A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Anderson, R W; Pember, R B; Elliott, N S
2002-10-19
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Anderson, R W; Pember, R B; Elliott, N S
2004-01-28
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
Simulation of Steady Laser Hardening by an Arbitrary Lagrangian Eulerian Method
Geijselaers, H.J.M.; Huetink, J.
2004-01-01
One of the most practical methods for simulation of steady state thermal processing is the Arbitrary Lagrangian- Eulerian method. Each calculation step is split into two phases. In the first phase, the Lagrangian phase, the element mesh remains attached to the material. The evolution of the state va
Simulation of Steady Laser Hardening by an Arbitrary Lagrangian Eulerian Method
Geijselaers, Hubertus J.M.; Huetink, Han
2004-01-01
One of the most practical methods for simulation of steady state thermal processing is the Arbitrary Lagrangian- Eulerian method. Each calculation step is split into two phases. In the first phase, the Lagrangian phase, the element mesh remains attached to the material. The evolution of the state
Acoustic Streaming: An Arbitrary Lagrangian-Eulerian Perspective
Nama, Nitesh; Costanzo, Francesco
2016-01-01
We analyze acoustic streaming flows using an ALE perspective. The formulation stems from an explicit separation of time-scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacosutofluidic devices. After the formulation's exposition, we present numerical re...
Institute of Scientific and Technical Information of China (English)
USAMA Umer; XIE Lijing; WANG Xibin
2006-01-01
A two-dimensional finite element (FE) model for the high speed turning operations when orthogonally machining AISI H13 tool steel at 49HRC using poly crystalline cubic boron nitride(PCBN) is described. An arbitrary Lagrangian Eulerian (ALE) method has been adopted which does not need any chip separation criteria as opposed to the traditional Lagrangian approach. Through FE simulations temperature and stresses distributions are presented that could be helpful in predicting tool life and improving process parameters. The results show that high temperatures are generated along the tool rake face as compared to the shear zone temperatures due to high thermal conductivity of PCBN tools.
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.
Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary
Stankiewicz, W.; Roszak, R.; Morzyński, M.
2013-06-01
Flow-induced deflections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like flutter or buffeting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the flow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto space spanned by modes obtained from high-fidelity computations. The motion of the boundary and mesh is defined in Arbitrary Lagrangian-Eulerian (ALE) approach and results in additional convective term in Galerkin system. The developed system is demonstrated on the example of a flow around an oscillating wing.
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.
Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-Eulerian method
Energy Technology Data Exchange (ETDEWEB)
Darlington, R
1999-12-01
This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian Eulerian (ALE) simulations of Rayleigh-Taylor instability. First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over Eulerian simulations are shown. Next, the behavior of the LES is examined in a more complicated ALE simulation of Rayleigh-Taylor instability. The effects of eddy viscosity and stochastic backscatter are examined. The LES is also coupled with ALE to increase grid resolution in areas where it is needed. Finally, the methods studied above are applied to two sets of experimental simulations. In these simulations, ALE allows the mesh to follow expanding experimental targets, while LES can be used to mimic the effect of unresolved instability modes.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Solution of the Euler Equations
Energy Technology Data Exchange (ETDEWEB)
Anderson, R W; Elliott, N S; Pember, R B
2003-02-14
A new method that combines staggered grid arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the methods are driven by the need to reconcile traditional AMR techniques with the staggered variables and moving, deforming meshes associated with Lagrange based ALE schemes. We develop interlevel solution transfer operators and interlevel boundary conditions first in the case of purely Lagrangian hydrodynamics, and then extend these ideas into an ALE method by developing adaptive extensions of elliptic mesh relaxation techniques. Conservation properties of the method are analyzed, and a series of test problem calculations are presented which demonstrate the utility and efficiency of the method.
Towards Modeling Local Foam Drainage Using the Arbitrary Lagrangian Eulerian Method
Brandon, Andrew; Ananth, Ramagopal
2014-11-01
Liquid drainage in foams is a multi-scale, multi-dimensional phenomena that is tied directly to how well a foam performs. For example, the amount of metal within a metal foam after it solidifies affects the strength of the foam and the amount of liquid within an aqueous fire fighting foam determines how effective it is at extinguishing a fire. Liquid drainage is driven by gravity and is governed by the liquid's density and viscosity as well as the surface tension at the liquid gas interface. There are numerous one dimensional, single phase models that approximate liquid drainage by employing a global description but there are no multidimensional models that use a local description. In this presentation, I will describe an ongoing effort to develop a two dimensional, multiphase, Arbitrary Lagrangian Eulerian model for the study of local liquid drainage in foams. I will present an improved algorithm for the solution of the incompressible fluid equations in the Arbitrary Lagrangian Eulerian method, the novel method used for moving the domain in time, and results from this model development effort.
Yu, Qifeng; Pan, Tongyan
2017-05-01
Two microscale numerical models are developed in this work using a moving-mesh approach to investigate the growth process of pitting in different iron phases and the corrosion prevention capability of polyaniline (PANi) on steels. The distributions of corrosion potential and current in the electrolyte-coating-steel system are computed to evaluate the anti-corrosion ability of PANi. The arbitrary Lagrangian-Eulerian approach was used to accomplish the continuous remesh process as was needed to simulate the dynamic growing forefront of the modeled pitting domain. Experimental validation of the numerical models was conducted using the technique of scanning kelvin probe force microscopy (SKPFM). The SKPFM-scanned surface topography and Volta potential difference exhibit comparable results to and thereby prove the numerical results. The potential distribution in the electrolyte phase of the validated models shows that the corrosion pit grows faster in the epoxy-only-coated steel than that in the PANi-primer-coated steel over the simulation time; also, the corrosion pit grows faster in the ferrite phase than in the cementite phase. The simulation results indicate that the epoxy-only coating lost its anti-corrosion capability as the coating was penetrated by electrolyte, while the PANi-based coating can still protect the steel from corrosion after the electrolyte penetration. The models developed in this work can be used to study the mechanisms of pitting corrosion as well as develop more effective corrosion prevention strategies for general metallic materials.
Yu, Qifeng; Pan, Tongyan
2017-03-01
Abstracts Two microscale numerical models are developed in this work using a moving-mesh approach to investigate the growth process of pitting in different iron phases and the corrosion prevention capability of polyaniline (PANi) on steels. The distributions of corrosion potential and current in the electrolyte-coating-steel system are computed to evaluate the anti-corrosion ability of PANi. The arbitrary Lagrangian-Eulerian approach was used to accomplish the continuous remesh process as was needed to simulate the dynamic growing forefront of the modeled pitting domain. Experimental validation of the numerical models was conducted using the technique of scanning kelvin probe force microscopy (SKPFM). The SKPFM-scanned surface topography and Volta potential difference exhibit comparable results to and thereby prove the numerical results. The potential distribution in the electrolyte phase of the validated models shows that the corrosion pit grows faster in the epoxy-only-coated steel than that in the PANi-primer-coated steel over the simulation time; also, the corrosion pit grows faster in the ferrite phase than in the cementite phase. The simulation results indicate that the epoxy-only coating lost its anti-corrosion capability as the coating was penetrated by electrolyte, while the PANi-based coating can still protect the steel from corrosion after the electrolyte penetration. The models developed in this work can be used to study the mechanisms of pitting corrosion as well as develop more effective corrosion prevention strategies for general metallic materials.
Ganesan, Sashikumaar
2014-01-01
An arbitrary Lagrangian--Eulerian (ALE) finite element scheme for computations of soluble surfactant droplet impingement on a horizontal surface is presented. The numerical scheme solves the time-dependent Navier--Stokes equations for the fluid flow, scalar convection-diffusion equation for the surfactant transport in the bulk phase, and simultaneously, surface evolution equations for the surfactants on the free surface and on the liquid-solid interface. The effects of surfactants on the flow dynamics are included into the model through the surfactant-dependent surface tension and dynamic contact angle. In particular, the dynamic contact angle of the droplet is defined as a function of surfactants using the nonlinear equation of state for surface tension. Further, the surface forces are included in the model using the Boussinesq-Scriven law that allows to incorporate the Marangoni effects without evaluating the gradients of surfactant concentration on the free surface. In addition to a mesh convergence study ...
Su, Xiaohui; Cao, Yuanwei; Zhao, Yong
2016-06-01
In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.
Sahin, Mehmet
2010-01-01
A new geometrically conservative arbitrary Lagrangian-Eulerian (ALE) formulation is presented for the moving boundary problems in the swirl-free cylindrical coordinates. The governing equations are multiplied with the radial distance and integrated over arbitrary moving Lagrangian-Eulerian quadrilateral elements. Therefore, the continuity and the geometric conservation equations take very simple form similar to those of the Cartesian coordinates. The continuity equation is satisfied exactly within each element and a special attention is given to satisfy the geometric conservation law (GCL) at the discrete level. The equation of motion of a deforming body is solved in addition to the Navier-Stokes equations in a fully-coupled form. The mesh deformation is achieved by solving the linear elasticity equation at each time level while avoiding remeshing in order to enhance numerical robustness. The resulting algebraic linear systems are solved using an ILU(k) preconditioned GMRES method provided by the PETSc librar...
On the integration of the arbitrary Lagrangian-Eulerian concept and non-equilibrium thermodynamics
Knobbe, E.M.
2010-01-01
The aim of this treatise is to present a harmonious mathematical formulation of an explicit moving mesh method that can be used as a basis for many numerical techniques. In most cases a moving mesh is only used to include arbitrary motions and deformations of a geometry into the simulation of a phys
On the integration of the arbitrary Lagrangian-Eulerian concept and non-equilibrium thermodynamics
Knobbe, E.M.
2010-01-01
The aim of this treatise is to present a harmonious mathematical formulation of an explicit moving mesh method that can be used as a basis for many numerical techniques. In most cases a moving mesh is only used to include arbitrary motions and deformations of a geometry into the simulation of a
Boscheri, Walter; Dumbser, Michael
2017-10-01
We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total
A hybrid Eulerian-Lagrangian flow solver
Palha, Artur; Ferreira, Carlos Simao; van Bussel, Gerard
2015-01-01
Currently, Eulerian flow solvers are very efficient in accurately resolving flow structures near solid boundaries. On the other hand, they tend to be diffusive and to dampen high-intensity vortical structures after a short distance away from solid boundaries. The use of high order methods and fine grids, although alleviating this problem, gives rise to large systems of equations that are expensive to solve. Lagrangian solvers, as the regularized vortex particle method, have shown to eliminate (in practice) the diffusion in the wake. As a drawback, the modelling of solid boundaries is less accurate, more complex and costly than with Eulerian solvers (due to the isotropy of its computational elements). Given the drawbacks and advantages of both Eulerian and Lagrangian solvers the combination of both methods, giving rise to a hybrid solver, is advantageous. The main idea behind the hybrid solver presented is the following. In a region close to solid boundaries the flow is solved with an Eulerian solver, where th...
Evaluation of the Eulerian-Lagrangian spray atomisation (ELSA) in spray simulations
Hoyas, S.; Pastor Enguídanos, José Manuel; KHUONG, ANH DUNG; MOMPÓ LABORDA, JUAN MANUEL; Ravet, Frederic
2011-01-01
Many approaches have been used to simulate the spray structure especially in modelling fuel sprays, i.e., Eulerian, Lagrangian, Lagrangian- Eulerian, Eulerian-Eulerian and Eulerian-Lagrangian approaches. The present study uses an Eulerian-Lagrangian spray atomisation (ELSA) method which is an integrated model for capturing the whole spray evolution starting directly from injector nozzle still the end. Our goal in this study is to evaluate the ELSA model which is implementing into the commerci...
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.
The hybrid Eulerian Lagrangian numerical scheme tested with Chemistry
Directory of Open Access Journals (Sweden)
A. B. Hansen
2012-11-01
Full Text Available A newly developed advection scheme, the Hybrid Eulerian Lagrangian (HEL scheme, has been tested, including a module for atmospheric chemistry, including 58 chemical species, and compared to two other traditional advection schemes; a classical pseudospectral Eulerian method the Accurate Space Derivative (ASD scheme and the bi-cubic semi-Lagrangian (SL scheme using classical rotation tests. The rotation tests have been designed to test and compare the advection schemes for different spatial and temporal resolutions in different chemical conditions (rural and urban and for different shapes (cone and slotted cylinder giving the advection schemes different challenges with respect to relatively slow or fast chemistry and smooth or sharp gradients, respectively. In every test, error measures have been calculated and used for ranking of the advection schemes with respect to performance, i.e. lowest overall errors for all chemical species. Furthermore, the HEL and SL schemes have been compared in a shallow water model, demonstrating the performance in a more realistic non-linear deformation flow.
The results in this paper show that the new advection scheme, HEL, by far outperforms both the Eulerian and semi-Lagrangian schemes with very low error estimates compared to the two other schemes. Although no analytic solution can be obtained for the performance in the non-linear shallow water model flow, the tracer distribution appears realistic as compared to LMCSL when a mixing between local parcel concentrations is introduced in HEL.
Mixed Lagrangian-Eulerian and Eulerian Approach to Discretizing Richards' Equation
Yeh, G. T.; Tsai, C. H.
2014-12-01
This paper presents a robust, efficient numerical solution involving the use of the mixed Lagrangian-Eulerian (LE) method and the Eulerian (L) approach for three dimensional simulations of variably saturated subsurface flow that is described by Richard's equation. The LE approach with its particle tracking algorithm and/or finite element methods (FEM) were employed to discretize interior nodes while the finite element method is selected to set up algebraic equations for boundary nodes. The use of FEM for boundary nodes alleviate the difficulty in dealing with flux and gradient types of boundary conditions. Extrapolations are no longer needed to handle flux or gradient type boundary conditions. In this new mixed LE&E approach, subsurface flow in variably saturated media can be efficiently dealt with. Three examples are provided to demonstrate the efficiency of the proposed approach. First, a one-dimensional column problem is used to compare the accuracy of the mixed LE&E approach versus the traditional Eulerian approach. Second, a three-dimensional drainage problem was simulated to compare the CPU time between two approaches. Third, a three-dimensional pumping well problem was simulated. In all three examples, the mixed LE&E using relatively large time steps yielded superior results in terms of the accuracy and computational efficiency in comparison with the conventional Eulerian approach. The proposed mixed LE&E approach may contribute to the efficient numerical solutions of problems involving moving sharp fronts problems such as groundwater in real-world watersheds.
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.
A High-order Eulerian-Lagrangian Finite Element Method for Coupled Electro-mechanical Systems
Brandstetter, Gerd
The main focus of this work is on the development of a high-order Eulerian-Lagrangian finite element method for the simulation of electro-mechanical systems. The coupled problem is solved by a staggered scheme, where the mechanical motion is discretized by standard Lagrangian finite elements, and the electrical field is solved on a fixed Eulerian grid with embedded boundary conditions. Traditional Lagrangian-Lagrangian or arbitrary Lagrangian-Eulerian (ALE) methods encounter deficiencies, for example, when dealing with mesh distortion due to large deformations, or topology changes due to contacting bodies. The presented Eulerian-Lagrangian approach addresses these issues in a natural way. Within this context we develop a high-order immersed boundary discontinuous-Galerkin (IB-DG) method, which is shown to be necessary for (i) the accurate representation of the electrical gradient along nonlinear boundary features such as singular corners, and (ii) to achieve full convergence during the iterative global solution. We develop an implicit scheme based on the mid-point rule, as well as an explicit scheme based on the centered-difference method, with the incorporation of energy conserving, frictionless contact algorithms for an elastic-to-rigid-surface contact. The performance of the proposed method is assessed for several benchmark tests: the electro-static force vector around a singular corner, the quasi-static pull-in of an electro-mechanically actuated switch, the excitation of a carbon nanotube at resonance, and the cyclic impact simulation of a micro-electro-mechanical resonant-switch. We report improved accuracy for the high-order method as compared to low-order methods, and linear convergence in the iterative solution of the staggered scheme. Additionally, we investigate a Newton-Krylov shooting scheme in order to directly find cyclic steady states of electro-mechanical devices excited at resonance-- as opposed to a naive time-stepping from zero initial
Coupled Eulerian-Lagrangian transport of large debris by tsunamis
Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos
2016-04-01
Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-Eulerian coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian and Eulerian solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed Eulerian-Lagrangian formulation and the resolution of the mesh used in the Eulerian solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the
Currents in the Dead Sea: Lagrangian and Eulerian observations
Ozer, Tal; Gertman, Isaac; Katsenelson, Boris; Bodzin, Raanan; Lensly, Nadav
2015-04-01
The Dead Sea is a terminal hypersaline lake located in the lowest surface on Earth (currently -429 m bsl). The physical properties of the brine are significantly different than in common marine systems: the DS brine density is ~1.24 gr/cc and its viscosity ~3 times higher than marine systems. We present observational data on wind and currents in the Dead Sea. The observation setup includes a few fixed (Eulerian) stations which are equipped with wind meter and current meter profiler that covers the entire water column (ADCP). Thermal stratification is continuously measured in some of the stations using a thermistor chain. Lagrangian drifters that record the shallow water currents were released in liner array of single drifters between the fixed stations, and also in triplets (15 m triangle). The results include the measured time series data of wind (atmospheric forcing) and the measured current profiles from the fixed stations. Data of the Lagrangian drifters is presented as trajectories along with vector time series. Quality control check included comparison of drifter data and ADCP data whenever the drifters passed by the fixed stations; a very good agreement was found between the different measuring approaches. We discuss the following issues : (i) the relation between the wind and current data, (ii) the Lagrangian trajectories and transport aspects.
