-Interim sea surface temperatures. High humidity overlying the PBL can reduce cloud top cooling by counteracting radiative cooling and by reducing evaporation within the entrainment zone. Both of these effects can slow the entrainment rate and change cloud evolution. To discern which effect is more important the humidity profile is broken into two distinct components: the specific humidity directly above the inversion, which is entraining into the boundary layer, and the column of specific humidity above that layer, which is radiatively interacting with the PBL, but not directly entraining. These two measures of humidity are compared in the Lagrangian framework. Results suggest that humidity above the PBL has a stronger effect on the Lagrangian PBL deepening rate compared to lower tropospheric stability. A comparison of PBL deepening rates driven by the entraining humidity versus the radiating humidity shows that the radiative effects of overlying humidity are dominant with respect to entrainment. However, the entraining effects of humidity are more important in prolonging cloud lifetime.
Bresch, D.; Fernández-Nieto, E. D.; Ionescu, I. R.; Vigneaux, P.
In this paper we propose a well-balanced finite volume/augmented Lagrangian method for compressible visco-plastic models focusing on a compressible Bingham type system with applications to dense avalanches. For the sake of completeness we also present a method showing that such a system may be derived for a shallow flow of a rigid-viscoplastic incompressible fluid, namely for incompressible Bingham type fluid with free surface. When the fluid is relatively shallow and spreads slowly, lubrication-style asymptotic approximations can be used to build reduced models for the spreading dynamics, see for instance [N.J. Balmforth et al., J. Fluid Mech (2002)]. When the motion is a little bit quicker, shallow water theory for non-Newtonian flows may be applied, for instance assuming a Navier type boundary condition at the bottom. We start from the variational inequality for an incompressible Bingham fluid and derive a shallow water type system. In the case where Bingham number and viscosity are set to zero we obtain the classical Shallow Water or Saint-Venant equations obtained for instance in [J.F. Gerbeau, B. Perthame, DCDS (2001)]. For numerical purposes, we focus on the one-dimensional in space model: We study associated static solutions with sufficient conditions that relate the slope of the bottom with the Bingham number and domain dimensions. We also propose a well-balanced finite volume/augmented Lagrangian method. It combines well-balanced finite volume schemes for spatial discretization with the augmented Lagrangian method to treat the associated optimization problem. Finally, we present various numerical tests.
An efficient Lagrangian stochastic model of vertical dispersion in the convective boundary layer
Franzese, Pasquale; Luhar, Ashok K.; Borgas, Michael S.
We consider the one-dimensional case of vertical dispersion in the convective boundary layer (CBL) assuming that the turbulence field is stationary and horizontally homogeneous. The dispersion process is simulated by following Lagrangian trajectories of many independent tracer particles in the turbulent flow field, leading to a prediction of the mean concentration. The particle acceleration is determined using a stochastic differential equation, assuming that the joint evolution of the particle velocity and position is a Markov process. The equation consists of a deterministic term and a random term. While the formulation is standard, attention has been focused in recent years on various ways of calculating the deterministic term using the well-mixed condition incorporating the Fokker-Planck equation. Here we propose a simple parameterisation for the deterministic acceleration term by approximating it as a quadratic function of velocity. Such a function is shown to represent well the acceleration under moderate velocity skewness conditions observed in the CBL. The coefficients in the quadratic form are determined in terms of given turbulence statistics by directly integrating the Fokker-Planck equation. An advantage of this approach is that, unlike in existing Lagrangian stochastic models for the CBL, the use of the turbulence statistics up to the fourth order can be made without assuming any predefined form for the probability distribution function (PDF) of the velocity. The main strength of the model, however, lies in its simplicity and computational efficiency. The dispersion results obtained from the new model are compared with existing laboratory data as well as with those obtained from a more complex Lagrangian model in which the deterministic acceleration term is based on a bi-Gaussian velocity PDF. The comparison shows that the new model performs well.
International Nuclear Information System (INIS)
Samba, G.
1985-04-01
It is often desirable to solve the two dimensional multigroup transport equation for (r-z) geometries directly given by hydrodynamic calculations. Usually, only Monte-Carlo codes are able to compute α or k eigenvalues on such geometries. Most deterministic codes use an orthogonal mesh or restrict the mesh to a regular triangular grid. Other methods were developed in C.E.A. and Los Alamos but do not solve the problem of sliding between two Lagrangian blocks. Thus, we have developed a production code which solves these problems and is able to get α or k eigenvalues with a good accuracy for such geometries
Effective meson lagrangian with chiral and heavy quark symmetries from quark flavor dynamics
International Nuclear Information System (INIS)
Ebert, D.; Feldmann, T.; Friedrich, R.; Reinhardt, H.
1994-06-01
By bosonization of an extended NJL model we derive an effective meson theory which describes the interplay between chiral symmetry and heavy quark dynamics. This effective theory is worked out in the low-energy regime using the gradient expansion. The resulting effective lagrangian describes strong and weak interactions of heavy B and D mesons with pseudoscalar Goldstone bosons and light vector and axial-vector mesons. Heavy meson weak decay constants, coupling constants and the Isgur-Wise function are predicted in terms of the model parameters partially fixed from the light quark sector. Explicit SU(3) F symmetry breaking effects are estimated and, if possible, confronted with experiment. (orig.)