A hybrid Eulerian Lagrangian numerical scheme for solving prognostic equations in fluid dynamics
Directory of Open Access Journals (Sweden)
E. Kaas
2013-07-01
Full Text Available A new hybrid Eulerian Lagrangian numerical scheme (HEL for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place, i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.
COMPARISON OF THE EULERIAN AND LAGRANGIAN TIDAL RESIDUALS IN THE BOHAI SEA
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Tidal residual is very important to the transport of water particles, nutrients, plankton, etc. in the coastal sea. Eulerian scheme and Lagrangian scheme are two different ways to get the time averaged residual. Solution of the Bohai Sea's hydrodynamic system using a semi-implicit layer averaged numerical model yielded different direction Eulerian and Lagrangian tidal residuals. The latter were stronger than the former in most sea areas. Their different directions produced different circulation pattern in some areas. Compared with the Eulerian residual, the Lagrangian residual seemed to be more in accord with the observation.
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
Felici, Helene Marie
1992-06-01
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.
Eulerian-Lagrangian Simulation of an Explosive Dispersal of Particles
Rollin, Bertrand; Ouellet, Frederick; Koneru, Rahul; Annamalai, Subramanian
2016-11-01
Explosive dispersal of solid particles can be observed in a wide variety of contexts, notably in natural phenomenon such as volcanic eruptions or in engineering applications such as detonation of multiphase explosives. As the initial blast wave crosses the surrounding layer of particles, compaction occurs shortly before particles disperse radially outward at high speed. During the dispersion phase, complex multiphase interactions occurs between particles and detonation products of the explosive. Using a Eulerian-Lagrangian approach, namely point particle simulations, we study the case of a bed of particles of cylindrical shape surrounding an explosive chord. Our interest lies in predicting the behavior of particles after detonation. In particular, capturing and describing the mechanisms responsible for late-time formation of stable particle jets is sought. Therefore, detonation of the explosive material is not simulated. Instead an equivalent energy source is used to initiate the simulation. We present a detailed description of our approach to solving this problem, and our most recent progress in the analysis of particles explosive dispersal. This work was supported by the U.S. DoE, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.
COMPARISON OF THE EULERIAN AND LAGRANGIAN TIDAL RESIDUALS IN THE BOHAI SEA
Institute of Scientific and Technical Information of China (English)
魏皓; 赵亮; 冯士笮
2001-01-01
Tidal residual is very important to the transport of water particles, nutrients, plank-ton, etc. in the coastal sea. Eulerian scheme and Lagrangian scheme are two different ways to get the time averaged residual. Solution of the Bohai Sea's hydrodynamic system using a semi-implicit layer aver-aged numerical model yielded different direction Eulerian and Lagrangian tidal residuals. The latter were stronger than the former in most sea areas. Their different directions produced different ciretdation pattern in some areas. Compared with the Eulerian residual, the Lagranglan residual seemed to be more in accord with the observation.
Bridging from Eulerian to Lagrangian statistics in 3D hydro- and magnetohydrodynamic turbulent flows
Energy Technology Data Exchange (ETDEWEB)
Homann, H [CNRS, Universite de Nice-Sophia Antipolis, Observatoire de la Cote d' Azur, Lab. Cassiopee, Bd. de l' Observatoire, 06300 Nice (France); Kamps, O [Center for Nonlinear Science, Universitaet Muenster, 48149 Muenster (Germany); Friedrich, R [Theoretische Physik, Universitaet Muenster, 48149 Muenster (Germany); Grauer, R [Theoretische Physik I, Ruhr-Universitaet, 44780 Bochum (Germany)], E-mail: grauer@tp1.rub.de
2009-07-15
We present measurements of conditional probability density functions (PDFs) that allow one to systematically bridge from Eulerian to Lagrangian statistics in fully developed 3D turbulence. The transition is investigated for hydro- as well as magnetohydrodynamic flows and comparisons are drawn. Significant differences in the transition PDFs are observed for these flows and traced back to the differing coherent structures. In particular, we address the problem of an increasing degree of intermittency going from Eulerian to Lagrangian coordinates by means of the conditional PDFs involved in this transformation. First simple models of these PDFs are investigated in order to distinguish different contributions to the degree of Lagrangian intermittency.
A LES-based Eulerian-Lagrangian approach to predict the dynamics of bubble plumes
Fraga, Bruño; Stoesser, Thorsten; Lai, Chris C. K.; Socolofsky, Scott A.
2016-01-01
An approach for Eulerian-Lagrangian large-eddy simulation of bubble plume dynamics is presented and its performance evaluated. The main numerical novelties consist in defining the gas-liquid coupling based on the bubble size to mesh resolution ratio (Dp/Δx) and the interpolation between Eulerian and Lagrangian frameworks through the use of delta functions. The model's performance is thoroughly validated for a bubble plume in a cubic tank in initially quiescent water using experimental data obtained from high-resolution ADV and PIV measurements. The predicted time-averaged velocities and second-order statistics show good agreement with the measurements, including the reproduction of the anisotropic nature of the plume's turbulence. Further, the predicted Eulerian and Lagrangian velocity fields, second-order turbulence statistics and interfacial gas-liquid forces are quantified and discussed as well as the visualization of the time-averaged primary and secondary flow structure in the tank.
Directory of Open Access Journals (Sweden)
Baoyan Li
2003-09-01
Full Text Available We study the hp version of three families of Eulerian-Lagrangian mixed discontinuous finite element (MDFE methods for the numerical solution of advection-diffusion problems. These methods are based on a space-time mixed formulation of the advection-diffusion problems. In space, they use discontinuous finite elements, and in time they approximately follow the Lagrangian flow paths (i.e., the hyperbolic part of the problems. Boundary conditions are incorporated in a natural and mass conservative manner. In fact, these methods are locally conservative. The analysis of this paper focuses on advection-diffusion problems in one space dimension. Error estimates are explicitly obtained in the grid size h, the polynomial degree p, and the solution regularity; arbitrary space grids and polynomial degree are allowed. These estimates are asymptotically optimal in both h and p for some of these methods. Numerical results to show convergence rates in h and p of the Eulerian-Lagrangian MDFE methods are presented. They are in a good agreement with the theory.
Modeling and simulation challenges in Eulerian-Lagrangian computations of multiphase flows
Diggs, Angela; Balachandar, S.
2017-01-01
The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Grid-Based (GB) methods, the volume fraction is first obtained within each cell as an Eulerian quantity and then interpolated to each particle. In Particle-Based (PB) methods, the particle volume fraction is obtained at each particle and then projected onto the Eulerian grid. Traditionally, GB methods are used in multiphase flow, but sub-grid resolution can be obtained through use of PB methods. By evaluating the total error and its components we compare the performance of GB and PB methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities.
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
Fluid structure interaction using an arbitrary lagrangian eulerian formulation
Garelli, Luciano
2012-01-01
Los problemas acoplados multidisciplinarios y multifísicos representan hoy en día un campo desafiante cuando se estudian cada vez problemas mas complejos que aparecen tanto en la naturaleza como en nuevas tecnologías (Ej. Magnetohidrodinámica, Microelectromecánica, Termomecánica, Interacción Fluido-Estructura, etc.). En particular, cuando se tratan problemas de interacción fluido-estructura se plantean varias preguntas, como ser el algoritmo de acople, la estrategia empleada en el movimiento...
Fluid structure interaction using an arbitrary lagrangian eulerian formulation
Garelli, Luciano
2012-01-01
Los problemas acoplados multidisciplinarios y multifísicos representan hoy en día un campo desafiante cuando se estudian cada vez problemas mas complejos que aparecen tanto en la naturaleza como en nuevas tecnologías (Ej. Magnetohidrodinámica, Microelectromecánica, Termomecánica, Interacción Fluido-Estructura, etc.). En particular, cuando se tratan problemas de interacción fluido-estructura se plantean varias preguntas, como ser el algoritmo de acople, la estrategia empleada en el movimiento...
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.
The Eulerian- and Lagrangian-mean flows induced by stationary, dissipating planetary waves
Takahashi, M.; Uryu, M.
1981-01-01
The Eulerian- and the Lagrangian-mean flows induced by stationary, dissipating planetary waves are discussed by employing a simple channel model on a beta-plane. It is assumed that the wave is excited by the bottom undulation and dissipated by Newtonian cooling with relaxation time alpha and by Rayleigh friction with (lambda)(alpha), lambda being constant. Three cases where lambda is equal to one are discussed: (1) the basic zonal wind U sub 0 and the dissipation rate alpha are both constant; (2) U sub 0 varies with height while alpha is constant; and (3) U sub 0 and alpha both vary with height. In case (1), the Eulerian- and the Lagrangian-mean fields are shown to depend on the difference between the dissipation scale-height and the density scale-height. In case (2) and case (3), it is shown that the results for case (1) are modified under slightly more realistic situations.
Eulerian and modified Lagrangian approaches to multi-dimensional condensation and coagulation
Li, Xiang-Yu; Haugen, N E L; Svensson, G
2016-01-01
Turbulence is believed to play a crucial role in cloud droplet growth. It makes the collision process of inertial particles strongly nonlinear, which motivates the study of two rather different numerical schemes. Here, an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and coagulation. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow, or just gravitational acceleration without gas flow. Discrepancies between different schemes are most strongly exposed when condensation and coagulation are studied separately, while their combined effects tend to result in smaller discrepancies. In the Eulerian approach, the late growth of the mean particle radius slows down for finer mass bins, especially for collisions caused by different particle sizes. In the Lagrangian approach it is nearly independent of grid resolution at early times and weak...
Andreussi, T.; Morrison, P. J.; Pegoraro, F.
2016-10-01
Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamically accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example, we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi et al. [Phys. Plasmas 20, 092104 (2013)] that makes it possible to reformulate Eulerian equilibria with flows as Lagrangian equilibria in the relabeled variables. The procedures detailed in the present article provide a paradigm that can be applied to more general plasma configurations and in addition extended to more general plasma descriptions where dissipation is absent.
Andreussi, T; Pegoraro, F
2016-01-01
Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamical accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi {\\it et al.}\\ [Phys.\\ Plasmas {\\bf20}, 092104 (2013)] that makes it possible to reformulate Eulerian equilibria with flows as Lagrangian equilibria in the relabeled variables. The procedures detailed in the present article provide a paradigm that can be applied to more general plasma configurations and in addition extended to more general plasma descriptions where dissipation is abse...
An Eulerian-Lagrangian open source solver for bubbly flow in vertical pipes
Energy Technology Data Exchange (ETDEWEB)
Pena-Monferrer, C.; Munoz-Cobo, J. L.; Monros-Andreu, G.; Martinez-Cuenca, R.; Chiva, S.
2014-07-01
Air-water two-phase flow is present in natural and industrial processes of different nature as nuclear reactors. An accurate local prediction of the boiling flow could support safety and operation analyses of nuclear reactors. An Eulerian-Lagrangian approach is investigated in this contribution as it can be used as a virtual facility to investigate the two-phase flow phenomena. A solver based on the PISO algorithm coupled with the Lagrangian equation of motion have been implemented for computing incompressible bubbly flows. (Author)
2012-09-30
codes are parallelized using message passing interface (MPI) based on domain decomposition. For SPH , graphics processing unit (GPU) computing, which is...aims at developing a numerical capability using a Lagrangian Smoothed Particle Hydrodynamics ( SPH ) method and an Eulerian Level-Set Method (LSM) for...the SPH and LSM with environmental input provided by coupled wind and wave simulations at far field; (2) Use the numerical method developed in (1
Increasing numerical efficiency in coupled Eulerian-Lagrangian metal forming simulations
Hammelmüller, Franz; Zehetner, Christian
2015-01-01
The coupled Eulerian-Lagrangian formulation is an efficient tool for modelling and simulation of metal forming processes with large deformation. In many cases, thermo-mechanical coupling has to be considered. Usually the numerical effort is very high for such processes, and large simulation times are the consequence. In this paper, strategies for reducing the simulation time are investigated, based on the example of a hot forming process.
An Eulerian-Lagrangian Form for the Euler Equations in Sobolev Spaces
Pooley, Benjamin C.; Robinson, James C.
2016-12-01
In 2000 Constantin showed that the incompressible Euler equations can be written in an "Eulerian-Lagrangian" form which involves the back-to-labels map (the inverse of the trajectory map for each fixed time). In the same paper a local existence result is proved in certain Hölder spaces {C^{1,μ}}. We review the Eulerian-Lagrangian formulation of the equations and prove that given initial data in H s for {n ≥ 2} and {s > n/2+1}, a unique local-in-time solution exists on the n-torus that is continuous into H s and C 1 into H s-1. These solutions automatically have C 1 trajectories. The proof here is direct and does not appeal to results already known about the classical formulation. Moreover, these solutions are regular enough that the classical and Eulerian-Lagrangian formulations are equivalent, therefore what we present amounts to an alternative approach to some of the standard theory.
A hybrid Lagrangian-Eulerian numerical model for sea-ice dynamics
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A hybrid Lagrangian-Eulerian (HLE) method is developed for sea ice dynamics, which combines the high computational efficiency of finite difference method (FDM) with the high numerical accuracy of smoothed particle hydrodynamics (SPH). In this HLE model, the sea ice cover is represented by a group of Lagrangian ice particles with their own thicknesses and concentrations. These ice variables are interpolated to the Eularian gird nodes using the Gaussian interpolation function. The FDM is used to determine the ice velocities at Eulerian grid nodes, and the velocities of Lagrangian ice particles are interpolated from these grid velocities with the Gaussian function also. The thicknesses and concentrations of ice particles are determined based on their new locations. With the HLE numerical model, the ice ridging process in a rectangular basin is simulated, and the simulated results are validated with the analytical solution. This method is also applied to the simulation of sea ice dynamics in a vortex wind field. At last, this HLE model is applied to the Bohai Sea, and the simulated concentration, thickness and velocity match the satellite images and the field observed data well.
Morrison, P. J.; Andreussi, T.; Pegoraro, F.
2016-10-01
In a series of papers we have investigated general properties of equilibria and their stability in each of the Lagrangian, Eulerian, and Dynamically Accessible stability formulations of magnetohydrodynamics. In our latest work we compare and contrast stability results with these formulations for two applications: stratified convection and rotating pinch equilibrium configurations. The former example, emphasizes the role played entropy, while the later demonstrates the utility of a relabeling transformation that we introduced in our earlier work. Comparisons to classical works, in particular on interchange instability, are made. DOE DE-FG02-04ER-54742.
HybridN-order Lagrangian Interpolation Eulerian-Lagrangian Method for Salinity Calculation
Institute of Scientific and Technical Information of China (English)
吴炎成; 朱首贤; 周林; 游小宝; 张文静
2016-01-01
The Eulerian−Lagrangian method (ELM) has been used by many ocean models as the solution of the advection equation, but the numerical error caused by interpolation imposes restriction on its accuracy. In the present study, hybrid N-order Lagrangian interpolation ELM (LiELM) is put forward in which theN-order Lagrangian interpolation is used at first, then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower. The calculation results of a step-shaped salinity advection model are analyzed, which show that higher order (N=3−8) LiELM can reduce the mean numerical error of salinity calculation, but the numerical oscillation error is still significant. Even number order LiELM makes larger numerical oscillation error than its adjacent odd number order LiELM. HybridN-order LiELM can remove numerical oscillation, and it significantly reduces the mean numerical error whenN is even and the current is in fixed direction, while it makes less effect on mean numerical error whenNis odd or the current direction changes periodically. Hybrid odd number order LiELM makes less mean numerical error than its adjacent even number order LiELM when the current is in the fixed direction, while the mean numerical error decreases asN increases when the current direction changes periodically, so odd number ofN may be better for application. Among various types of HybridN-order LiELM, the scheme reducingN-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.
Flow Modeling in Pelton Turbines by an Accurate Eulerian and a Fast Lagrangian Evaluation Method
Directory of Open Access Journals (Sweden)
A. Panagiotopoulos
2015-01-01
Full Text Available The recent development of CFD has allowed the flow modeling in impulse hydro turbines that includes complex phenomena like free surface flow, multifluid interaction, and unsteady, time dependent flow. Some commercial and open-source CFD codes, which implement Eulerian methods, have been validated against experimental results showing satisfactory accuracy. Nevertheless, further improvement of accuracy is still a challenge, while the computational cost is very high and unaffordable for multiparametric design optimization of the turbine’s runner. In the present work a CFD Eulerian approach is applied at first, in order to simulate the flow in the runner of a Pelton turbine model installed at the laboratory. Then, a particulate method, the Fast Lagrangian Simulation (FLS, is used for the same case, which is much faster and hence potentially suitable for numerical design optimization, providing that it can achieve adequate accuracy. The results of both methods for various turbine operation conditions, as also for modified runner and bucket designs, are presented and discussed in the paper. In all examined cases the FLS method shows very good accuracy in predicting the hydraulic efficiency of the runner, although the computed flow evolution and the torque curve exhibit some systematic differences from the Eulerian results.
Numerical Simulation of the Friction Stir Welding Process Using Coupled Eulerian Lagrangian Method
Iordache, M.; Badulescu, C.; Iacomi, D.; Nitu, E.; Ciuca, C.
2016-08-01
Friction Stir Welding (FSW) is a solid state joining process that relies on frictional heating and plastic deformation realized at the interaction between a non-consumable welding tool that rotates on the contact surfaces of the combined parts. The experiments are often time consuming and costly. To overcome these problems, numerical analysis has frequently been used in last years. Several simplified numerical models were designed to elucidate various aspects of the complex thermo-mechanical phenomena associated with FSW. This research investigates a thermo-mechanical finite element model based on Coupled Eulerian Lagrangian method to simulate the friction stir welding of the AA 6082-T6 alloy. Abaqus/cae software is used in order to simulate the welding stage of the Friction Stir Welding process. This paper presents the steps of the numerical simulation using the finite elements method, in order to evaluate the boundary conditions of the model and the geometry of the tools by using the Coupled Eulerian Lagrangian method.
Directory of Open Access Journals (Sweden)
Y. Koyama
2011-04-01
Full Text Available This study assesses the advantages of using a coupled atmospheric-tracer transport model, comprising a global Eulerian model and a global Lagrangian particle dispersion model, to improve the reproducibility of tracer-gas variations affected by the near-field surface emissions and transport around observation sites. The ability to resolve variability in atmospheric composition on an hourly time-scale and a spatial scale of several kilometers would be beneficial for analyzing data from continuous ground-based monitoring and from upcoming space-based observations. The coupled model yields an increase in the horizontal resolution of transport and fluxes, and has been tested in regional-scale studies of atmospheric chemistry. By applying the Lagrangian component to the global domain, we extend this approach to the global scale, thereby enabling computationally efficient global inverse modeling and data assimilation. To validate the coupled model, we compare model-simulated CO_{2} concentrations with continuous observations at three sites: two operated by the National Oceanic and Atmospheric Administration, USA, and one operated by the National Institute for Environmental Studies, Japan. As the goal of this study is limited to introducing the new modeling approach, we selected a transport simulation at these three sites to demonstrate how the model may perform at various geographical areas. The coupled model provides improved agreement between modeled and observed CO_{2} concentrations in comparison to the Eulerian model. In an area where variability in CO_{2} concentration is dominated by a fossil fuel signal, the correlation coefficient between modeled and observed concentrations increases by between 0.05 to 0.1 from the original values of 0.5–0.6 achieved with the Eulerian model.
Flow-Driven Cloud Formation and Fragmentation: Results From Eulerian and Lagrangian Simulations
Heitsch, Fabian; Walch, Stefanie
2011-01-01
The fragmentation of shocked flows in a thermally bistable medium provides a natural mechanism to form turbulent cold clouds as precursors to molecular clouds. Yet because of the large density and temperature differences and the range of dynamical scales involved, following this process with numerical simulations is challenging. We compare two-dimensional simulations of flow-driven cloud formation without self-gravity, using the Lagrangian Smoothed Particle Hydrodynamics (SPH) code VINE and the Eulerian grid code Proteus. Results are qualitatively similar for both methods, yet the variable spatial resolution of the SPH method leads to smaller fragments and thinner filaments, rendering the overall morphologies different. Thermal and hydro-dynamical instabilities lead to rapid cooling and fragmentation into cold clumps with temperatures below 300K. For clumps more massive than 1 Msun/pc, the clump mass function has an average slope of -0.8. The internal velocity dispersion of the clumps is nearly an order of ma...
Huetink, J.; Vanderlugt, J.
1988-08-01
A mixed Eulerian-Lagrangian finite element method is developed by which nodal point locations can be adapted independently from the actual material displacements. Numerical difficulties due to large element distortions, as many occur when the updated Lagrange method is applied, can be avoided by this method. Movement of (free) surfaces can be taken into account by adapting nodal surface points in a way that they remain on the surface. Hardening and other deformation path dependent properties are determined by incremental treatment of convective terms. A local and a weighed global smoothing procedure is introduced in order to avoid numerical instabilities. The method has been applied to simulations of an upsetting process, a wire drawing process and a cold rolling process. In the simulation of the rolling process, both workpiece and roll are simultaneously analyzed in order to predict the flattening of the roll. Special contact-slip elements are developed for the tool-workpiece interface.
Oliveira, J.L.G.; Geld, van der C.W.M.; Kuerten, J.G.M.
2013-01-01
Three-dimensional particle tracking velocimetry (3D-PTV) measurements have provided accurate Eulerian and Lagrangian high-order statistics of velocity and acceleration fluctuations and correlations at Reynolds number 10,300, based on the bulk velocity and the pipe diameter. Spatial resolution requir
Tongne, A.; Robe, H.; Desrayaud, C.; Jahazi, M.; Feulvarch, E.
2016-10-01
A finite element model has been developed by means of a coupled Eulerian-Lagrangian approach. The banded structure which is related to the periodical material deposition is predicted in two dimensions as the experimental investigation shows that, during FSW with trigonal tool, the material flow operates mainly in the welded plates plan.
Mass Transport Modelling in low permeability Fractured Rock: Eulerian versus Lagrangian approaches.
Capilla, J. E.; Rodrigo, J.; Llopis, C.; Grisales, C.; Gomez-Hernandez, J. J.
2003-04-01
Modeling flow and mass transport in fractured rocks can not be always successfully addressed by means of discrete fracture models which can fail due to the difficulty to be calibrated to experimental measurements. This is due to the need of having an accurate knowledge of fractures geometry and of the bidimensional distribution of hydrodynamic parameters on them. Besides, these models tend to be too rigid in the sense of not being able to re-adapt themselves correcting deficiencies or errors in the fracture definition. An alternative approach is assuming a pseudo-continuum media in which fractures are represented by the introduction of discretization blocks of very high hydraulic conductivity (K). This kind of model has been successfully tested in some real cases where the stochastic inversion of the flow equation has been performed to obtain equally likely K fields. However, in this framework, Eulerian mass transport modeling yields numerical dispersion and oscillations that make very difficult the analysis of tracer tests and the inversion of concentration data to identify K fields. In this contribution we present flow and mass transport modelling results in a fractured medium approached by a pseudo-continuum. The case study considered is based on data from a low permeability formation and both Eulerian and Lagrangian approaches have been applied. K fields in fractures are modeled as realizations of a stochastic process conditional to piezometric head data. Both a MultiGaussian and a non-multiGaussian approches are evaluated. The final goal of this research is obtaining K fields able to reproduce field tracer tests. Results show the important numerical problems found when applying an Eurelian approach and the possibilities of avoiding them with a 3D implementation of the Lagrangian random walk method. Besides, we see how different can be mass transport predictions when Gaussian and non-Gaussian models are assumed for K fields in fractures.
Directory of Open Access Journals (Sweden)
Y. Koyama
2010-11-01
Full Text Available This study assesses the advantages of using a coupled atmospheric-tracer transport model, comprising a global Eulerian model and a global Lagrangian particle dispersion model, for reproducibility of tracer gas variation affected by near field around observation sites. The ability to resolve variability in atmospheric composition on an hourly time scale and a spatial scale of several kilometers would be beneficial for analyzing data from continuous ground-based monitoring and upcoming space-based observations. The coupled model yields increased horizontal resolution of transport and fluxes, and has been tested in regional-scale studies of atmospheric chemistry. By applying the Lagrangian component to the global domain, we extend this approach to the global scale, thereby enabling global inverse modeling and data assimilation. To validate the coupled model, we compare model-simulated CO_{2} concentrations with continuous observations at two sites operated by the National Oceanic and Atmospheric Administration, USA and one site operated by National Institute for Environmental Studies, Japan. As the purpose of this study is limited to demonstration of the new modeling approach, we select a small subset of 3 sites to highlight use of the model in various geographical areas. To explore the capability of the coupled model in simulating synoptic-scale meteorological phenomena, we calculate the correlation coefficients and variance ratios between deseasonalized model-simulated and observed CO_{2} concentrations. Compared with the Eulerian model alone, the coupled model yields improved agreement between modeled and observed CO_{2} concentrations.
Jarauta, Alex; Ryzhakov, Pavel; Secanell, Marc; Waghmare, Prashant R.; Pons-Prats, Jordi
2016-08-01
An embedded Eulerian-Lagrangian formulation for the simulation of droplet dynamics within a polymer electrolyte fuel cell (PEFC) channel is presented. Air is modeled using an Eulerian formulation, whereas water is described with a Lagrangian framework. Using this framework, the gas-liquid interface can be accurately identified. The surface tension force is computed using the curvature defined by the boundary of the Lagrangian mesh. The method naturally accounts for material property changes across the interface and accurately represents the pressure discontinuity. A sessile drop in a horizontal surface, a sessile drop in an inclined plane and droplets in a PEFC channel are solved for as numerical examples and compared to experimental data. Numerical results are in excellent agreement with experimental data. Numerical results are also compared to results obtained with the semi-analytical model previously developed by the authors in order to discuss the limitations of the semi-analytical approach.
A lagrangian-eulerian description of debris transport by a tsunami in the Lisbon waterfront
Conde, Daniel; Canelas, Ricardo; Baptista, Maria Ana; João Telhado, Maria; Ferreira, Rui M. L.
2013-04-01
Several major tsunamis are known to have struck the Portuguese coast over the past millennia (Baptista and Miranda, 2009). The Tagus estuary has great exposure to tsunami occurrences and, being bordered by the largest metropolitan area in the country, is a particularly worrisome location in what concerns safety of populations and economic losses due to disruption of built infrastructures. The last major earthquake and tsunami combination known to have critically affected the Tagus estuary dates back to November 1st 1755. This catastrophe critically damaged Lisbon's infrastructures, led to numerous casualties and priceless heritage losses. The urban tissue of the present city still bears visible the effects of the catastrophe and of the ensuing protection measures. The objective of this work is to simulate the propagation of debris carried by a 1755-like tsunami along the present-day bathimetric and altimetric conditions of Lisbon waterfront. Particular emphasis was directed to the modeling of vehicles since the tsunami is likely to affect areas that are major traffic nodes such as Alcântara, with more than 1500 vehicles in road network of about 3 km. The simulation tool employed is based on a 2DH spatial (eulerian) shallow-flow approach suited to complex and dynamic bottom boundaries. The discretization technique relies on a finite-volume scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver (Canelas et al. 2013). Two formulations were employed to model the advection of debris: a fully coupled continuum approach, where solid bodies are described by the concentration only and an uncoupled material (lagrangian) formulation where solid bodies are tracked between two time-steps once the flow field is determined by the eulerian solver. In the latter case, concentrations are updated after tracking the solid bodies thus correcting the mass and momentum balance to be used for the next time-step. The urban tissue was
Eulerian-Lagrangian Simulations of Bubbly Flows in A Vertical Square Duct
Liu, Rui; Vanka, Surya P.; Thomas, Brian G.
2013-11-01
We report results of Eulerian-Lagrangian simulations of developing upward and downward bubbly flows in a vertical square duct with a bulk Reynolds number of 5000. The continuous fluid is simulated with DNS, solving the Navier-Stokes equations by a second-order accurate finite volume fractional step method. Bubbles of sizes comparable to the Kolmogorov scale are injected at the duct entrance with a mean bulk volume fraction below 10-2. A two-way coupling approach is adopted for the interaction between the continuous fluid phase and dispersed bubble phase. The bubbles are tracked by a Lagrangian method including drag and lift forces due to buoyancy and Saffman lift. A in-house code, CU-FLOW, implemented on Graphic Processing Unit (GPU) is used for simulations in this work. The preferential distributions of bubbles and their impact on local turbulence structures and their effects on turbulent kinetic energy budgets are studied. Results between an upward flow and a downward flow with the bubbles are compared. Work Supported by Continuous Casting Consortium at UIUC.
A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms
Benson, David A.; Aquino, Tomás; Bolster, Diogo; Engdahl, Nicholas; Henri, Christopher V.; Fernàndez-Garcia, Daniel
2017-01-01
When laboratory-measured chemical reaction rates are used in simulations at the field-scale, the models typically overpredict the apparent reaction rates. The discrepancy is primarily due to poorer mixing of chemically distinct waters at the larger scale. As a result, realistic field-scale predictions require accurate simulation of the degree of mixing between fluids. The Lagrangian particle-tracking (PT) method is a now-standard way to simulate the transport of conservative or sorbing solutes. The method's main advantage is the absence of numerical dispersion (and its artificial mixing) when simulating advection. New algorithms allow particles of different species to interact in nonlinear (e.g., bimolecular) reactions. Therefore, the PT methods hold a promise of more accurate field-scale simulation of reactive transport because they eliminate the masking effects of spurious mixing due to advection errors inherent in grid-based methods. A hypothetical field-scale reaction scenario is constructed and run in PT and Eulerian (finite-volume/finite-difference) simulators. Grid-based advection schemes considered here include 1st- to 3rd-order spatially accurate total-variation-diminishing flux-limiting schemes, both of which are widely used in current transport/reaction codes. A homogeneous velocity field in which the Courant number is everywhere unity, so that the chosen Eulerian methods incur no error when simulating advection, shows that both the Eulerian and PT methods can achieve convergence in the L1 (integrated concentration) norm, but neither shows stricter pointwise convergence. In this specific case with a constant dispersion coefficient and bimolecular reaction A + B → P , the correct total amount of product is 0.221MA0, where MA0 is the original mass of reactant A. When the Courant number drops, the grid-based simulations can show remarkable errors due to spurious over- and under-mixing. In a heterogeneous velocity field (keeping the same constant and
Winschall, A.; Pfahl, S.; Sodemann, H.; Wernli, H.
2014-07-01
Moisture convergence from different sources is an important prerequisite for a heavy-precipitation event. The contributions from different source regions can, however, hardly be quantified from observations, and their assessment based on model results is complex. Two conceptually different numerical methods are widely used for the quantification of moisture sources: Lagrangian approaches based on the analysis of humidity variations along backward trajectories and Eulerian methods based on the implementation of moisture tracers into a numerical model. In this study the moisture sources for a high-impact, heavy-precipitation event that affected eastern Europe in May 2010 are studied with both Eulerian and Lagrangian moisture source diagnostics. The precipitation event was connected to a cyclone that developed over northern Africa, moved over the Mediterranean towards eastern Europe and induced transport of moist air towards the Carpathian Mountains. Heavy precipitation and major flooding occurred in Poland, the Czech Republic and Slovakia between 16 and 18 May 2010. The Lagrangian and Eulerian diagnostics consistently indicate a wide spatial and temporal range of moisture sources contributing to the event. The source with the largest share is local evapotranspiration from the European land surface, followed by moisture from the North Atlantic. Further contributions come from tropical western Africa (10-20° N) and the Mediterranean Sea. Contrary to what could be expected, the Mediterranean contribution of about 10% is relatively small. A detailed analysis of exemplary trajectories corroborates the general consistency of the two approaches, and underlines their complementarity. The Lagrangian method allows for mapping out moisture source regions with computational efficiency, whereas the more elaborate Eulerian model requires predefined moisture sources, but includes also processes such as precipitation, evaporation and turbulent mixing. However, in the Eulerian model
Directory of Open Access Journals (Sweden)
A. Winschall
2014-07-01
Full Text Available Moisture convergence from different sources is an important prerequisite for a heavy-precipitation event. The contributions from different source regions can, however, hardly be quantified from observations, and their assessment based on model results is complex. Two conceptually different numerical methods are widely used for the quantification of moisture sources: Lagrangian approaches based on the analysis of humidity variations along backward trajectories and Eulerian methods based on the implementation of moisture tracers into a numerical model. In this study the moisture sources for a high-impact, heavy-precipitation event that affected eastern Europe in May 2010 are studied with both Eulerian and Lagrangian moisture source diagnostics. The precipitation event was connected to a cyclone that developed over northern Africa, moved over the Mediterranean towards eastern Europe and induced transport of moist air towards the Carpathian Mountains. Heavy precipitation and major flooding occurred in Poland, the Czech Republic and Slovakia between 16 and 18 May 2010. The Lagrangian and Eulerian diagnostics consistently indicate a wide spatial and temporal range of moisture sources contributing to the event. The source with the largest share is local evapotranspiration from the European land surface, followed by moisture from the North Atlantic. Further contributions come from tropical western Africa (10–20° N and the Mediterranean Sea. Contrary to what could be expected, the Mediterranean contribution of about 10% is relatively small. A detailed analysis of exemplary trajectories corroborates the general consistency of the two approaches, and underlines their complementarity. The Lagrangian method allows for mapping out moisture source regions with computational efficiency, whereas the more elaborate Eulerian model requires predefined moisture sources, but includes also processes such as precipitation, evaporation and turbulent mixing. However
Vérèmes, H.; Cammas, J.-P.; Baray, J.-L.; Keckhut, P.; Barthe, C.; Posny, F.; Tulet, P.; Dionisi, D.; Bielli, S.