Lagrangian Particle Hydrodynamics for Fluid Structure Collision Analysis in Advanced Aerostructures
Bayandor, Javid
2008-11-01
One of the key aerostructure certification criteria pertaining to the design phase, particularly in advanced structural concepts, addresses fluid-structure crash scenarios such as aircraft ditching on the water surface and bird-strike. Destructive trials on full-scale aerospace prototypes to evaluate damage sustained during fluid-structure collisions are extremely costly. Therefore, efforts have been made to numerically model such events with sufficient accuracy to significantly reduce the minimum number of tests required for design approval procedures. This presentation identifies the simulation strategies adopted using the Lagrangian particle hydrodynamics methodology in pursuit of such an investigation.
ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code
Energy Technology Data Exchange (ETDEWEB)
Noble, Charles R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Anderson, Andrew T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Barton, Nathan R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Bramwell, Jamie A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Capps, Arlie [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Chang, Michael H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Chou, Jin J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Dawson, David M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Diana, Emily R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Dunn, Timothy A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Faux, Douglas R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Fisher, Aaron C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Greene, Patrick T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Heinz, Ines [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kanarska, Yuliya [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Khairallah, Saad A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Liu, Benjamin T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Margraf, Jon D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nichols, Albert L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nourgaliev, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Puso, Michael A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Reus, James F. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Robinson, Peter B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Shestakov, Alek I. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Solberg, Jerome M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Taller, Daniel [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Tsuji, Paul H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); White, Christopher A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); White, Jeremy L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-05-23
ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian- Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid finite element and finite volume formulation to model fluid and elastic-plastic response of materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates many physical phenomena.
Using an Augmented Lagrangian Method and block fracturing in the DDA method
International Nuclear Information System (INIS)
Lin, C.T.; Amadei, B.; Sture, S.
1994-01-01
This paper presents two extensions to the Discontinuous Deformation Analysis (DDA) method orginally proposed by Shi for modeling the response of blocky rock masses to mechanical loading. The first extension consists of improving the block contact algorithm. An Augmented Lagrangian Method is used to replace the Penalty Method orginally proposed. It allows Lagrange multipliers to be introduced without increasing the number of equations that need to be solved and thus, block contract forces can be calculated more accurately. A block fracturing capability based on a three-parameter Mohr-Coulomb criterion represents the second extension. It allows for shear or tensile fracturing of intact blocks and the formation of smaller blocks
International Nuclear Information System (INIS)
Mordant, Maurice.
1981-04-01
To solve a multigroup stationary neutron transport equation in two-dimensional geometries (X-Y), (R-O) or (R-Z) generally on uses discrete ordinates and rectangular meshes. The way to do it is then well known, well documented and somewhat obvious. If one needs to treat awkward geometries or distorted meshes, things are not so easy and the way to do it is no longer straightforward. We have studied this problem at Limeil Nuclear Center and as an alternative to Monte Carlo methods and code we have implemented in ZEPHYR code at least two efficient finite element solutions for Lagrangian meshes involving any kind of triangles and quadrilaterals
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.
Directory of Open Access Journals (Sweden)
M. Wei
2013-09-01
Full Text Available A number of real-time ocean model forecasts were carried out successfully at Naval Research Laboratory (NRL to provide modeling support and numerical guidance to the CARTHE GLAD at-sea experiment during summer 2012. Two RELO ensembles and three single models using NCOM and HYCOM with different resolutions were carried out. A calibrated ensemble system with enhanced spread and reliability was developed to better support this experiment. The calibrated ensemble is found to outperform the un-calibrated ensemble in forecasting accuracy, skill, and reliability for all the variables and observation spaces evaluated. The metrics used in this paper include RMS error, anomaly correlation, PECA, Brier score, spread reliability, and Talagrand rank histogram. It is also found that even the un-calibrated ensemble outperforms the single forecast from the model with the same resolution. The advantages of the ensembles are further extended to the Lagrangian framework. In contrast to a single model forecast, the RELO ensemble provides not only the most likely Lagrangian trajectory for a particle in the ocean, but also an uncertainty estimate that directly reflects the complicated ocean dynamics, which is valuable for decision makers. The examples show that the calibrated ensemble with more reliability can capture trajectories in different, even opposite, directions, which would be missed by the un-calibrated ensemble. The ensembles are applied to compute the repelling and attracting Lagrangian coherent structures (LCSs, and the uncertainties of the LCSs, which are hard to obtain from a single model forecast, are estimated. It is found that the spatial scales of the LCSs depend on the model resolution. The model with the highest resolution produces the finest, small-scale, LCS structures, while the model with lowest resolution generates only large-scale LCSs. The repelling and attracting LCSs are found to intersect at many locations and create complex mesoscale
A New Lagrangian Relaxation Method Considering Previous Hour Scheduling for Unit Commitment Problem
Khorasani, H.; Rashidinejad, M.; Purakbari-Kasmaie, M.; Abdollahi, A.