2016-12-01
Signatures of multiple stratospheric intrusions were observed on simultaneous and collocated ozone and water vapor profiles retrieved by lidars and radiosondes at the Maïdo Observatory, Reunion Island (21°S, 55°E, 2160 m above sea level), during MAïdo LIdar Calibration CAmpaign in April 2013. A singular structure of the ozone vertical profile with three peaks (in excess of 90 ppbv, at 8, 10, and 13 km altitude) embedded in a thick dry layer of air suggested stratospheric intrusions with multiple origins. The hypothesis is corroborated by a synoptic analysis based on re-analyses. European Centre for Medium-Range Weather Forecasts ERA-Interim temporal series associated with 5 days Lagrangian back trajectories initialized on each ozone peak allows to capture their stratospheric origin. The ozone peak at the lowest altitude is associated with an irreversible tropopause folding process along the polar jet stream during an extratropical cutoff low formation. Simultaneous lidar water vapor profiles of this peak show that the anticorrelation with ozone has been removed, due to mixing processes. Back trajectories indicate that the two other ozone peaks observed at higher altitudes are associated with the dynamics of the subtropical jet stream and the lower stratosphere. The observations confirm the recent stratospheric origins. The highest ozone peak is explained by the horizontal distribution of the intrusion. Use of a Lagrangian Reverse Domain Filling model and of the Meso-NH Eulerian mesoscale model with a passive stratospheric tracer allow to further document the stratosphere-troposphere transport processes and to describe the detailed potential vorticity and ozone structures in which are embedded in the observed multiple stratospheric intrusions.
Jiang, Jiming
2013-06-01
This paper presents a new wireless platform designed for an integrated traffic monitoring system based on combined Lagrangian (mobile) and Eulerian (fixed) sensing. The sensor platform is built around a 32-bit ARM Cortex M4 micro-controller and a 2.4GHz 802.15.4 ISM compliant radio module, and can be interfaced with fixed traffic sensors, or receive data from vehicle transponders. The platform is specially designed and optimized to be integrated in a solar-powered wireless sensor network in which traffic flow maps are computed by the nodes directly using distributed computing. A MPPT circuitry is proposed to increase the power output of the attached solar panel. A self-recovering unit is designed to increase reliability and allow periodic hard resets, an essential requirement for sensor networks. A radio monitoring circuitry is proposed to monitor incoming and outgoing transmissions, simplifying software debug. An ongoing implementation is briefly discussed, and compared with existing platforms used in wireless sensor networks. © 2013 IEEE.
Parallel octree-based hexahedral mesh generation for eulerian to lagrangian conversion.
Energy Technology Data Exchange (ETDEWEB)
Staten, Matthew L.; Owen, Steven James
2010-09-01
Computational simulation must often be performed on domains where materials are represented as scalar quantities or volume fractions at cell centers of an octree-based grid. Common examples include bio-medical, geotechnical or shock physics calculations where interface boundaries are represented only as discrete statistical approximations. In this work, we introduce new methods for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to ASC codes such as CTH and Alegra. New procedures for generating all-hexahedral finite element meshes from volume fraction data are introduced. A new primal-contouring approach is introduced for defining a geometric domain. New methods for refinement, node smoothing, resolving non-manifold conditions and defining geometry are also introduced as well as an extension of the algorithm to handle tetrahedral meshes. We also describe new scalable MPI-based implementations of these procedures. We describe a new software module, Sculptor, which has been developed for use as an embedded component of CTH. We also describe its interface and its use within the mesh generation code, CUBIT. Several examples are shown to illustrate the capabilities of Sculptor.
Ohkitani, K; Constantin, P
2008-12-01
We study reconnection phenomena in magnetohydrodynamics on the basis of a magnetohydrodynamic version of the Eulerian-Lagrangian analysis. We find that the methods are useful in capturing time scales associated with magnetic reconnection both in two and three dimensions. Visualizations show that the determinants of the Jacobian determinants of the diffusive labels are small where active reconnection takes place. The resetting of the diffusive labels extracts a short time scale during reconnection.
ICECO-CEL: a coupled Eulerian-Lagrangian code for analyzing primary system response in fast reactors
Energy Technology Data Exchange (ETDEWEB)
Wang, C.Y.
1981-02-01
This report describes a coupled Eulerian-Lagrangian code, ICECO-CEL, for analyzing the response of the primary system during hypothetical core disruptive accidents. The implicit Eulerian method is used to calculate the fluid motion so that large fluid distortion, two-dimensional sliding interface, flow around corners, flow through coolant passageways, and out-flow boundary conditions can be treated. The explicit Lagrangian formulation is employed to compute the response of the containment vessel and other elastic-plastic solids inside the reactor containment. Large displacements, as well as geometrical and material nonlinearities are considered in the analysis. Marker particles are utilized to define the free surface or the material interface and to visualize the fluid motion. The basic equations and numerical techniques used in the Eulerian hydrodynamics and Lagrangian structural dynamics are described. Treatment of the above-core hydrodynamics, sodium spillage, fluid cavitation, free-surface boundary conditions and heat transfer are also presented. Examples are given to illustrate the capabilities of the computer code. Comparisons of the code predictions with available experimental data are also made.
Lagrangian and Eulerian biventricular strains from anatomical NURBS models using tagged MRI
Tustison, Nicholas J.; Amini, Amir A.
2005-04-01
We present current research in which both left and right ventricular deformation is estimated from tagged cardiac magnetic resonance imaging using volumetric deformable models constructed from nonuniform rational B-splines (NURBS). The four model types considered include Cartesian-based NURBS models with both a cylindrical and prolate-spheroidal parameterization, prolate spheroidal-based NURBS models with a prolate-spheroidal parameterization, and cylindrical-based NURBS models with a cylindrical parameterization. For each frame subsequent to end-diastole, a NURBS model is constructed by fitting two surfaces with the same parameterization to the corresponding set of epicardial and endocardial contours from which a volumetric model is created. Using normal displacements of the three sets of orthogonal tag planes as well as displacements of contour/tag line intersection points and tag plane intersection points, one can solve for the optimal homogeneous coordinates, in a weighted least squares sense, of the control points of the deformed NURBS model at end-diastole using quadratic programming. This allows for subsequent forward displacement fitting from end-diastole to all later time frames. After fitting to all time points of data, lofting the NURBS model at each time point creates a comprehensive 4-D NURBS model. From this model, we can extract 3-D myocardial deformation fields and corresponding strain maps which are local measures of non-rigid deformation. The results show that, in the case of simulated data, the quadratic Cartesian-based NURBS model outperformed its counterparts in predicting normal strain. This model was used to then calculate normal Lagrangian and Eulerian strains in canine data.
Directory of Open Access Journals (Sweden)
Lukas Papritz
2013-03-01
Full Text Available In this idealised modelling study, the development of a downstream cyclone, which closely follows the life-cycle of a Shapiro-Keyser cyclone, is addressed from a quasi-geostrophic kinetic energy perspective. To this end a simulation of a dry, highly idealised, dispersive baroclinic wave, developing a primary and a downstream cyclone, is performed. Kinetic energy and processes contributing to its tendency – in particular baroclinic conversion and ageostrophic geopotential fluxes – are investigated in three dimensions both in an Eulerian and a Lagrangian framework from the genesis of the downstream cyclone as an upper-level kinetic energy centre, over frontal fracture to the fully developed cyclone showing the characteristic T-bone surface frontal structure, with a strong low-level jet along the bent-back front. Initially the downstream cyclone grows by the convergence of ageostrophic geopotential fluxes from the primary cyclone, but as vertical motions intensify this process is replaced by baroclinic conversion in the warm sector. We show that kinetic energy released in the warm sector is radiated away at all levels by ageostrophic geopotential fluxes: in the upper troposphere they are directed downstream, while in the lower troposphere they radiate kinetic energy to the rear of the cyclone. Thereby, vertical ageostrophic geopotential fluxes, their location and divergence, are identified to play a major role in the intensification of the cyclone in the lower troposphere and for the formation of the low-level jet. Low-level rearward ageostrophic geopotential fluxes converging along the bent-back front are shown to be a general characteristic of an eastward propagating baroclinic wave.
Vié, Aymeric; Pouransari, Hadi; Zamansky, Rémi; Mani, Ali
2015-01-01
International audience; The goal of the present work is to assess the ability of Eulerian moment methods to reproduce the physics of two-way coupled particle-laden turbulent flow systems. Previous investigations have been focused on effects such as preferential concentration, and turbulence modulation, but in regimes in which turbulence is sustained by an imposed external forcing. We show that in such regimes, Eulerian methods need resolutions finer than nominal Kolmogorov scale in order to c...
Li, Linmin; Li, Baokuan
2016-08-01
In ladle metallurgy, bubble-liquid interaction leads to complex phase structures. Gas bubble behavior, as well as the induced slag layer behavior, plays a significant role in the refining process and the steel quality. In the present work, a mathematical model using the large eddy simulation (LES) is developed to investigate the bubble transport and slag layer behavior in a water model of an argon-stirred ladle. The Eulerian volume of fluid model is adopted to track the liquid steel-slag-air free surfaces while the Lagrangian discrete phase model is used for tracking and handling the dynamics of discrete bubbles. The bubble coalescence is considered using O'Rourke's algorithm to solve the bubble diameter redistribution and bubbles are removed after leaving the air-liquid interface. The turbulent liquid flow that is induced by bubble-liquid interaction is solved by LES. The slag layer fluactuation, slag droplet entrainment and spout eye open-close phenomenon are well revealed. The bubble diameter distribution and the spout eye size are compared with the experiment. The results show that the hybrid Eulerian-Lagrangian-LES model provides a valid modeling framework to predict the unsteady gas bubble-slag layer coupled behaviors.
Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander
2016-02-01
We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated
Liu, Zhongqiu; Sun, Zhenbang; Li, Baokuan
2016-12-01
Lagrangian tracking model combined with Eulerian multi-phase model is employed to predict the time-dependent argon-steel-slag-air quasi-four-phase flow inside a slab continuous casting mold. The Eulerian approach is used for the description of three phases (molten steel, liquid slag, and air at the top of liquid slag layer). The dispersed argon bubble injected from the SEN is treated in the Lagrangian way. The complex interfacial momentum transfers between various phases are considered. Validation is supported by the measurement data of cold model experiments and industrial practice. Close agreements were achieved for the gas volume fraction, liquid flow pattern, level fluctuation, and exposed slag eye phenomena. Many known phenomena and new predictions were successfully reproduced using this model. The vortex slag entrapment phenomenon at the slag-steel interface was obtained using this model, some small slag drops are sucked deep into the liquid pool of molten steel. Varying gas flow rates have a large effect on the steel flow pattern in the upper recirculation zone. Three typical flow patterns inside the mold with different argon gas flow rates have been obtained: double roll, three roll, and single roll. Effects of argon gas flow rate, casting speed, and slag layer thickness on the exposed slag eye and level fluctuation at the slag-steel interface were studied. A dimensionless value of H ave/h was proposed to describe the time-averaged level fluctuation of slag-steel interface. The exposed slag eye near the SEN would be formed when the value of H ave/h is larger than 0.4.
Treyssède, Fabien; Gabard, Gwénaël; Ben Tahar, Mabrouk
2003-02-01
A nonstandard wave equation, established by Galbrun in 1931, is used to study sound propagation in nonuniform flows. Galbrun's equation describes exactly the same physical phenomenon as the linearized Euler's equations (LEE) but is derived from an Eulerian-Lagrangian description and written only in term of the Lagrangian perturbation of the displacement. This equation has interesting properties and may be a good alternative to the LEE: only acoustic displacement is involved (even in nonhomentropic cases), it provides exact expressions of acoustic intensity and energy, and boundary conditions are easily expressed because acoustic displacement whose normal component is continuous appears explicitly. In this paper, Galbrun's equation is solved using a finite element method in the axisymmetric case. With standard finite elements, the direct displacement-based variational formulation gives some corrupted results. Instead, a mixed finite element satisfying the inf-sup condition is proposed to avoid this problem. A first set of results is compared with semianalytical solutions for a straight duct containing a sheared flow (obtained from Pridmore-Brown's equation). A second set of results concerns a more complex duct geometry with a potential flow and is compared to results obtained from a multiple-scale method (which is an adaptation for the incompressible case of Rienstra's recent work).
Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.
Suk, Heejun
2016-07-01
MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes.
2011-09-01
that evolve during the course of the detonation event. Neuberger et al. [13] examined the scaling of flat plate deformation with excitation from...Solids, 57(8), pp. 1139–1164. [13] Neuberger , A., Peles, S., and Rittel, D., 2007. “Scaling the response of circular plates subjected to large and
Maniatis, Georgios
2017-04-01
Fluvial sediment transport is controlled by hydraulics, sediment properties and arrangement, and flow history across a range of time scales. One reference frame descriptions (Eulerian or Lagrangian) yield useful results but restrict the theoretical understanding of the process as differences between the two phases (liquid and solid) are not explicitly accounted. Recently, affordable Inertial Measurement Units (IMUs) that can be embedded in coarse (100 mm diameter scale) natural or artificial particles became available. These sensors are subjected to technical limitations when deployed for natural sediment transport. However, they give us the ability to measure for the first time the inertial dynamics (acceleration and angular velocity) of moving sediment grains under fluvial transport. Theoretically, the assumption of an ideal (IMU), rigidly attached at the centre of the mass of a sediment particle can simplify greatly the derivation of a general Eulerian-Lagrangian (E-L) model. This approach accounts for inertial characteristics of particles in a Lagrangian (particle fixed) frame, and for the hydrodynamics in an independent Eulerian frame. Simplified versions of the E-L model have been evaluated in laboratory experiments using real-IMUs [Maniatis et. al 2015]. Here, experimental results are presented relevant to the evaluation of the complete E-L model. Artificial particles were deployed in a series of laboratory and field experiments. The particles are equipped with an IMU capable of recording acceleration at ± 400 g and angular velocities at ± 1200 rads/sec ranges. The sampling frequency ranges from 50 to 200 Hz for the total IMU measurement. Two sets of laboratory experiments were conducted in a 0.9m wide laboratory flume. The first is a set of entrainment threshold experiments using two artificial particles: a spherical of D=90mm (A) and an ellipsoid with axes of 100, 70 and 30 mm (B). For the second set of experiments, a spherical artificial enclosure of D
Di Bernardino, Annalisa; Monti, Paolo; Leuzzi, Giovanni; Querzoli, Giorgio
2017-07-01
Lagrangian and Eulerian statistics are obtained from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. The objective is to quantify the Eulerian (TE) and Lagrangian (TL) time scales of the turbulence above the canopy layer as well as to investigate their dependence on the aspect ratio of the canopy, AR, as the latter is the ratio of the width (W) to the height (H) of the canyon. Experiments are also conducted for the case of flat terrain, which can be thought of as equivalent to a classical one-directional shear flow. The values found for the Eulerian time scales on flat terrain are in agreement with previous numerical results found in the literature. It is found that both the streamwise and vertical components of the Lagrangian time scale, T_u^L and T_w^L , follow Raupach's linear law within the constant-flux layer. The same holds true for T_w^L in both the canopies analyzed (AR= 1 and AR= 2 ) and also for T_u^L when AR = 1 . In contrast, for AR = 2 , T_u^L follows Raupach's law only above z=2H . Below that level, T_u^L is nearly constant with height, showing at z=H a value approximately one order of magnitude greater than that found for AR = 1 . It is shown that the assumption usually adopted for flat terrain, that β =TL/TE is proportional to the inverse of the turbulence intensity, also holds true even for the canopy flow in the constant-flux layer. In particular, γ /i_u fits well β _u =T_u^L /T_u^E in both the configurations by choosing γ to be 0.35 (here, i_u =σ _u / \\bar{u} , where \\bar{u} and σ _u are the mean and the root-mean-square of the streamwise velocity component, respectively). On the other hand, β _w =T_w^L /T_w^E follows approximately γ /i_w =0.65/( {σ _w /\\bar{u} } ) for z > 2H , irrespective of the AR value. The second main objective is to estimate other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum (KT) and the Kolmogorov constant (C_0) . It
Adesemowo, Morakinyo; Shelton, John
2016-11-01
Previous experimental and numerical investigations involving lid-driven cavity flows with particle suspensions have primarily focused on particle tracking and the visualization of complex three-dimensional structures that compose the flow field. However, these particle suspensions and their resulting particle-particle interactions could also be viewed as a system of time-dependent perturbation equations to the steady-state Navier-Stokes equations and could affect both the stability and steady-state characteristics of the two-dimensional lid-driven cavity system. In this investigation, an Eulerian-Lagrangian approach to modeling particle suspensions in the lid-driven cavity is utilized in FV-CFD simulations to investigate the effect particle density, area fraction, and Reynolds number have on the two-dimensional flow characteristics of a laminar fluid. Observations have indicated that the development of the primary vortex in the lid-driven cavity varies according to the area fraction of particle suspensions in the system; transitioning from development via an adverse pressure gradient at the top-right corner of the cavity towards particle-laden behavior where particle-particle interactions dominate the development of the primary vortex. Dynamic responses were also observed for particle systems of less dense particles. Finally, a comparison between flows perturbed using disturbance velocities and from particle interactions was performed.
Heberton, C.I.; Russell, T.F.; Konikow, L.F.; Hornberger, G.Z.
2000-01-01
This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.
Directory of Open Access Journals (Sweden)
José L. Muñoz-Cobo
2012-09-01
Full Text Available A set of air-water experiments has been performed under isothermal upward concurrent flow conditions, in a vertical column. The interfacial velocity, the bubble interfacial area and the void fraction distributions have been measured. Numerical simulation of these experiments were performed by coupling a Lagrangian code which tracks the 3D motion of the individual bubbles, with an Eulerian one. In the Eulerian solver the velocity and turbulence fields of the liquid phase were computed by solving the time dependent conservation equations in its Reynolds Averaged Transport Equation form (RANS. The turbulent kinetic energy k, and the dissipation rate transport equations were simultaneously solved by using the k, epsilon model in a (r,z grid by the finite volume method and the SIMPLER algorithm. Both Lagrangian and Eulerian calculations were performed in parallel and an iterative self-consistent method was developed. The turbulence induced by the bubbles is an important issue considered in this paper, in order to obtain good predictions of the void fraction distribution and the interfacial velocity at different gas and liquid flow conditions. The Eulerian Code was upgraded from an axisymmetric 2D code to a 3D code in order to improve the turbulence solution. The results of the 3D CFD code have been tested and show a good agreement with the experimental results. In this paper special attention is given to the coupling between the different models.
Eulerian and Lagrangian accelerations in the intermediate field of turbulent circular jets
Kim, Jin-Tae; Liberzon, Alex; Chamorro, Leonardo P.
2016-11-01
Particle tracking velocimetry is used to study the structure of various acceleration components, vorticity, and strain within the intermediate field of a circular jet at Re = 6000. The total acceleration is decomposed into three sets: a) streamwise-radial; b) tangential-normal; and c) local-convective components. Probability density function (PDF) and joint PDFs of each set are characterized at various radial locations within a streamwise band contained within 16 and 17 pipe diameters. Results show that the acceleration components are described by two distributions; one of them exhibits symmetry and heavy tails, while the other is best fitted by a power-law type. The PDF tails are heavier with increasing the radial distance. The growing departure from the Gaussian distribution is a result of the comparatively increase in turbulence promoted by the mean shear of the jet. The variation of third and fourth moments between the streamwise-tangential and the radial-normal accelerations indicates the anisotropy of the jet. Although joint PDFs show distinctive distribution and depend on the distance from the jet core, the relative angles between the Lagrangian acceleration with velocity, vorticity and strain show similar PDF across radial distances.
Directory of Open Access Journals (Sweden)
U. Karstens
2012-01-01
Full Text Available We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM. The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian on models' spatial resolution is further investigated. A case study using airborne measurements during which both models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km. Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data. Thus suggests that it is reasonable to use STILT as an adjoint model of WRF atmospheric transport.
Directory of Open Access Journals (Sweden)
U. Karstens
2012-10-01
Full Text Available We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM. The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian on models' spatial resolution is further investigated. A case study using airborne measurements during which two models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km. Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data.
Shippee, N. J.; Atkinson, D. E.
2014-12-01
The idea of considering the "end user perspective" regarding storm activity and objective tracking methods used to compile information on their behaviour is particularly important in the Alaskan region. Annually, coastal regions in the North are exposed to stormy conditions, though most impacts occur during periods where multiple storms track over the same area in a short period of time (serial cyclones) or where strong storms occur without the presence of a protective sea ice buffer. From a fixed perspective (i.e. Eulerian), a storm may be identified more by the impacts that it generates at that location (winds, sea state, erosion). From a Lagrangian (tracking) view, the intensity, duration, and characteristics of the synoptic environment may prove more relevant for understanding. The overall "effectiveness" of an objective tracking method depends on the intended use of the provided information. While pitting different methods against each other is not necessarily a fruitful exercise (Mesquita et al. 2009), the reality is that one method may better reflect the reality of storm activity and impacts to those experiencing the weather first hand. One of the more subtle points in extra-tropical cyclone tracking and comparison work is the method by which a storm is defined. Most cyclones are analyzed on MSLP fields; others define a cyclone by relative vorticity (ζ) maxima at 850 hPa (NH) and minima (SH). Storms can also be defined by wind events, or even impacts, at a location. Using counts of strong wind events at a grid point or location can account for pressure gradients both associated with storms and absent of a synoptic event. Three separate tracking algorithms are analyzed to determine the method most likely to produce a long-term homogeneous dataset that can be used to train a statistical seasonal prediction method. These methods include the Serreze algorithm, Hodges TRACK algorithm, and Atkinson algorithm. Both the Serreze and Hodges methods provide a tracking
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Yeh, Gour-Tsyh [Pennsylvania State Univ., University Park, PA (United States). Dept. of Civil and Environmental Engineering; Carpenter, S.L. [Univ. of New Mexico, Albuquerque, NM (United States). Dept. of Earth and Planetary Sciences; Hopkins, P.L.; Siegel, M.D. [Sandia National Labs., Albuquerque, NM (United States)
1995-11-01
The computer program LEHGC is a Hybrid Lagrangian-Eulerian Finite-Element Model of HydroGeo-Chemical (LEHGC) Transport Through Saturated-Unsaturated Media. LEHGC iteratively solves two-dimensional transport and geochemical equilibrium equations and is a descendant of HYDROGEOCHEM, a strictly Eulerian finite-element reactive transport code. The hybrid Lagrangian-Eulerian scheme improves on the Eulerian scheme by allowing larger time steps to be used in the advection-dominant transport calculations. This causes less numerical dispersion and alleviates the problem of calculated negative concentrations at sharp concentration fronts. The code also is more computationally efficient than the strictly Eulerian version. LEHGC is designed for generic application to reactive transport problems associated with contaminant transport in subsurface media. Input to the program includes the geometry of the system, the spatial distribution of finite elements and nodes, the properties of the media, the potential chemical reactions, and the initial and boundary conditions. Output includes the spatial distribution of chemical element concentrations as a function of time and space and the chemical speciation at user-specified nodes. LEHGC Version 1.1 is a modification of LEHGC Version 1.0. The modification includes: (1) devising a tracking algorithm with the computational effort proportional to N where N is the number of computational grid nodes rather than N{sup 2} as in LEHGC Version 1.0, (2) including multiple adsorbing sites and multiple ion-exchange sites, (3) using four preconditioned conjugate gradient methods for the solution of matrix equations, and (4) providing a model for some features of solute transport by colloids.
Directory of Open Access Journals (Sweden)
F. Khosrawi
2005-01-01
Full Text Available During the CRISTA-1 mission three pronounced fingerlike structures reaching from the lower latitudes to the mid-latitudes, so-called streamers, were observed in the measurements of several trace gases in early November 1994. A simulation of these streamers in previous studies employing the KASIMA (Karlsruhe Simulation Model of the Middle Atmosphere and ROSE (Research on Ozone in the Stratosphere and its Evolution model, both being Eulerian models, show that their formation is due to adiabatic transport processes. Here, the impact of mixing on the development of these streamers is investigated. These streamers were simulated with the CLaMS model (Chemical Lagrangian Model of the Stratosphere, a Lagrangian model, using N2O as long-lived tracer. Using several different initialisations the results were compared to the KASIMA simulations and CRISTA (Cryogenic Infrared Spectrometer and Telescope for the Atmosphere observations. Further, since the KASIMA model was employed to derive a 9-year climatology, the quality of the reproduction of streamers from such a study was tested by the comparison of the KASIMA results with CLaMS and CRISTA. The streamers are reproduced well for the Northern Hemisphere in the simulations of CLaMS and KASIMA for the 6 November 1994. However, in the CLaMS simulation a stronger filamentation is found while larger discrepancies between KASIMA and CRISTA were found especially for the Southern Hemisphere. Further, compared to the CRISTA observations the mixing ratios of N2O are in general underestimated in the KASIMA simulations. An improvement of the simulations with KASIMA was obtained for a simulation time according to the length of the CLaMS simulation. To quantify the differences between the simulations with CLaMS and KASIMA, and the CRISTA observations, the probability density function technique (PDF is used to interpret the tracer distributions. While in the PDF of the KASIMA simulation the small scale structures
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Munoz-Cobo, J.L. [Univ. Politecnica de Valencia, Inst. de Ingenieria Energetica, Valencia (Spain); Chiva, S. [Univ. Jaume I, Dept. of Mechnical Engineering and Construction, Castellon (Spain); Abd El Aziz Essa, M. [Univ. Politecnica de Valencia, Inst. de Ingenieria Energetica, Valencia (Spain); Mendes, S. [Univ. Autonoma de Nuevo Leon, Facultad de Ingenieria Mecanica y Electrica (Mexico)
2011-07-01
A set of air-water experiments have been performed under isothermal upward concurrent flow in a vertical column. The interfacial velocity, interfacial area of the bubbles and the void fraction distributions was obtained. Numerical validation of these results for bubbly flow conditions were performed by coupling a Lagrangian code which tracks the 3D motion of the individual bubbles, with an Eulerian one. Both Lagrangian and Eulerian calculations were performed in parallel and iterative self-consistent method was developed. The bubbles-induced turbulence is an important issue considered, to obtain good predictions of experimental results. (author)
Pavish, D. L.; Spaulding, M. L.
1977-01-01
A computer coded Lagrangian marker particle in Eulerian finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.
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Garcia, Jr., W. J.; Viecelli, J. A.
1976-06-01
This report is intended to be a ''user manual'' for the Lawrence Livermore Laboratory version of the Eulerian incompressible hydrodynamic computer code ABMAC. The theory of the numerical model is discussed in general terms. The format for data input and data printout is described in detail. A listing and flow chart of the computer code are provided.
Lagrangian continuum dynamics in ALEGRA.
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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.
Directory of Open Access Journals (Sweden)
Angelo ROLLA
2010-02-01
Full Text Available The paper describes a numerical study for estimating the spatial distribution of the hydraulic residence time in Lago Maggiore. A 3D eulerian time-dependent CFD code has been applied under real conditions, taking into account the effects of the monthly mean values of the mass flow rates and temperatures of all the tributaries, mass flow rate of the Ticino effluent and meteorological, hydrogeological and limnological parameters available from the rich data-base of CNR-ISE (Pallanza. The velocity distributions from these simulations were used to compute the paths of a number of massless markers with different initial positions and so evaluate their residence times within the lake. The results presented here follow a two-year simulation and show encouraging agreement with the mechanisms of mixing and of deep water oxygenation revealed by recent limnological studies carried out at CNR-ISE. Further studies are in progress to improve the results and extend the research over a time period of at least four years.
Arbogast, Todd
2012-01-01
Motivated by possible generalizations to more complex multiphase multicomponent systems in higher dimensions, we develop an Eulerian-Lagrangian numerical approximation for a system of two conservation laws in one space dimension modeling a simplified two-phase flow problem in a porous medium. The method is based on following tracelines, so it is stable independent of any CFL constraint. The main difficulty is that it is not possible to follow individual tracelines independently. We approximate tracing along the tracelines by using local mass conservation principles and self-consistency. The two-phase flow problem is governed by a system of equations representing mass conservation of each phase, so there are two local mass conservation principles. Our numerical method respects both of these conservation principles over the computational mesh (i.e., locally), and so is a fully conservative traceline method. We present numerical results that demonstrate the ability of the method to handle problems with shocks and rarefactions, and to do so with very coarse spatial grids and time steps larger than the CFL limit. © 2012 Society for Industrial and Applied Mathematics.
Dodin, I Y; Fraiman, G M
2003-01-01
The Lagrangian and Hamiltonian functions describing average motion of a relativistic particle under the action of intensive high-frequency electromagnetic radiation are obtained. In weak, low-frequency background fields, such a particle on average drifts with an effective, relativistically invariant mass, which depends on the intensity of the electromagnetic field.
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Dr. Dale M. Snider
2011-02-28
This report gives the result from the Phase-1 work on demonstrating greater than 10x speedup of the Barracuda computer program using parallel methods and GPU processors (General-Purpose Graphics Processing Unit or Graphics Processing Unit). Phase-1 demonstrated a 12x speedup on a typical Barracuda function using the GPU processor. The problem test case used about 5 million particles and 250,000 Eulerian grid cells. The relative speedup, compared to a single CPU, increases with increased number of particles giving greater than 12x speedup. Phase-1 work provided a path for reformatting data structure modifications to give good parallel performance while keeping a friendly environment for new physics development and code maintenance. The implementation of data structure changes will be in Phase-2. Phase-1 laid the ground work for the complete parallelization of Barracuda in Phase-2, with the caveat that implemented computer practices for parallel programming done in Phase-1 gives immediate speedup in the current Barracuda serial running code. The Phase-1 tasks were completed successfully laying the frame work for Phase-2. The detailed results of Phase-1 are within this document. In general, the speedup of one function would be expected to be higher than the speedup of the entire code because of I/O functions and communication between the algorithms. However, because one of the most difficult Barracuda algorithms was parallelized in Phase-1 and because advanced parallelization methods and proposed parallelization optimization techniques identified in Phase-1 will be used in Phase-2, an overall Barracuda code speedup (relative to a single CPU) is expected to be greater than 10x. This means that a job which takes 30 days to complete will be done in 3 days. Tasks completed in Phase-1 are: Task 1: Profile the entire Barracuda code and select which subroutines are to be parallelized (See Section Choosing a Function to Accelerate) Task 2: Select a GPU consultant company and
Zhao, Tong; Yao, Jiafeng; Liu, Kai; Takei, Masahiro
2016-03-01
The inertial migration of neutrally buoyant spherical particles in high particle concentration (αpi > 3%) suspension flow in a square microchannel was investigated by means of the multi-electrodes sensing method which broke through the limitation of conventional optical measurement techniques in the high particle concentration suspensions due to interference from the large particle numbers. Based on the measured particle concentrations near the wall and at the corner of the square microchannel, particle cross-sectional migration ratios are calculated to quantitatively estimate the migration degree. As a result, particle migration to four stable equilibrium positions near the centre of each face of the square microchannel is found only in the cases of low initial particle concentration up to 5.0 v/v%, while the migration phenomenon becomes partial as the initial particle concentration achieves 10.0 v/v% and disappears in the cases of the initial particle concentration αpi ≥ 15%. In order to clarify the influential mechanism of particle-particle interaction on particle migration, an Eulerian-Lagrangian numerical model was proposed by employing the Lennard-Jones potential as the inter-particle potential, while the inertial lift coefficient is calculated by a pre-processed semi-analytical simulation. Moreover, based on the experimental and simulation results, a dimensionless number named migration index was proposed to evaluate the influence of the initial particle concentration on the particle migration phenomenon. The migration index less than 0.1 is found to denote obvious particle inertial migration, while a larger migration index denotes the absence of it. This index is helpful for estimation of the maximum initial particle concentration for the design of inertial microfluidic devices.
Wongwathanarat, Annop; Müller, Ewald
2016-01-01
We present a new fourth-order finite-volume hydrodynamics code named Apsara. The code employs the high-order finite-volume method for mapped coordinates developed by Colella et al. (2011) with extensions for non-linear hyperbolic conservation laws by McCorquodale & Colella (2011) and Guzik et al. (2012). Using the mapped-grid technique Apsara can handle arbitrary structured curvilinear meshes in three spatial dimensions. The code has successfully passed several hydrodynamic test problems including the advection of a Gaussian density profile and a non-linear vortex, as well as the propagation of linear acoustic waves. For these test problems Apsara produces fourth-order accurate results in case of smooth grid mappings. The order of accuracy is reduced to first-order when using the non-smooth circular grid mapping of Calhoun et al. (2008). When applying the high-order method by McCorquodale & Colella (2011) to simulations of low-Mach number flows, e.g. the Gresho vortex and the Taylor-Green vortex, we d...
Wongwathanarat, A.; Grimm-Strele, H.; Müller, E.
2016-10-01
We present a new fourth-order, finite-volume hydrodynamics code named Apsara. The code employs a high-order, finite-volume method for mapped coordinates with extensions for nonlinear hyperbolic conservation laws. Apsara can handle arbitrary structured curvilinear meshes in three spatial dimensions. The code has successfully passed several hydrodynamic test problems, including the advection of a Gaussian density profile and a nonlinear vortex and the propagation of linear acoustic waves. For these test problems, Apsara produces fourth-order accurate results in case of smooth grid mappings. The order of accuracy is reduced to first-order when using the nonsmooth circular grid mapping. When applying the high-order method to simulations of low-Mach number flows, for example, the Gresho vortex and the Taylor-Green vortex, we discover that Apsara delivers superior results to codes based on the dimensionally split, piecewise parabolic method (PPM) widely used in astrophysics. Hence, Apsara is a suitable tool for simulating highly subsonic flows in astrophysics. In the first astrophysical application, we perform implicit large eddy simulations (ILES) of anisotropic turbulence in the context of core collapse supernova (CCSN) and obtain results similar to those previously reported.
Muñoz-Cobo, José; Chiva, Sergio; El Aziz Essa, Mohamed; Mendes, Santos
2012-08-01
Two phase flow experiments with different superficial velocities of gas and water were performed in a vertical upward isothermal cocurrent air-water flow column with conditions ranging from bubbly flow, with very low void fraction, to transition flow with some cap and slug bubbles and void fractions around 25%. The superficial velocities of the liquid and the gas phases were varied from 0.5 to 3 m/s and from 0 to 0.6 m/s, respectively. Also to check the effect of changing the surface tension on the previous experiments small amounts of 1-butanol were added to the water. These amounts range from 9 to 75 ppm and change the surface tension. This study is interesting because in real cases the surface tension of the water diminishes with temperature, and with this kind of experiments we can study indirectly the effect of changing the temperature on the void fraction distribution. The following axial and radial distributions were measured in all these experiments: void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter and turbulence intensity. The range of values of the gas superficial velocities in these experiments covered the range from bubbly flow to the transition to cap/slug flow. Also with transition flow conditions we distinguish two groups of bubbles in the experiments, the small spherical bubbles and the cap/slug bubbles. Special interest was devoted to the transition region from bubbly to cap/slug flow; the goal was to understand the physical phenomena that take place during this transition A set of numerical simulations of some of these experiments for bubbly flow conditions has been performed by coupling a Lagrangian code, that tracks the three dimensional motion of the individual bubbles in cylindrical coordinates inside the field of the carrier liquid, to an Eulerian model that computes the magnitudes of continuous phase and to a 3D random walk model that takes on account the fluctuation in the velocity field of the
Petersen, T Kyle
2015-01-01
This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, ...