2009-08-01
Generation scheduling is a crucial challenge in power systems especially under new environment of liberalization of electricity industry. A new Lagrangian relaxation method for unit commitment (UC) has been presented for solving generation scheduling problem. This paper focuses on the economical aspect of UC problem, while the previous hour scheduling as a very important issue is studied. In this paper generation scheduling of present hour has been conducted by considering the previous hour scheduling. The impacts of hot/cold start-up cost have been taken in to account in this paper. Case studies and numerical analysis presents significant outcomes while it demonstrates the effectiveness of the proposed method.
Lagrangian evolution of deformation of finite-size bubbles in turbulent multiphase flow
Masuk, Ashik Ullah Mohammad; Salibindla, Ashwanth; Ni, Rui
2017-11-01
Finite-size bubbles tend to deform in a strong turbulent environment because of the complex interfacial momentum transfer between them. We have utilized the new V-ONSET turbulence multiphase flow facility to track the deformation and the couplings between two phases in a 3D Lagrangian framework. This rich dataset allows us to understand the roles played by the dynamic pressure and viscous stress, as well as different forces that contribute to the interfacial momentum transfer. Financial support for this project was provided by National Science Foundation under Grant Number: 1653389 and 1705246.
A new Lagrangian random choice method for steady two-dimensional supersonic/hypersonic flow
Loh, C. Y.; Hui, W. H.
1991-01-01
Glimm's (1965) random choice method has been successfully applied to compute steady two-dimensional supersonic/hypersonic flow using a new Lagrangian formulation. The method is easy to program, fast to execute, yet it is very accurate and robust. It requires no grid generation, resolves slipline and shock discontinuities crisply, can handle boundary conditions most easily, and is applicable to hypersonic as well as supersonic flow. It represents an accurate and fast alternative to the existing Eulerian methods. Many computed examples are given.
Lagrangian duality applied to the vehicle routing problem with time windows
DEFF Research Database (Denmark)
Kallehauge, Brian; Larsen, Jesper; Madsen, Oli B.G.
2006-01-01
This paper considers the vehicle routing problem with time windows, where the service of each customer must start within a specified time interval. We consider the Lagrangian relaxation of the constraint set requiring that each customer must be served by exactly one vehicle yielding a constrained......) algorithm for the VRPTW. Making use of this acceleration strategy at the master problem level gives a significant speed-up compared to algorithms in the literature based on traditional column generation. We have solved two test problems introduced in 2001 by Gehring and Homberger with 400 and 1000 customers...
Energy Technology Data Exchange (ETDEWEB)
Bartels, J.; Peters, D. [Rostock Univ. (Germany). Inst. fuer Atmosphaerenphysik
1997-12-31
The poleward advection of upper-tropospheric air is investigated for poleward Rossby wave breaking events. During boreal winter months the isentropic deformations of the tropopause are examined using maps of Ertel`s potential vorticity (EPV) and contour advection (CA) calculations. The role of ambient baro-tropic flow is further examined by idealized numerical models. In the vicinity of the tropopause the characteristic Lagrangian transport of air masses for ECMWF-analysis data are compared with high resolution (T106) ECHAM4 experiments. (author) 3 refs.
Mixmaster cosmological model in theories of gravity with a quadratic Lagrangian
International Nuclear Information System (INIS)
Barrow, J.D.; Sirousse-Zia, H.
1989-01-01
We use the method of matched asymptotic expansions to examine the behavior of the vacuum Bianchi type-IX mixmaster universe in a gravity theory derived from a purely quadratic gravitational Lagrangian. The chaotic behavior characteristic of the general-relativistic mixmaster model disappears and the asymptotic behavior is of the monotonic, nonchaotic form found in the exactly soluble Bianchi type-I models of the quadratic theory. The asymptotic behavior far from the singularity is also found to be of monotonic nonchaotic type
Dynamics and mission design near libration points
Gómez, G; Llibre, J; Martínez, R
2001-01-01
It is well known that the restricted three-body problem has triangular equilibrium points. These points are linearly stable for values of the mass parameter, µ , below Routh's critical value, µ 1 . It is also known that in the spatial case they are nonlinearly stable, not for all the initial conditions in a neighborhood of the equilibrium points L 4 , L 5 but for a set of relatively large measures. This follows from the celebrated Kolmogorov-Arnold-Moser theorem. In fact there are neighborhoods of computable size for which one obtains "practical stability" in the sense that the massless partic
Higher-Order Advection-Based Remap of Magnetic Fields in an Arbitrary Lagrangian-Eulerian Code
Cornille, Brian; White, Dan
2017-10-01
We will present methods formulated for the Eulerian advection stage of an arbitrary Lagrangian-Eulerian code for the new addition of magnetohydrodynamic (MHD) effects. The various physical fields are advanced in time using a Lagrangian formulation of the system. When this Lagrangian motion produces substantial distortion of the mesh, it can be difficult or impossible to progress the simulation forward. This is overcome by relaxation of the mesh while the physical fields are frozen. The code has already successfully been extended to include evolution of magnetic field diffusion during the Lagrangian motion stage. This magnetic field is discretized using an H(div) compatible finite element basis. The advantage of this basis is that the divergence-free constraint of magnetic fields is maintained exactly during the Lagrangian motion evolution. Our goal is to preserve this property during Eulerian advection as well. We will demonstrate this property and the importance of MHD effects in several numerical experiments. In pulsed-power experiments magnetic fields may be imposed or spontaneously generated. When these magnetic fields are present, the evolution of the experiment may differ from a comparable configuration without magnetic fields. Prepared by LLNL under Contract DE-AC52-07NA27344. Supported by DOE CSGF under Grant Number DE-FG02-97ER25308.