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Munoz-Cobo, Jose L., E-mail: jlcobos@iqn.upv.es [Instituto de Ingenieria Energetica, Universidad Politecnica de Valencia, Valencia (Spain); Chiva, Sergio [Department of Mechanical Engineering and Construction, Universitat Jaume I, Castellon (Spain); Essa, Mohamed Ali Abd El Aziz [Instituto de Ingenieria Energetica, Universidad Politecnica de Valencia, Valencia (Spain); Mendes, Santos [Facultad de Ingenieria Mecanica y Electrica, Universidad Autonoma de Nuevo Leon (Mexico)
2012-01-15
Highlights: Black-Right-Pointing-Pointer We have simulated bubbly flow in vertical pipes by coupling a Lagrangian model to an Eulerian one, and to a 3D random walk model. Black-Right-Pointing-Pointer A set of experiments in a vertical column with isothermal co-current two phase flow have been performed and used to validate the previous model. Black-Right-Pointing-Pointer We have investigated the influence of the turbulence induced by the bubbles on the results. Black-Right-Pointing-Pointer Comparison of experimental and computed results has been performed for different boundary conditions. - Abstract: A set of two phase flow experiments for different conditions ranging from bubbly flow to cap/slug flow have been performed under isothermal concurrent upward air-water flow conditions in a vertical column of 3 m height. Special attention in these experiments was devoted to the transition from bubbly to cap/slug flow. The interfacial velocity of the bubbles and the void fraction distribution was obtained using 2 and 4 sensors conductivity probes. Numerical simulations of these experiments for bubbly flow conditions were performed by coupling a Lagrangian code with an Eulerian one. The first one tracks the 3D motion of the individual bubbles in cylindrical coordinates (r, {phi}, z) inside the fluid field under the action of the following forces: buoyancy, drag, lift, wall lubrication. Also we have incorporated a 3D stochastic differential equation model to account for the random motion of the individual bubbles in the turbulent velocity field of the carrier liquid. Also we have considered the deformations undergone by the bubbles when they touch the walls of the pipe and are compressed until they rebound. The velocity and turbulence fields of the liquid phase were computed by solving the time dependent conservation equations in its Reynolds Averaged Transport Equation form (RANS). The turbulent kinetic energy k, and the dissipation rate {epsilon} transport equations
General Eulerian Numbers and Eulerian Polynomials
Directory of Open Access Journals (Sweden)
Tingyao Xiong
2013-01-01
Full Text Available We will generalize the definitions of Eulerian numbers and Eulerian polynomials to general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian numbers and polynomials to the general Eulerian polynomials and numbers.
The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows
Lufkin, Eric A.; Hawley, John F.
1993-01-01
We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.
Institute of Scientific and Technical Information of China (English)
匡翠萍; 黄静; 陈思宇; 刘曙光
2012-01-01
建立了适合河口复杂边界的二维潮流盐度数学模型.其中,网格模块是通过多元最小二乘重构的无结构三角网格；潮流模块基于消除了稳定性条件限制的半隐的欧拉-拉格朗日法,并用干湿判断法实现动边界的处理；盐度输运模块采用有限体积法进行离散,并通过用周围单元平均浓度值重构界面浓度的方法得到与连续性离散方程相协调的二阶对流扩散离散方程.通过纯对流和纯扩散数值测试对模型进行了验证,结果表明模型能够较好地模拟盐度输运的对流扩散问题,且具有较高的精度.最后,将模型应用于长江口盐水入侵的模拟计算,计算结果表明:模型计算的潮位、流速和盐度过程与实测资料一致.%A 2D numerical model to simulate tidal flow and salinity in complex estuaries is developed. The grid module is designed under unstructured triangular grid with second order accuracy by cell reconstruction using multiple least square methods to remove stability limitations associated with surface gravity wave. The circulation module is based on semi-implicit Eulerian-Lagrangian method and free from CFL condition constraint, and the wetting and drying are addressed by movable boundary techniques. The salinity module is designed in the frame-work of finite-volume method with a second-order resolution in coordination with the discreted continuity equation, through the cell face concentration reconstructed from surrounding cell averaged by complex interpolation combined with a mono-tonicity criterion. The model has been tested by a pure advection case and a pure diffusion case, which demonstrates that the model has a high accuracy. Finally, this model has been applied to simulating the saline intrusion in the Yangtze (Changjiang) River Estuary and the results show that the simulated tidal levels, velocities and salinities agree well with the measured ones.
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.
Lagrangian description of nonlinear chromatography
Institute of Scientific and Technical Information of China (English)
LIANG Heng; LIU Xiaolong
2004-01-01
Under the framework of non-equilibrium thermodynamic separation theory (NTST), Local Lagrangian approach (LLA) was proposed to deal with the essential issues of the convection and diffusion (shock waves) phenomena in nonlinear chromatography with recursion equations based on the three basic theorems, Lagrangian description, continuity axiom and local equilibrium assumption (LEA). This approach remarkably distinguished from the system of contemporary chromatographic theories (Eulerian description-partial differential equations), and can felicitously match modern cybernetics.
Directory of Open Access Journals (Sweden)
Charles Suffel
1982-01-01
Full Text Available A graph is subeulerian if it is spanned by an eulerian supergraph. Boesch, Suffel and Tindell have characterized the class of subeulerian graphs and determined the minimum number of additional lines required to make a subeulerian graph eulerian.
Ehrenborg, Richard; Readdy, Margaret
2010-01-01
The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecomposable, we determine the length of the longest interval one needs to check to verify Eulerianness. Furthermore, we show that every level Eulerian poset associated to an indecomposable matrix has even order. A condition for verifying shellability is introduced and is automated using the algebra of walks. Applying the Skolem--Mahler--Lech theorem, the ${\\bf ab}$-series of a level poset is shown to be a rational generating function in the non-commutative variables ${\\bf a}$ and ${\\bf b}$. In the case the poset is also Eulerian, the analogous result holds for the ${\\bf cd}$-series. Using coalgebraic techniques a method is developed to recognize the ${\\bf cd}$-series matrix of a level Eulerian poset.
Frei, S.; Richter, T.; Wick, T.
2016-09-01
In this work, we develop numerical schemes for mechano-chemical fluid-structure interactions with long-term effects. We investigate a model of a growing solid interacting with an incompressible fluid. A typical example for such a situation is the formation and growth of plaque in blood vessels. This application includes two particular difficulties: First, growth may lead to very large deformations, up to full clogging of the fluid domain. We derive a simplified set of equations including a fluid-structure interaction system coupled to an ODE model for plaque growth in Arbitrary Lagrangian Eulerian (ALE) coordinates and in Eulerian coordinates. The latter novel technique is capable of handling very large deformations up to contact. The second difficulty stems from the different time scales: while the dynamics of the fluid demand to resolve a scale of seconds, growth typically takes place in a range of months. We propose a temporal two-scale approach using local small-scale problems to compute an effective wall stress that will enter a long-scale problem. Our proposed techniques are substantiated with several numerical tests that include comparisons of the Eulerian and ALE approaches as well as convergence studies.
Objective Eulerian Coherent Structures
Serra, M
2015-01-01
We define objective Eulerian Coherent Structures (OECSs) in two-dimensional, non-autonomous dynamical systems as instantaneously most influential material curves. Specifically, OECSs are stationary curves of the averaged instantaneous material stretching-rate or material shearing-rate functionals. From these objective (frame-invariant) variational principles, we obtain explicit differential equations for hyperbolic, elliptic and parabolic OECSs. As illustration, we compute OECSs in an unsteady ocean velocity data set. In comparison to structures suggested by other common Eulerian diagnostic tools, we find OECSs to be the correct short-term cores of observed trajectory deformation patterns.
Numerical Analysis of Cold Spray Particles Impacting Behavior by the Eulerian Method: A Review
Li, W. Y.; Yang, K.; Yin, S.; Guo, X. P.
2016-12-01
Numerical simulations have been widely used to study particles impacting behavior in cold spraying. Among the used simulation methods, the Eulerian frame becomes increasingly attractive for its absence of mesh distortion which happens in the Lagrangian frame. It has been proved that particle deformation behaviors upon impacting calculated by the Eulerian method are well comparable to the experimental observations. In this review article, the literature on modeling particle impacting by the Eulerian method was summarized. In the second part, the Eulerian method was detailedly introduced. In the third part, the particle/substrate impacting behavior, and its influencing factors, i.e., mesh resolution, particle impacting velocity, preheating (particle or/and substrate) and oxide film, were summarized. Additionally, the prediction of critical velocity and residual stresses by using the Eulerian method was also discussed in detail. Finally, the current issues, problems and prospects existing in the Eulerian simulations of particle impacting were explored.
Numerical Analysis of Cold Spray Particles Impacting Behavior by the Eulerian Method: A Review
Li, W. Y.; Yang, K.; Yin, S.; Guo, X. P.
2016-08-01
Numerical simulations have been widely used to study particles impacting behavior in cold spraying. Among the used simulation methods, the Eulerian frame becomes increasingly attractive for its absence of mesh distortion which happens in the Lagrangian frame. It has been proved that particle deformation behaviors upon impacting calculated by the Eulerian method are well comparable to the experimental observations. In this review article, the literature on modeling particle impacting by the Eulerian method was summarized. In the second part, the Eulerian method was detailedly introduced. In the third part, the particle/substrate impacting behavior, and its influencing factors, i.e., mesh resolution, particle impacting velocity, preheating (particle or/and substrate) and oxide film, were summarized. Additionally, the prediction of critical velocity and residual stresses by using the Eulerian method was also discussed in detail. Finally, the current issues, problems and prospects existing in the Eulerian simulations of particle impacting were explored.
Institute of Scientific and Technical Information of China (English)
杨吉忠; 毕海权; 翟婉明
2009-01-01
利用有限体积法对横风作用下列车周围的空气流场进行计算.结合车辆-轨道耦合动力学,采用任意拉格朗日-欧拉(ALE)方法处理列车与空气间存在的运动边界,实现了车辆系统动力学与计算流体力学之间的结合.以某国产客运列车为例,计算列车在20 m/s的横风作用下以160 km/h的速度运行时的动力学响应,给出列车周围的流场分布;分析了考虑与不考虑风-车之间流固耦合效应时,作用在车辆上的气动力和气动力矩的变化情况.结果表明,流固耦合效应对车体摇头力矩的影响比较大,而对于车体垂向、横向位移和加速度的影响甚微.
Oger, G.; Marrone, S.; Le Touzé, D.; de Leffe, M.
2016-05-01
This paper addresses the accuracy of the weakly-compressible SPH method. Interpolation defects due to the presence of anisotropic particle structures inherent to the Lagrangian character of the Smoothed Particle Hydrodynamics (SPH) method are highlighted. To avoid the appearance of these structures which are detrimental to the quality of the simulations, a specific transport velocity is introduced and its inclusion within an Arbitrary Lagrangian Eulerian (ALE) formalism is described. Unlike most of existing particle disordering/shifting methods, this formalism avoids the formation of these anisotropic structures while a full consistency with the original Euler or Navier-Stokes equations is maintained. The gain in accuracy, convergence and numerical diffusion of this formalism is shown and discussed through its application to various challenging test cases.
Tsunami intrusion in wide meandering channels: a Lagrangian numerical experiment
Couston, L. A.; Alam, M. R.
2015-12-01
Among the many difficulties of tsunami forecast, wave runup on sloped beaches remains a major obstacle in numerical simulations. Traditional Eulerian models must adjust the fluid flow domain continuously due to the moving shorelines, which can significantly affect the computational cost and results accuracy. An efficient though uncommon alternative for accurate runup predictions still exists, consisting in using a Lagrangian model as recently shown by e.g. Couston et al. (2015) who studied the runup of landslide tsunamis in lakes with a non-dispersive Lagrangian model. Here we introduce a fully-nonlinear Boussinesq-type model derived in the Lagrangian framework to investigate various cases of long-wave runup on curved beaches and meandering channels. The governing equations are expressed in terms of curvilinear Lagrangian coordinates, making the model suitable for accurate runup computations at shorelines of arbitrary geometry while retaining the inherent simplicity of a physical model discretized on a fixed and structured grid. We implement an elliptic grid generation algorithm to map the physical space to the computational space, and a high-order finite-difference scheme for time integration. The numerical model has a linear complexity in the number of unknowns when neglecting dispersive effects. We show that the formation of edge waves due to the sloped banks of a wide channel has a significant influence on the capability of a meander or constriction in reflecting the intruding tsunami, and we investigate the effect of dispersion. Reference: Couston, L.-A., Mei, C. C., & Alam, M.-R. (2015). Landslide tsunamis in lakes. Journal of Fluid Mechanics, 772, 784-804.
The Cauchy-Lagrangian method for numerical analysis of Euler flow
Podvigina, O; Frisch, U
2015-01-01
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle, only limited spatial smoothness of the initial data. Efficient generation of high-order time-Taylor coefficients is made possible by simple recurrence relations that follow from the Cauchy invariants formulation of the Euler equations (Zheligovsky & Frisch, J. Fluid Mech. 2014, 749, 404-430). Truncated time-Taylor series of very high order allow the use of time steps vastly exceeding the Courant-Friedrichs-Lewy limit, without compromising the accuracy of the solution. Tests performed on the two-dimensional Euler equation indicate that the Cauchy-Lagrangian method is more --- and occasionally much more --- efficient and less prone to instability than Eulerian Runge-Kutta methods and less prone to rapid growth of rounding errors than the high-order Eulerian time-Taylor algor...
Lagrangian Space Nonlinear $E$-mode clustering
Yu, Hao-Ran; Zhu, Hong-Ming
2016-01-01
We study the nonlinear $E$-mode clustering in Lagrangian space by using large scale structure (LSS) $N$-body simulations and use the displacement field information in Lagrangian space to recover the primordial linear density field. We find that, compared to Eulerian nonlinear density fields, the $E$-mode displacement fields in Lagrangian space improves the cross-correlation scale $k$ with initial density field by factor of 6 $\\sim$ 7, containing 2 orders of magnitude more primordial information. This illustrates ability of potential density reconstruction algorithms, to improve the baryonic acoustic oscillation (BAO) measurements from current and future large scale structure surveys.
Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.
Holm, Darryl D.
2002-06-01
We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.
Energy Technology Data Exchange (ETDEWEB)
Chagras, V.
2004-03-15
The aim of this work is to contribute to the numerical modeling of turbulent gas-solid flows in vertical or horizontal non isothermal pipes, which can be found in many industrial processes (pneumatic transport, drying, etc). The model is based on an Eulerian-Lagrangian approach allowing a fine description of the interactions between the two phases (action of the fluid upon the particles (dispersion), action of the particles upon the fluid (two way coupling) and between particles (collisions)), more or less influential according to the characteristics of the flow. The influence of the gas phase turbulence on the particle motion is taken into account using a non-isotropic dispersion model, which allows the generation of velocity and temperature fluctuations of the fluid seen by the particles. The numerical developments brought to the model for vertical and horizontal pipe flow have been validated by comparison with available experimental results from the literature. The sensitivity tests highlight the influence of the dispersion model, collisions and turbulence modulation (direct and non direct modifications ) on the dynamic and thermal behavior of the suspension. The model is able to predict the heat exchanges in the presence of particles for a wide range of flows in vertical and horizontal pipes. However numerical problems still exist in two-way coupling for very small particles and loading ratios above one. This is related to the problems encountered when modeling the coupling terms between the two phases (parameters C{sub {epsilon}}{sub 2} and C{sub {epsilon}}{sub 3} ) involved in the turbulence dissipation balance. (author)
Institute of Scientific and Technical Information of China (English)
杜龙
2012-01-01
Along with large-scale application of composite materials in aircraft structures,a bird striking problem has become more prominent. Numerical simulations for bird striking on a composite wing leading edge were performed using ABAQUS based on Eulerian-Lagrangian method. Parametric analyses for the dynamic response of bird striking were performed with different bird velocities,densities and wing skin ply arrangements. The damage due to bird striking in the composite wing was simulated when the leading edge was filled with foam core. The destructive mechanism due to bird striking of the composite wing skin was analysed. The results gave a reference for engineering designs.%复合材料大面积用于飞机结构后,其鸟撞问题变得更加突出.利用大型通用有限元程序ABAQUS,采用耦合欧拉-拉格朗日方法(CEL)对某型无人机复合材料机翼前缘的鸟撞问题进行模拟,研究鸟体速度、密度和蒙皮铺层形式等对鸟撞动响应的影响,计算机翼前缘填充泡沫后的鸟撞损伤,对复合材料蒙皮的鸟撞破坏机理进行分析,所得结果对工程设计具有参考意义.
Nucci, M. C.; Leach, P. G. L.
2007-01-01
Searching for a Lagrangian may seem either a trivial endeavour or an impossible task. In this paper we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H Goldstein, {\\it Classical Mechanics}, 2nd edition (Addison-Wesley, Reading, 1980)] and the damped harmonic ...