Yuan, Kai; Knoop, Victor L.; Hoogendoorn, Serge P.
2017-01-01
On freeways, congestion always leads to capacity drop. This means the queue discharge rate is lower than the pre-queue capacity. Our recent research findings indicate that the queue discharge rate increases with the speed in congestion, that is the capacity drop is strongly correlated with the congestion state. Incorporating this varying capacity drop into a kinematic wave model is essential for assessing consequences of control strategies. However, to the best of authors' knowledge, no such a model exists. This paper fills the research gap by presenting a Lagrangian kinematic wave model. "Lagrangian" denotes that the new model is solved in Lagrangian coordinates. The new model can give capacity drops accompanying both of stop-and-go waves (on homogeneous freeway section) and standing queues (at nodes) in a network. The new model can be applied in a network operation. In this Lagrangian kinematic wave model, the queue discharge rate (or the capacity drop) is a function of vehicular speed in traffic jams. Four case studies on links as well as at lane-drop and on-ramp nodes show that the Lagrangian kinematic wave model can give capacity drops well, consistent with empirical observations.
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.
Lana, Arancha; Fernández, Vicente; Orfila, Alejandro; Troupin, Charles; Tintoré, Joaquín
2015-04-01
SOCIB High Frequency (HF) radar is one component of a multi-platform system located in the Balearic Islands and made up of Lagrangian platforms (profilers and drifting buoys), fixed stations (sea-level, weather, mooring and coastal), beach monitoring (camera), gliders, a research vessel as well as an ocean forecast system (waves and hydrodynamics). The HF radar system overlooks the Ibiza Channel, known as a 'choke point" where Atlantic and Mediterranean water masses interact and where meridional exchanges of water mass properties between the Balearic and the Algerian sub-basins take place. In order to determine the reliability of surface velocity measurements in this area, a quality assessment of the HF Radar is essential. We present the results of several validation experiments performed in the Ibiza Channel in 2013 and 2014. Of particular interest is an experiment started in September 2014 when a set of 13 surface drifters with different shapes and drogue lengths were released in the area covered by the HF radar. The drifter trajectories can be examined following the SOCIB Deployment Application (DAPP): http://apps.socib.es/dapp. Additionally, a 1-year long time series of surface currents obtained from a moored surface current-meter located in the Ibiza Channel, inside the area covered by the HF radar, was also used as a useful complementary validation exercise. Direct comparison between both radial surface currents from each radar station and total derived velocities against drifters and moored current meter velocities provides an assessment of the HF radar data quality at different temporal periods and geographical areas. Statistics from these comparisons give good correlation and low root-mean-square deviation. The results will be discussed for different months, geographical areas and types of surface drifters and wind exposure. Moreover, autonomous underwater glider constitutes an additional source of information for the validation of the observed velocity
Yearsley, J. R.
2017-12-01
The semi-Lagrangian numerical scheme employed by RBM, a model for simulating time-dependent, one-dimensional water quality constituents in advection-dominated rivers, is highly scalable both in time and space. Although the model has been used at length scales of 150 meters and time scales of three hours, the majority of applications have been at length scales of 1/16th degree latitude/longitude (about 5 km) or greater and time scales of one day. Applications of the method at these scales has proven successful for characterizing the impacts of climate change on water temperatures in global rivers and on the vulnerability of thermoelectric power plants to changes in cooling water temperatures in large river systems. However, local effects can be very important in terms of ecosystem impacts, particularly in the case of developing mixing zones for wastewater discharges with pollutant loadings limited by regulations imposed by the Federal Water Pollution Control Act (FWPCA). Mixing zone analyses have usually been decoupled from large-scale watershed influences by developing scenarios that represent critical scenarios for external processes associated with streamflow and weather conditions . By taking advantage of the particle-tracking characteristics of the numerical scheme, RBM can provide results at any point in time within the model domain. We develop a proof of concept for locations in the river network where local impacts such as mixing zones may be important. Simulated results from the semi-Lagrangian numerical scheme are treated as input to a finite difference model of the two-dimensional diffusion equation for water quality constituents such as water temperature or toxic substances. Simulations will provide time-dependent, two-dimensional constituent concentration in the near-field in response to long-term basin-wide processes. These results could provide decision support to water quality managers for evaluating mixing zone characteristics.
Investigation of erosion behavior in different pipe-fitting using Eulerian-Lagrangian approach
Kulkarni, Harshwardhan; Khadamkar, Hrushikesh; Mathpati, Channamallikarjun
2017-11-01
Erosion is a wear mechanism of piping system in which wall thinning occurs because of turbulent flow along with along with impact of solid particle on the pipe wall, because of this pipe ruptures causes costly repair of plant and personal injuries. In this study two way coupled Eulerian-Lagrangian approach is used to solve the liquid solid (water-ferrous suspension) flow in the different pipe fitting namely elbow, t-junction, reducer, orifice and 50% open gate valve. Simulations carried out using incomressible transient solver in OpenFOAM for different Reynolds's number (10k, 25k, 50k) and using WenYu drag model to find out possible higher erosion region in pipe fitting. Used transient solver is a hybrid in nature which is combination of Lagrangian library and pimpleFoam. Result obtained from simulation shows that exit region of elbow specially downstream of straight, extradose of the bend section more affected by erosion. Centrifugal force on solid particle at bend affect the erosion behavior. In case of t-junction erosion occurs below the locus of the projection of branch pipe on the wall. For the case of reducer, orifice and a gate valve reduction area as well as downstream is getting more affected by erosion because of increase in velocities.
The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems
Koon, Wang Sang; Marsden, Jerrold E.
1997-08-01
This paper compares the Hamiltonian approach to systems with nonholonomic constraints (see [31, 2, 4, 29] and references therein) with the Lagrangian approach (see [16, 27, 9]). There are many differences in the approaches and each has its own advantages; some structures have been discovered on one side and their analogues on the other side are interesting to clarify. For example, the momentum equation and the reconstruction equation were first found on the Lagrangian side and are useful for the control theory of these systems, while the failure of the reduced two-form to be closed (i.e., the failure of the Poisson bracket to satisfy the Jacobi identity) was first noticed on the Hamiltonian side. Clarifying the relation between these approaches is important for the future development of the control theory and stability and bifurcation theory for such systems. In addition to this work, we treat, in this unified framework, a simplified model of the bicycle (see [12, 13]), which is an important underactuated (nonminimum phase) control system.
Cauchy's almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow
Frisch, Uriel; Villone, Barbara
2014-09-01
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to Göttingen University, contain major discoveries on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy's formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation theorem was to be rediscovered independently by William Thomson (Kelvin) in 1869. Cauchy's invariants were only occasionally cited in the 19th century - besides Hankel, foremost by George Stokes and Maurice Lévy - and even less so in the 20th until they were rediscovered via Emmy Noether's theorem in the late 1960, but reattributed to Cauchy only at the end of the 20th century by Russian scientists.
International Nuclear Information System (INIS)
Babic, M.; Kljenak, I.
2007-01-01
The purposes of containment spray system operation during a severe accident in a light water reactor (LWR) nuclear power plant (NPP) are to depressurize the containment by steam condensation on spray droplets, to reduce the risk of hydrogen burning by mixing the containment atmosphere, and to collect radioactive aerosols from the containment atmosphere. While the depressurization may be predicted fairly well using lumped-parameter codes, the prediction of mixing and collection of aerosols requires a local description of transport phenomena. In the present work, modelling of sprays on local instantenous scale is presented and the Design of Experiment (DOE) method is used to assess the influence of boundary conditions on the simulation results. Simulation results are compared to the TOSQAN 101 spray test, which was used for a benchmarking exercise in the European Severe accident research network of excellence (SARNET). The modelling approach is based on a Lagrangian description of the dispersed liquid phase (droplets), an Eulerian approach for the description of the continuous gas phase, and a two-way interaction between the phases. The simulations are performed using a combination of the computational fluid dynamics (CFD) code CFX4.4, which solves the gas transport equations, and of a newly proposed dedicated Lagrangian droplet-tracking code. (author)
Lagrangian mass-flow investigations of inorganic contaminants in wastewater-impacted streams
Barber, L.B.; Antweiler, Ronald C.; Flynn, J.L.; Keefe, S.H.; Kolpin, D.W.; Roth, D.A.; Schnoebelen, D.J.; Taylor, Howard E.; Verplanck, P.L.
2011-01-01
Understanding the potential effects of increased reliance on wastewater treatment plant (WWTP) effluents to meet municipal, agricultural, and environmental flow requires an understanding of the complex chemical loading characteristics of the WWTPs and the assimilative capacity of receiving waters. Stream ecosystem effects are linked to proportions of WWTP effluent under low-flow conditions as well as the nature of the effluent chemical mixtures. This study quantifies the loading of 58 inorganic constituents (nutrients to rare earth elements) from WWTP discharges relative to upstream landscape-based sources. Stream assimilation capacity was evaluated by Lagrangian sampling, using flow velocities determined from tracer experiments to track the same parcel of water as it moved downstream. Boulder Creek, Colorado and Fourmile Creek, Iowa, representing two different geologic and hydrologic landscapes, were sampled under low-flow conditions in the summer and spring. One-half of the constituents had greater loads from the WWTP effluents than the upstream drainages, and once introduced into the streams, dilution was the predominant assimilation mechanism. Only ammonium and bismuth had significant decreases in mass load downstream from the WWTPs during all samplings. The link between hydrology and water chemistry inherent in Lagrangian sampling allows quantitative assessment of chemical fate across different landscapes. ?? 2011 American Chemical Society.