Lagrangian supersymmetries depending on derivatives. Global analysis and cohomology
Giachetta, G; Sardanashvily, G
2004-01-01
Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed. In particular, the first variational formula and conservation laws for Lagrangian systems on graded manifolds using contact supersymmetries are obtained.
Lagrangian Transport Through Surfaces in Volume-Preserving Flows
Karrasch, Daniel
2015-01-01
Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The recent development of highly accurate semi-Lagrangian methods for solving scalar conservation laws and of Lagrangian approaches to coherent structures in turbulent (geophysical) fluid flows necessitate a new approach to transport from the (Lagrangian) material perspective. We present a Lagrangian framework for calculating transport of conserved quantities through a given surface in $n$-dimensional, fully aperiodic, volume-preserving flows. Our approach does not involve any dynamical assumptions on the surface or its boundary.
Lagrangian-Only Quantum Theory
Wharton, K B
2013-01-01
Despite the importance of the path integral, there have been relatively few attempts to look to the Lagrangian for a more realistic framework that might underlie quantum theory. While such realism is not available for the standard path integral or quantum field theory, a promising alternative is to only consider field histories for which the Lagrangian density is always zero. With this change, it appears possible to replace amplitudes with equally-weighted probabilities. This paper demonstrates a proof-of-principle for this approach, using a toy Lagrangian that corresponds to an arbitrary spin state. In this restricted framework one can derive both the Born rule and its limits of applicability. The fact that the Lagrangian obeys future boundary constraints also results in the first continuous, spacetime-based, hidden-variable description of a Bell-inequality-violating system.
Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data
2015-09-30
estimation based on governing equations and information theory is one of the critical motivation for our effort. Our aim is not to shy away from the...Transfer Learning for Ocean Modeling (N00014-11-1-0337) benefits from the test cases we develop for the present study. STUDENT SUPPORTED: This project...supported one graduate student . A summer visiting student from India, A. Gupta, contributed to the project for a second summer. Mr. Matt Swezey - LT
Assimilation of drifter observations for the reconstruction of eulerian circulation field.
Molcard, A.; Ozgokmen, T.; Piterbarg, L.; Griffa, A.
2003-04-01
In light of the increasing number of drifting buoys in the ocean, and recent advances in the realism of ocean general circulation models toward oceanic forecasting, the problem of assimilation of Lagrangian observations data in Eulerian models is investigated. A new and general rigorous approach is developed based on optimal interpolation methods, which takes into account directly the Lagrangian nature of the observations. An idealized version of this general formulation is tested in the framework of identical twin-experiments using a reduced-gravity, quasi-geostrophic model. An extensive study is conducted to quantify the effectiveness of Lagrangian data assimilation as a function of the number of drifters, the frequency of assimilation and uncertainties associated with the forcing functions driving the ocean model. The performance of the Lagrangian assimilation technique is also compared to that of conventional methods of assimilating drifters as moving current meters, and assimilation of Eulerian data, such as fixed-point velocities. Overall the results are very favorable for the assimilation of Lagrangian observations to improve the Eulerian velocity field in ocean models. The results of our assimilation twin experiments imply an optimal sampling frequency for oceanic Lagrangian instruments in the range of 20-50% of the Lagrangian integral time scale of the flow field. The method is extended to primitive equation ocean models by using a dynamical relationship between velocity components and layer thickness based on geostrophy. The method is implemented in an idealized MICOM of midlatitude circulation, and performances of three different techniques, Pseudo-Lagrangian OI, Lagrangian OI and Pseudo-Lagrangian Kalman Filter (based on Chin et al., 1999) are compared using a comprehensive set of experiments. The main finding of this study is that two different strategies of data assimilation are simultaneously supported: (i) the strategy of adopting well
Comparison of Joint Modeling Approaches Including Eulerian Sliding Interfaces
Energy Technology Data Exchange (ETDEWEB)
Lomov, I; Antoun, T; Vorobiev, O
2009-12-16
Accurate representation of discontinuities such as joints and faults is a key ingredient for high fidelity modeling of shock propagation in geologic media. The following study was done to improve treatment of discontinuities (joints) in the Eulerian hydrocode GEODYN (Lomov and Liu 2005). Lagrangian methods with conforming meshes and explicit inclusion of joints in the geologic model are well suited for such an analysis. Unfortunately, current meshing tools are unable to automatically generate adequate hexahedral meshes for large numbers of irregular polyhedra. Another concern is that joint stiffness in such explicit computations requires significantly reduced time steps, with negative implications for both the efficiency and quality of the numerical solution. An alternative approach is to use non-conforming meshes and embed joint information into regular computational elements. However, once slip displacement on the joints become comparable to the zone size, Lagrangian (even non-conforming) meshes could suffer from tangling and decreased time step problems. The use of non-conforming meshes in an Eulerian solver may alleviate these difficulties and provide a viable numerical approach for modeling the effects of faults on the dynamic response of geologic materials. We studied shock propagation in jointed/faulted media using a Lagrangian and two Eulerian approaches. To investigate the accuracy of this joint treatment the GEODYN calculations have been compared with results from the Lagrangian code GEODYN-L which uses an explicit treatment of joints via common plane contact. We explore two approaches to joint treatment in the code, one for joints with finite thickness and the other for tight joints. In all cases the sliding interfaces are tracked explicitly without homogenization or blending the joint and block response into an average response. In general, rock joints will introduce an increase in normal compliance in addition to a reduction in shear strength. In the
Generalized Superfield Lagrangian Quantization
Lavrov, P M; Moshin, P Y
2002-01-01
We consider an extension of the gauge-fixing procedure in the framework of the Lagrangian superfield BRST and BRST-antiBRST quantization schemes for arbitrary gauge theories, taking into account the possible ambiguity in the choice of the superfield antibracket. We show that this ambiguity is fixed by the algebraic properties of the antibracket and the form of the BRST and antiBRST transformations, realized in terms of superspace translations. The Ward identities related to the generalized gauge-fixing procedure are obtained.
Nucci, M. C.; Leach, P. G. L.
2007-12-01
Searching for a Lagrangian may seem either a trivial endeavor or an impossible task. In this paper, we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H. Goldstein, Classical Mechanics, 2nd edition (Addison-Wesley, Reading, MA, 1980)], and the damped harmonic oscillator. This is the first paper in a series dedicated to this subject.
Continuous Time Random Walks for the Evolution of Lagrangian Velocities
Dentz, Marco; Comolli, Alessandro; Borgne, Tanguy Le; Lester, Daniel R
2016-01-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have non-stationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and non-stationary conditions. We provide explicit expressions for the Lagrangian velocity statistics, and determine the behaviors of...
Plasma transport in an Eulerian AMR code
Vold, E. L.; Rauenzahn, R. M.; Aldrich, C. H.; Molvig, K.; Simakov, A. N.; Haines, B. M.
2017-04-01
A plasma transport model has been implemented in an Eulerian AMR radiation-hydrodynamics code, xRage, which includes plasma viscosity in the momentum tensor, viscous dissipation in the energy equations, and binary species mixing with consistent species mass and energy fluxes driven by concentration gradients, ion and electron baro-diffusion terms and temperature gradient forces. The physics basis, computational issues, numeric options, and results from several test problems are discussed. The transport coefficients are found to be relatively insensitive to the kinetic correction factors when the concentrations are expressed with the molar fractions and the ion mass differences are large. The contributions to flow dynamics from plasma viscosity and mass diffusion were found to increase significantly as scale lengths decrease in an inertial confinement fusion relevant Kelvin-Helmholtz instability mix layer. The mixing scale lengths in the test case are on the order of 100 μm and smaller for viscous effects to appear and 10 μm or less for significant ion species diffusion, evident over durations on the order of nanoseconds. The temperature gradient driven mass flux is seen to deplete a high Z tracer ion at the ion shock front. The plasma transport model provides the generation of the atomic mix per unit of interfacial area between two species with no free parameters. The evolution of the total atomic mix then depends also on an accurate resolution or estimate of the interfacial area between the species mixing by plasma transport. High resolution simulations or a more Lagrangian-like treatment of species interfaces may be required to distinguish plasma transport and numerical diffusion in an Eulerian computation of complex and dynamically evolving mix regions.
Prospects for Eulerian CFD analysis of helicopter vortex flows
Drela, Mark; Murman, Earll M.
1987-01-01
The applicability of current finite-volume CFD algorithms based on the Euler equations to the vortex flow over a helicopter in forward flight is investigated analytically. The general characteristics of the flow are reviewed; existing Euler, Navier-Stokes, perturbation, high-order, and adaptive methods are briefly characterized; and a novel Eulerian/Lagrangian approach with entropy and vorticity corrections is presented in detail. Numerical results for simple convection of a finite-core Lamb vortex moving downstream with its axis perpendicular to the flow are presented in graphs, and the possibility of extending the method to three-dimensional, viscous, and shock flows is discussed.
Estimating Eulerian spectra from pairs of drifters
LaCasce, Joe
2017-04-01
GPS-tracked surface drifters offer the possibility of sampling energetic variations at the ocean surface on scales of only 10s of meters, much less than that resolved by satellite. Here we investigate whether velocity differences between pairs of drifters can be used to estimate kinetic energy spectra. Theoretical relations between the spectrum and the second-order longitudinal structure function for 2D non-divergent flow are derived. The structure function is a natural statistic for particle pairs and is easily calculated. However it integrates contributions across wavenumber, and this tends to obscure the spectral dependencies when turbulent inertial ranges are of finite extent. Nevertheless, the transform from spectrum to structure function is robust, as illustrated with Eulerian data collected from aircraft. The inverse transform, from structure function to spectrum, is much less robust, yielding poor results in particular at large wavenumbers. This occurs because the transform involves a filter function which magnifies contributions from large pair separations, which tend to be noisy. Fitting the structure function to a polynomial improves the spectral estimate, but not sufficiently to distinguish correct inertial range dependencies. Thus with Lagrangian data, it is appears preferable to focus on structure functions, despite their shortcomings.
Estimating Eulerian Energy Spectra from Drifters
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J. H. LaCasce
2016-10-01
Full Text Available The relations between the kinetic energy spectrum and the second-order longitudinal structure function for 2D non-divergent flow are derived, and several examples are considered. The transform from spectrum to structure function is illustrated using idealized power-law spectra of turbulent inertial ranges. The results illustrate how the structure function integrates contributions across wavenumber, which can obscure the dependencies when the inertial ranges are of finite extent. The transform is also applied to the kinetic energy spectrum of Nastrom and Gage (1985, derived from aircraft data in the upper troposphere; the resulting structure function agrees well with that of Lindborg (1999, calculated with the same data. The transform from structure function to spectrum is then tested with data from 2D turbulence simulations. When applied to the (Eulerian structure function obtained from the transform of the spectrum, the result closely resembles the original spectrum, except at the largest wavenumbers. The deviation at large wavenumbers occurs because the transform involves a filter function which magnifies contributions from large separations. The results are noticeably worse when applied to the structure function obtained from pairs of particles in the flow, as this is usually noisy at large separations. Fitting the structure function to a polynomial improves the resulting spectrum, but not sufficiently to distinguish the correct inertial range dependencies. Furthermore, the transform of steep (non-local spectra is largely unsuccessful. Thus, it appears that with Lagrangian data, it is probably preferable to focus on structure functions, despite their shortcomings.
Eulerian Formulation of Spatially Constrained Elastic Rods
Huynen, Alexandre
Slender elastic rods are ubiquitous in nature and technology. For a vast majority of applications, the rod deflection is restricted by an external constraint and a significant part of the elastic body is in contact with a stiff constraining surface. The research work presented in this doctoral dissertation formulates a computational model for the solution of elastic rods constrained inside or around frictionless tube-like surfaces. The segmentation strategy adopted to cope with this complex class of problems consists in sequencing the global problem into, comparatively simpler, elementary problems either in continuous contact with the constraint or contact-free between their extremities. Within the conventional Lagrangian formulation of elastic rods, this approach is however associated with two major drawbacks. First, the boundary conditions specifying the locations of the rod centerline at both extremities of each elementary problem lead to the establishment of isoperimetric constraints, i.e., integral constraints on the unknown length of the rod. Second, the assessment of the unilateral contact condition requires, in principle, the comparison of two curves parametrized by distinct curvilinear coordinates, viz. the rod centerline and the constraint axis. Both conspire to burden the computations associated with the method. To streamline the solution along the elementary problems and rationalize the assessment of the unilateral contact condition, the rod governing equations are reformulated within the Eulerian framework of the constraint. The methodical exploration of both types of elementary problems leads to specific formulations of the rod governing equations that stress the profound connection between the mechanics of the rod and the geometry of the constraint surface. The proposed Eulerian reformulation, which restates the rod local equilibrium in terms of the curvilinear coordinate associated with the constraint axis, describes the rod deformed configuration
Combinatorial Interpretation of General Eulerian Numbers
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Tingyao Xiong
2014-01-01
Full Text Available Since the 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and q-Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on general arithmetic progressions a,a+d,a+2d,….
A cavitation model based on Eulerian stochastic fields
Magagnato, F.; Dumond, J.
2013-12-01
Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Multi-Scale Analysis of Lagrangian Properties of Turbulence
Wilczek, Michael; Lalescu, Cristian
2016-11-01
Turbulence is a multi-scale problem in space and time with a broad range of strongly interacting degrees of freedom. Lagrangian tracer particles advected with the flow sample this spatio-temporal complexity. This naturally leads to the question of how Lagrangian properties are affected by the scales of turbulence. We attempt to answer this question numerically and theoretically adopting a coarse-graining approach. In an extensive DNS (direct numerical simulation) study, we track tracer particles advected by spatially coarse-grained velocity fields. This allows to distinguish the impact of large-scale sweeping effects and small-scale intermittency on Lagrangian aspects of turbulence. In this presentation we will present results on Lagrangian particle dispersion and velocity fluctuations for various coarse-graining scales. The results will furthermore be discussed in the context of Eulerian-Lagrangian bridging relations.
Lakshminarayanan, Vasudevan; Thyagarajan, K
2002-01-01
Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Many features oflight propagation can be analyzed in terms ofrays,ofcourse, subtle effects near foci, caustics or turning points would need an analysis based on the wave natureoflight. Allofgeometric optics can be derived from Fermat's principle which is an extremum principle. The counterpart in classical mechanics is of course Hamilton's principle. There is a very close analogy between mechanics ofparticles and optics oflight rays. Much insight (and useful results) can be obtained by analyzing these analogies. Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, 1956), classical mechanics is only a geometrical optics approximation to a wave theory! In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of ray propagation through various media. Given the ...
Lagrangian Quantum Homology for Lagrangian cobordism
Singer, Berit
2015-01-01
We extend the definition of Lagrangian quantum homology to monotone Lagrangian cobordism and establish its general algebraic properties. In particular we develop a relative version of Lagrangian quantum homology associated to a cobordism relative to a part of its boundary and study relations of this invariant to the ambient quantum homology.
Estimation of the Lagrangian structure function constant ¤C¤_{0} from surface-layer wind data
DEFF Research Database (Denmark)
Anfossi, D.; Degrazia, G.; Ferrero, E.
2000-01-01
Eulerian turbulence observations, made in the surface layer under unstable conditions (z/L > 0), by a sonic anemometer were used to estimate the Lagrangian structure function constant C(0). Two methods were considered. The first one makes use of a relationship, widely used in the Lagrangian stoch...
Lagrangian 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.
On Making Directed Graphs Eulerian
Sorge, Manuel
2011-01-01
A directed graph is called Eulerian, if it contains a walk that traverses every arc in the graph exactly once. We study the problem of Eulerian Extension (EE) where a directed multigraph G and a weight function is given and it is asked whether G can be made Eulerian by adding arcs whose total weight does not exceed a given threshold. This problem is motivated through applications in vehicle routing and flowshop scheduling. However, EE is NP- hard and thus we use the parameterized complexity framework to analyze it. In parameterized complexity, the running time of algorithms is considered not only with respect to input length, but also with respect to other properties of the input-called "parameters". Dorn et al. proved that EE can be solved in O(4^k n^4) time, where k denotes the parameter "number of arcs that have to be added". In this thesis, we analyze EE with respect to the (smaller) parameters "number c of connected components in the input graph" and "sum b over indeg(v) - outdeg(v) for all vertices v in...
Energy Technology Data Exchange (ETDEWEB)
Kaufmann, A.
2004-03-15
Particle laden flows occur in industrial applications ranging from droplets in gas turbines to fluidized bed in chemical industry. Prediction of the dispersed phase properties such as concentration and dynamics are crucial for the design of more efficient devices that meet the new pollutant regulations of the European community. Numerical simulation coupling Lagrangian tracking of discrete particles with DNS or LES of the carrier phase provide a well established powerful tool to investigate particle laden flows. Such numerical methods have the drawback of being numerically very expensive for practical applications. Numerical simulations based on separate Eulerian balance equations for both phases, coupled through inter-phase exchange terms might be an effective alternative approach. This approach has been validated for the case of tracer particles with very low inertia that follow the carrier phase almost instantaneously due to their small response time compared with the micro-scale time scales of the carrier phase. Objective of this thesis is to extend this approach to more inertial particles that occur in practical applications such as fuel droplets in gas turbine combustors. Existing results suggest a separation of the dispersed phase velocity into a correlated and an uncorrelated component. The energy related to the uncorrelated component is about 30% of the total particle kinetic energy when the particle relaxation time is comparable to the Lagrangian integral time scale. The presence of this uncorrelated motion leads to stress terms in the Eulerian balance equation for the particle momentum. Models for this stress terms are proposed and tested. Numerical simulations in the Eulerian framework are validated by comparison with simulations using Lagrangian particle tracking. Additionally coupling of the Eulerian transport equations for the particles to combustion models is tested. (author)
Thermomechanical Simulation of Wear and Hot Bands in a Disc Brake by Adopting an Eulerian Approach
Rashid, Asim; Strömberg, Niclas
2013-01-01
In this paper frictional heating of a disc brake is simulated while taking wear into account. By performing thermomechanical finite element analysis, it is studied how the wear history will influence the development of hot bands. The frictional heat analysis is based on an Eulerian formulation of the disc, which requires significantly lower computational time as compared to a standard Lagrangian approach. A real disc-pad system to a heavy truck is considered, where complete three-dimensional ...