Lagrangian dynamics of the mistral during the HyMeX SOP2
Drobinski, Philippe; Alonzo, Bastien; Basdevant, Claude; Cocquerez, Philippe; Fourrié, Nadia; Nuret, Mathieu
2017-04-01
The mistral refers to a severe wind blowing over the Gulf of Lions after being channeled in the Rhone valley. It influences the western Mediterranean climate as it brings cold and dry continental air over the warm western Mediterranean, generating intense air-sea heat exchanges and sea surface cooling, inducing the formation of the western Mediterranean deep water that moves into the Atlantic Ocean. The mistral is frequently observed to extend as far as a few hundred kilometers from the coast, and its fine-scale dynamics over the sea is still only partially understood as finely resolved observations in time and space are lacking. The boundary layer pressurized balloons (BLPB) developed by the Centre National d'Etudes Spatiales and deployed during HyMeX SOP2 allowed the Lagrangian documentation of the mistral events that occurred between beginning of February to mid-March 2013. Analyzed in synergy with the AROME-WMED weather forecast model, all the terms of the Lagrangian formulation of the momentum conservation equation could be quantified showing three different regions: (1) an injection zone where the mistral flow is directed toward the center of the Genoa cyclone due to a strong zonal pressure gradient, enhanced friction, and entrainment in the mountain wake; (2) an ejection zone where the flow is deflected outward of the cyclone due to either the nonnegligible inertia pseudoforce or an inertial oscillation caused by a sudden friction decrease; and (3) a region of geostrophic deceleration due to the weakening of the pressure gradient.
An inkjet-printed buoyant 3-D lagrangian sensor for real-time flood monitoring
Farooqui, Muhammad Fahad
2014-06-01
A 3-D (cube-shaped) Lagrangian sensor, inkjet printed on a paper substrate, is presented for the first time. The sensor comprises a transmitter chip with a microcontroller completely embedded in the cube, along with a $1.5 \\\\lambda 0 dipole that is uniquely implemented on all the faces of the cube to achieve a near isotropic radiation pattern. The sensor has been designed to operate both in the air as well as water (half immersed) for real-time flood monitoring. The sensor weighs 1.8 gm and measures 13 mm$\\\\,\\\\times\\\\,$ 13 mm$\\\\,\\\\times\\\\,$ 13 mm, and each side of the cube corresponds to only $0.1 \\\\lambda 0 (at 2.4 GHz). The printed circuit board is also inkjet-printed on paper substrate to make the sensor light weight and buoyant. Issues related to the bending of inkjet-printed tracks and integration of the transmitter chip in the cube are discussed. The Lagrangian sensor is designed to operate in a wireless sensor network and field tests have confirmed that it can communicate up to a distance of 100 m while in the air and up to 50 m while half immersed in water. © 1963-2012 IEEE.
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
The Lagrangian-space Effective Field Theory of Large Scale Structures
Porto, Rafael A.; Zaldarriaga, Matias
2014-01-01
We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of extended objects in Lagrangian space. In LEFT the resulting finite size effects are described using a multipole expansion parameterized by a set of time dependent coefficients and organized in an expansion in powers of the ratio of the wavenumber of interest $k$ over the non-linear scale $k_{\\rm NL}$. The multipoles encode the effects of the short distance modes on the long-wavelength Universe and absorb UV divergences when present. There are no IR divergences in LEFT. Some of the parameters that control the perturbative approach are not assumed to be small and can be automatically resummed. We present an illustrative one-loop calculation for a power law Universe. We describe the dynamics both at the level of the equations of motion and through an action formalism.
On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory
Vandommelen, Leon L.; Cowley, Stephen J.
1989-01-01
Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.
On the Lagrangian description of unsteady boundary-layer separation. I - General theory
Van Dommelen, Leon L.; Cowley, Stephen J.
1990-01-01
Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.
Evaluation of the Monotonic Lagrangian Grid and Lat-Long Grid for Air Traffic Management
Kaplan, Carolyn; Dahm, Johann; Oran, Elaine; Alexandrov, Natalia; Boris, Jay
2011-01-01
The Air Traffic Monotonic Lagrangian Grid (ATMLG) is used to simulate a 24 hour period of air traffic flow in the National Airspace System (NAS). During this time period, there are 41,594 flights over the United States, and the flight plan information (departure and arrival airports and times, and waypoints along the way) are obtained from an Federal Aviation Administration (FAA) Enhanced Traffic Management System (ETMS) dataset. Two simulation procedures are tested and compared: one based on the Monotonic Lagrangian Grid (MLG), and the other based on the stationary Latitude-Longitude (Lat- Long) grid. Simulating one full day of air traffic over the United States required the following amounts of CPU time on a single processor of an SGI Altix: 88 s for the MLG method, and 163 s for the Lat-Long grid method. We present a discussion of the amount of CPU time required for each of the simulation processes (updating aircraft trajectories, sorting, conflict detection and resolution, etc.), and show that the main advantage of the MLG method is that it is a general sorting algorithm that can sort on multiple properties. We discuss how many MLG neighbors must be considered in the separation assurance procedure in order to ensure a five-mile separation buffer between aircraft, and we investigate the effect of removing waypoints from aircraft trajectories. When aircraft choose their own trajectory, there are more flights with shorter duration times and fewer CD&R maneuvers, resulting in significant fuel savings.
Rotor wake and flow analysis using a coupled Eulerian–Lagrangian method
Directory of Open Access Journals (Sweden)
Yongjie Shi
2016-01-01
Full Text Available A coupled Eulerian–Lagrangian methodology was developed in this paper in order to provide an efficient and accurate tool for rotor wake and flow prediction. A Eulerian-based Reynolds-averaged Navier–Stokes (RANS solver was employed to simulate the grid-covered near-body zone, and a grid-free Lagrangian-based viscous wake method (VWM was implemented to model the complicated rotor-wake dynamics in the off-body wake zone. A carefully designed coupling strategy was developed to pass the flow variables between two solvers. A sample case of a forward flying rotor was performed first in order to show the capabilities of the VWM for wake simulations. Next, the coupled method was applied to rotors in several representative flight conditions. Excellent agreement regarding wake geometry, chordwise pressure distribution and sectional normal force with available experimental data demonstrated the validity of the method. In addition, a comparison with the full computational fluid dynamics (CFD method is presented to illustrate the efficiency and accuracy of the proposed coupled method.
Flow Kinematics and Lagrangian Mixing Dynamics in a Darcy Scale Heterogeneous Porous Medium
Dentz, M.; de Barros, F.; Le Borgne, T.
2013-12-01
We study the mixing behavior of a solute blob that is transported through a two-dimensional Darcy scale heterogeneous porous medium. Flow heterogeneity is induced by spatial variability in hydraulic conductivity. The fundamental mechanism governing the evolution of the solute blob are the competition of the stretching and compression action within a fluid element, and diffusion. We formulate the transport problem in a Lagrangian framework and consider the motion of solute particles that form the blob, in the coordinate system attached to the fluid element on which it originates. The blob evolution is fully characterized by the time series of stretching and shear rates of the material segment in its own coordinate system. Associated stirring protocols, or spreading protocols may be different from the ones encountered in chaotic and turbulent flow and can be related to the evolution of center of mass velocities of an ensemble of solute blobs. The permeability variability is modeled using a stochastic approach, which renders the stretching and shear rate time series as stochastic processes. Theses stochastic series are investigated numerically using random walk particle tracking simulations, and quantified analytically in terms of multiplicative and additive stochastic processes for the strip elongation and shear deformation. In this stochastic framework, we study the ensemble concentration PDF, concentration entropy and scalar dissipation rate. We relate the mixing properties to the appearance of coherent structures as quantified by the Okubo-Weiss measure and its Lagrangian counterpart.
Reyes, Jonathan; Shadwick, B. A.
2016-10-01
Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.
Can lagrangian models reproduce the migration time of European eel obtained from otolith analysis?
Rodríguez-Díaz, L.; Gómez-Gesteira, M.
2017-12-01
European eel can be found at the Bay of Biscay after a long migration across the Atlantic. The duration of migration, which takes place at larval stage, is of primary importance to understand eel ecology and, hence, its survival. This duration is still a controversial matter since it can range from 7 months to > 4 years depending on the method to estimate duration. The minimum migration duration estimated from our lagrangian model is similar to the duration obtained from the microstructure of eel otoliths, which is typically on the order of 7-9 months. The lagrangian model showed to be sensitive to different conditions like spatial and time resolution, release depth, release area and initial distribution. In general, migration showed to be faster when decreasing the depth and increasing the resolution of the model. In average, the fastest migration was obtained when only advective horizontal movement was considered. However, faster migration was even obtained in some cases when locally oriented random migration was taken into account.
Development of Sliding Connections for Structural Analysis by a Total Lagrangian FEM Formulation
Directory of Open Access Journals (Sweden)
Tiago Morkis Siqueira
Full Text Available Abstract In this study a total lagrangian 2D finite element formulation is used to model plane frames developing large displacements and rotations considering sliding connections. This kind of connections is usually called prismatic and cylindrical joints. In order to be self-containing, the steps of the development of a frame finite element of any approximation order that considers the influence of shear strain by means of a generalized Reissner kinematics is presented. The adopted degrees of freedom are positions and rotations. Using positions as degrees of freedom simplifies the total lagrangian description and enables a comprehensive presentation of the proposed connections. Revolute connections are considered by direct degrees of freedom matching. Prismatic connections are modelled by the Lagrange multiplier technique that constrains positions and rotation of a sliding node to the varying position and rotation of a path element. Cylindrical joints are introduced in similar way by Lagrange multipliers releasing the sliding node rotation. The principle of stationary potential energy is used to write the non-linear equilibrium equation including the Lagrange multiplier influence. To solve the non-linear equation a Taylor expansion is carried out and the Newton-Raphson procedure is employed. The frame element is considered elastic, following the Saint-Venant-Kirchhoff constitutive model. Selected examples are used to validate the formulation and to show its possibilities of application.
Multiloop Euler-Heisenberg Lagrangians, Schwinger Pair Creation, and the Photon S-Matrix
Huet, I.; de Traubenberg, M. R.; Schubert, C.
2017-03-01
Although the perturbation series in quantum electrodynamics has been studied for eighty years concerning its high-order behavior, our present understanding is still poorer than for many other field theories. An interesting case is Schwinger pair creation in a constant electric field, which may possibly provide a window to high loop orders; simple non-perturbative closed-form expressions have been conjectured for the pair creation rate in the weak field limit, for scalar QED in 1982 by Affleck, Alvarez, and Manton, and for spinor QED by Lebedev and Ritus in 1984. Using Borel analysis, these can be used to obtain non-perturbative information on the on-shell renormalized N-photon amplitudes at large N and low energy. This line of reasoning also leads to a number of nontrivial predictions for the effective QED Lagrangian in either four or two dimensions at any loop order, and preliminary results of a calculation of the three-loop Euler-Heisenberg Lagrangian in two dimensions are presented.
Lagrangian coherent structures and turbulence characteristics downstream of prosthetic aortic valves
de Tullio, Marco D.
2015-11-01
The flowfield through prosthetic heart valves is investigated by means of direct numerical simulations, considering the fully coupled fluid-structure interaction problem. Two different aortic valve models are modeled: a bileaflet mechanical and a biological one. In order to reveal fluid flow structures and to better understand the transport mechanics, Lagrangian coherent structures (LCS) are used. LCS are distinguished material surfaces that can be identified as boundaries to regions with dynamically distinct behavior, and are revealed as hypersurfaces that locally maximize the finite-time Lyapunov exponent (FTLE) fields. Post-processing the flow simulation data, first FTLE fields are calculated integrating dense meshes of Lagrangian particles backward in time, and then attracting LCS are extracted. A three-jet configuration is distinctive of bi-leaflet mechanical valves, with higher turbulent shear stresses immediately distal to the valve leaflets, while a jet-like flow emerges from the central orifice of bio-prosthetic valves, with high turbulent shear stresses occurring at the edge of the jet. Details of the numerical methodology along with a thorough analysis of the different flow structures developing during the cardiac cycle for the two configurations will be provided.
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.
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.
Point-like bounding chains in open Gromov-Witten theory
Solomon, Jake P.; Tukachinsky, Sara B.
2016-01-01
We use $A_\\infty$ algebras to define open Gromov-Witten invariants with both boundary and interior constraints, associated to a Lagrangian submanifold $L\\subset X$ of arbitrary odd dimension. The boundary constraints are bounding chains, which are shown to behave like points. The interior constraints are arbitrary even degree classes in the cohomology of $X$ relative to $L.$ We show the invariants satisfy analogs of the axioms of closed Gromov-Witten theory. Our definition of invariants depen...
International Nuclear Information System (INIS)
Clarisse, J.M.
2007-01-01
A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)
Effect of δ meson and ρ-ω cross couplings in effective field theory motivated Lagrangian approach
International Nuclear Information System (INIS)
Jagota, R.K.; Dhiman, S.K.; Sharma, B.K.; Arumugam, P.; Patra, S.K.
2005-01-01
It is shown that the self and cross couplings of ω meson plays an important role to make the nuclear equation of state (EOS) softer. The parameter set G2, obtained from the effective field theory motivated Lagrangian (E-RMF) approach, is very successful to reproduce the nuclear matter properties including the structure of neutron star as well as of finite nuclei. The motivation of the present report is to see the effects of these terms in the E-RMF Lagrangian on infinite nuclear matter as well as finite nuclei
Dynamical attraction to stable processes
Fisher, Albert M.; Talet, Marina
2012-01-01
We apply dynamical ideas within probability theory, proving an almost-sure invariance principle in log density for stable processes. The familiar scaling property (self-similarity) of the stable process has a stronger expression, that the scaling flow on Skorokhod path space is a Bernoulli flow. We prove that typical paths of a random walk with i.i.d. increments in the domain of attraction of a stable law can be paired with paths of a stable process so that, after applying a non-random regula...
Stochastic Flows: Dispersion of a Mass Distribution and Lagrangian Observations of a Random Field.
Zirbel, Craig Lee
1993-01-01
We consider two classical problems from statistical fluid mechanics in the modern probabilistic setting of stochastic flows based on stochastic differential equations. Such flows model spatially coherent "noise" superimposed on classical velocity fields. Their theory was developed over the past fifteen years by Kunita, Harris, Baxendale, and Le Jan, among others. The first problem we treat is the dispersion of a mass distribution carried by an isotropic Brownian flow F = {F_{s,t}: 0 M_0 be a measure on IR^{d} and define a random measure M_{t} by M_{t}(R) = M_0( {xinIR^{d} : F_ {o,t}(x)in R}) for sets R in IR^{d}. Then M_{t}(R) is the amount of mass in set R at time t. The dispersion matrix D _{t} is the centered spatial second moment of M_{t}, which describes the spreading of M_{t} relative to its center of mass. We show that, in incompressible flows, {rm I!E }D_{t} grows linearly in t for large t and that deviations from linearity are of order sqrt{t}. This is a signature of classical diffusion. In one dimension we find that {rm I!E}D_{t } goes as sqrt{t} for large t. We give other results for the remaining cases. Our methods involve an exact analysis of a one-dimensional diffusion process and the use of comparison theorems. Finally, to sharpen our intuition about the evolution of M _{t}, we present plots of M _{t}>=nerated by numerical simulations of isotropic Brownian flows. The second problem we consider concerns Lagrangian observations of a random field A made by a particle carried by a general stochastic flow F. Assuming that A and F are homogeneous, we obtain a formula for the distribution of the Lagrangian observation A(F_{0,t }(x),t) in terms of the Eulerian distribution of A and a function representing a tracer density. This result extends the seminal work of Lumley; our proof refines other work along these lines. In addition, we introduce a class of flows which regenerate at certain random times. This independence assumption allows us to prove the