CSQII: a two-dimensional Eulerian code for computation of material motion in two dimensions
Energy Technology Data Exchange (ETDEWEB)
McGlaun, J M; Thompson, S L
1980-01-01
CSQII is a general-purpose code with a wide variety of options: rectangular or cylindrical coordinates, up to ten materials, allowance for void, elestic-plastic or distended material, inclusion of energy sources or gravity. The basic solution scheme integrates the Lagrangian form of the conservation equations through a time step and then explicity rezones back to the Eulerian grid. The following aspects are treated in some detail: equation of state, momentum balance, energy balance, rezoning, and radiation. (RWR)
Directory of Open Access Journals (Sweden)
Stephen Phillips
2013-09-01
Full Text Available States have international obligations to ensure that all deprivations of an individual’s liberty are consistent with international human rights law. The majority of provisions in the international human rights law instruments that deal with such deprivations of liberty contain the term ‘arbitrary’, yet there is no clear definition of what this entails. Arbitrariness is defined differently by different supervisory bodies in different cases, and in different contexts; understanding it requires awareness of the different factors affecting how individual deprivations of liberty are examined and understood.A longer version of this article can be found at:http://tinyurl.com/HRD-arbitrary-August2013
Lagrangian properties at the ocean submesoscales in presence of riverine outflows
Bracco, Annalisa; Choi, Jun
2017-04-01
A set of numerical simulations are used to characterize the impact of submesoscale circulations on surface Lagrangian statistics in the northern Gulf of Mexico over two months, February and August, representative of winter and summer. Whenever submesoscale circulations are resolved, the probability density functions (PDFs) of dynamical quantities such as vorticity and horizontal velocity divergence for Eulerian and Lagrangian fields differ, with particles preferentially mapping areas of elevated negative divergence and positive vorticity. The stronger are the submesoscale circulations the more skewed are the Lagrangian distributions and greater is the difference between Eulerian and Lagrangian PDFs. In winter Lagrangian distributions are modestly impacted by the presence of the riverine outflow, while increasing the model resolution from submesoscale permitting to submesoscale resolving has a more profound impact. In summer the presence of riverine induced buoyancy gradients is key to the development of submesoscale circulations and different Eulerian and Lagrangian PDFs. Finite Size Lyapunov Exponents (FSLEs) are used to characterize mixing rates. Whenever submesoscale circulations are resolved and riverine outflow is included, FSLEs slopes are broadly consistent with local stirring. Simulated slopes are close to -0.5 and support a velocity field where the ageostrophic and frontogenetic components are key to mixing for scales comprised between about 5-7 times the model resolution and 100 km. The robustness of Lagrangian statistics is further discussed in terms of their spatial and temporal variability, and of the number of particles used.
Simultaneous temperature and velocity Lagrangian measurements in turbulent thermal convection
Liot, O; Zonta, F; Chibbaro, S; Coudarchet, T; Gasteuil, Y; Pinton, J -F; Salort, J; Chillà, F
2015-01-01
We report joint Lagrangian velocity and temperature measurements in turbulent thermal convection. Measurements are performed using an improved version (extended autonomy) of the neutrally-buoyant instrumented particle that was used by to performed experiments in a parallelepipedic Rayleigh-Benard cell. The temperature signal is obtained from a RFtransmitter. Simultaneously, we determine particle's position and velocity with one camera, which grants access to the Lagrangian heat flux. Due to the extended autonomy of the present particle, we obtain well converged temperature and velocity statistics, as well as pseudo-eulerian maps of velocity and heat flux. Present experimental results have also been compared with the results obtained by a corresponding campaign of Direct Numerical Simulations and Lagrangian Tracking of massless tracers. The comparison between experimental and numerical results show the accuracy and reliability of our experimental measurements. Finally, the analysis of lagrangian velocity and t...
Relativistic Lagrangians for the Lorentz–Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Deguchi, Shinichi, E-mail: deguchi@phys.cst.nihon-u.ac.jp [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan); Nakano, Kunihiko [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan); Suzuki, Takafumi [Junior College Funabashi Campus, Nihon University, Narashinodai, Funabashi, Chiba 274-8501 (Japan)
2015-09-15
We present two types of relativistic Lagrangians for the Lorentz–Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz–Dirac equation with a source-like term.
Multi-symplectic, Lagrangian, one-dimensional gas dynamics
Webb, G. M.
2015-05-01
The equations of Lagrangian, ideal, one-dimensional, compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate m and time t as independent variables, and in which the Eulerian position of the fluid element x = x(m, t) is one of the dependent variables. This approach differs from the Eulerian, multi-symplectic approach using Clebsch variables. Lagrangian constraints are used to specify equations for xm, xt, and St consistent with the Lagrangian map, where S is the entropy of the gas. We require St = 0 corresponding to advection of the entropy S with the flow. We show that the Lagrangian Hamiltonian equations are related to the de Donder-Weyl multi-momentum formulation. The pullback conservation laws and the symplecticity conservation laws are discussed. The pullback conservation laws correspond to invariance of the action with respect to translations in time (energy conservation) and translations in m in Noether's theorem. The conservation law due to m-translation invariance gives rise to a novel nonlocal conservation law involving the Clebsch variable r used to impose ∂S(m, t)/∂t = 0. Translation invariance with respect to x in Noether's theorem is associated with momentum conservation. We obtain the Cartan-Poincaré form for the system, and use it to obtain a closed ideal of two-forms representing the equation system.
Eulerian BAO Reconstructions and N-Point Statistics
Schmittfull, Marcel; Beutler, Florian; Sherwin, Blake; Chu, Man Yat
2015-01-01
As galaxy surveys begin to measure the imprint of baryonic acoustic oscillations (BAO) on large-scale structure at the sub-percent level, reconstruction techniques that reduce the contamination from nonlinear clustering become increasingly important. Inverting the nonlinear continuity equation, we propose an Eulerian growth-shift reconstruction algorithm that does not require the displacement of any objects, which is needed for the standard Lagrangian BAO reconstruction algorithm. In our simulations, the algorithm yields 95% of the BAO signal-to-noise obtained from standard reconstruction. The reconstructed power spectrum is obtained by adding specific simple 3- and 4-point statistics to the pre-reconstruction power spectrum, making it very transparent how additional BAO information from higher-point statistics is included in the power spectrum through the reconstruction process. Analytical models of the reconstructed density for the two algorithms agree at second order. Based on similar modeling efforts, we ...
Lagrangian model for oil spill diffusion at sea
Energy Technology Data Exchange (ETDEWEB)
Lonin, Serguei A. [Centro de Investigaciones Oceanograficas e Hidrograficas, Escuela Naval, Cartagena de Indias (Colombia)
1999-07-01
The Eulerian and Lagrangian methods for oil spill simulations are discussed. A mathematical description of the vertical movement of an oil droplet in the ocean is proposed based on the Langeven equation and the analytical test results are presented to compare the results. The results are that the buoyant effect and the vertical turbulent variations are very important mechanisms for vertical movement of oil in the water column. (Author)
Potentials of Arbitrary Forces with Fractional Derivatives
Rabei, Eqab M.; Alhalholy, Tareq S.; Rousan, Akram
The Laplace transform of fractional integrals and fractional derivatives is used to develop a general formula for determining the potentials of arbitrary forces: conservative and nonconservative in order to introduce dissipative effects (such as friction) into Lagrangian and Hamiltonian mechanics. The results are found to be in exact agreement with Riewe's results of special cases. Illustrative examples are given.
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.
Forecasting for a Lagrangian aircraft campaign
Directory of Open Access Journals (Sweden)
A. Stohl
2004-05-01
Full Text Available A forecast system has been developed in preparation for an upcoming aircraft measurement campaign, where the same air parcels polluted by emissions over North America shall be sampled repeatedly as they leave the continent, during transport over the Atlantic, and upon their arrival over Europe. This paper describes the model system in advance of the campaign, in order to make the flight planners familiar with the novel model output. The aim of a Lagrangian strategy is to infer changes in the chemical composition and aerosol distribution occurring en route by measured upwind/downwind differences. However, guiding aircraft repeatedly into the same polluted air parcels requires careful forecasting, for which no suitable model system exists to date. This paper describes a procedure using both Eulerian-type (i.e. concentration fields and Lagrangian-type (i.e. trajectories model output from the Lagrangian particle dispersion model FLEXPART to predict the best opportunities for a Lagrangian experiment. The best opportunities are defined as being highly polluted air parcels which receive little or no emission input after the first measurement, which experience relatively little mixing, and which are reachable by as many aircraft as possible. For validation the system was applied to the period of the NARE 97 campaign where approximately the same air masses were sampled on different flights. Measured upwind/downwind differences in carbon monoxide (CO and ozone (O_{3} decreased significantly as the threshold values used for accepting cases as Lagrangian were tightened. This proves that the model system can successfully identify Lagrangian opportunities.
Parallel algorithms for semi-lagrangian advection
Malevsky, A. V.; Thomas, S. J.
1997-08-01
Numerical time step limitations associated with the explicit treatment of advection-dominated problems in computational fluid dynamics are often relaxed by employing Eulerian-Lagrangian methods. These are also known as semi-Lagrangian methods in the atmospheric sciences. Such methods involve backward time integration of a characteristic equation to find the departure point of a fluid particle arriving at a Eulerian grid point. The value of the advected field at the departure point is obtained by interpolation. Both the trajectory integration and repeated interpolation influence accuracy. We compare the accuracy and performance of interpolation schemes based on piecewise cubic polynomials and cubic B-splines in the context of a distributed memory, parallel computing environment. The computational cost and interprocessor communication requirements for both methods are reported. Spline interpolation has better conservation properties but requires the solution of a global linear system, initially appearing to hinder a distributed memory implementation. The proposed parallel algorithm for multidimensional spline interpolation has almost the same communication overhead as local piecewise polynomial interpolation. We also compare various techniques for tracking trajectories given different values for the Courant number. Large Courant numbers require a high-order ODE solver involving multiple interpolations of the velocity field.
Maxwell-like Lagrangians for higher spins
Campoleoni, Andrea
2012-01-01
We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless fields produce single-particle actions, while whenever trace constraints can be dispensed with the resulting Lagrangians display the same reducible, multi-particle spectra as those emerging from the tensionless limit of free open-string field theory. For all explored options the corresponding kinetic operators take essentially the same form as in the spin-one, Maxwell case.
Marom, Gil; Bluestein, Danny
2016-01-01
This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using Lagrangian methods with Eulerian computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and ti...
On Eulerian constitutive equations for modeling growth and residual stresses in arteries.
Volokh, K Y
2005-06-01
Recently Volokh and Lev (2005) argued that residual stresses could appear in growing arteries because of the arterial anisotropy. This conclusion emerged from a continuum mechanics theory of growth of soft biological tissues proposed by the authors. This theory included Lagrangian constitutive equations, which were formulated directly with respect to the reference configuration. Alternatively, it is possible to formulate Eulerian constitutive equations with respect to the current configuration and to 'pull them back' to the reference configuration. Such possibility is examined in the present work. The Eulerian formulation of the constitutive equations is used for a study of arterial growth. It is shown, particularly, that bending resultants are developed in the ring cross-section of the artery. These resultants may cause the ring opening or closing after cutting the artery in vitro as it is observed in experiments. It is remarkable that the results of the present study, based on the Eulerian constitutive equations, are very similar to the results of Volokh and Lev (2005), based on the Lagrangian constitutive equations. This strengthens the authors' argument that anisotropy is a possible reason for accumulation of residual stresses in arteries. This argument appears to be invariant with respect to the mathematical description.
Fox, Rodney O.; Vie, Aymeric; Laurent, Frederique; Chalons, Christophe; Massot, Marc
2012-11-01
Numerous applications involve a disperse phase carried by a gaseous flow. To simulate such flows, one can resort to a number density function (NDF) governed a kinetic equation. Traditionally, Lagrangian Monte-Carlo methods are used to solve for the NDF, but are expensive as the number of numerical particles needed must be large to control statistical errors. Moreover, such methods are not well adapted to high-performance computing because of the intrinsic inhomogeneity of the NDF. To overcome these issues, Eulerian methods can be used to solve for the moments of the NDF resulting in an unclosed Eulerian system of hyperbolic conservation laws. To obtain closure, in this work a multivariate bi-Gaussian quadrature is used, which can account for particle trajectory crossing (PTC) over a large range of Stokes numbers. This closure uses up to four quadrature points in 2-D velocity phase space to capture large-scale PTC, and an anisotropic Gaussian distribution around each quadrature point to model small-scale PTC. Simulations of 2-D particle-laden isotropic turbulence at different Stokes numbers are employed to validate the Eulerian models against results from the Lagrangian approach. Good agreement is found for the number density fields over the entire range of Stokes numbers tested. Research carried out at the Center for Turbulence Research 2012 Summer Program.
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
Institute of Scientific and Technical Information of China (English)
Zhou Qi
2012-01-01
To a large degree,language is arbitrary. But there are exceptions to prove that language is not always arbitrary. However,non-arbitrariness is itself inevitably arbitrary. In fact,arbitrariness and non-arbitrariness work together to complete a language. It seems that they contradict to each other, but they actually coexist as a whole in the same unity.
Introduction to Focus Issue: Lagrangian Coherent Structures.
Peacock, Thomas; Dabiri, John
2010-03-01
The topic of Lagrangian coherent structures (LCS) has been a rapidly growing area of research in nonlinear dynamics for almost a decade. It provides a means to rigorously define and detect transport barriers in dynamical systems with arbitrary time dependence and has a wealth of applications, particularly to fluid flow problems. Here, we give a short introduction to the topic of LCS and review the new work presented in this Focus Issue.
DEFF Research Database (Denmark)
Pang, Kar Mun; Jangi, Mehdi; Bai, X.-S.
generated similar results. The principal motivation for ESF compared to Lagrangian particle based PDF is the relative ease of implementation of the former into Eulerian computational fluid dynamics(CFD) codes [5]. Several works have attempted to implement the ESF model for the simulations of diesel spray...... temperature combustion regimes, are used. The associated ambient conditions and injection characteristics are provided in Table 1....
Ishizaka, Joji
1990-01-01
Surface phytoplankton biomass of the southeastern U.S. continental shelf area is discussed based on coastal zone color scanner (CZCS) images obtained in April 1980. Data of chlorophyll distributions are analyzed in conjunction with concurrent flow and temperature fields. Lagrangian particle tracing experiments show that the particles move consistently with the evolution of the chlorophyll patterns. A four-component physical-biological model for a horizontal plane at a nominal depth of 17 m is presented. Model simulations using various physical-biological dynamics and boundary conditions show that the variability of chlorophyll distributions is controlled by horizontal advection. Phytoplankton and nutrient fluxes, calculated using the model, show considerable variability with time. The chlorophyll distributions obtained from the CZCS images are assimilated into the model to improve the phytoplankton flux estimates.
Eulerian formulation of elastic rods
Huynen, Alexandre; Detournay, Emmanuel; Denoël, Vincent
2016-06-01
In numerous biological, medical and engineering applications, elastic rods are constrained to deform inside or around tube-like surfaces. To solve efficiently this class of problems, the equations governing the deflection of elastic rods are reformulated within the Eulerian framework of this generic tubular constraint defined as a perfectly stiff normal ringed surface. This reformulation hinges on describing the rod-deformed configuration by means of its relative position with respect to a reference curve, defined as the axis or spine curve of the constraint, and on restating the rod local equilibrium in terms of the curvilinear coordinate parametrizing this curve. Associated with a segmentation strategy, which partitions the global problem into a sequence of rod segments either in continuous contact with the constraint or free of contact (except for their extremities), this re-parametrization not only trivializes the detection of new contacts but also transforms these free boundary problems into classic two-points boundary-value problems and suppresses the isoperimetric constraints resulting from the imposition of the rod position at the extremities of each rod segment.
Improvements to SOIL: An Eulerian hydrodynamics code
Energy Technology Data Exchange (ETDEWEB)
Davis, C.G.
1988-04-01
Possible improvements to SOIL, an Eulerian hydrodynamics code that can do coupled radiation diffusion and strength of materials, are presented in this report. Our research is based on the inspection of other Eulerian codes and theoretical reports on hydrodynamics. Several conclusions from the present study suggest that some improvements are in order, such as second-order advection, adaptive meshes, and speedup of the code by vectorization and/or multitasking. 29 refs., 2 figs.
Tracing the Cosmic Web substructure with Lagrangian submanifold
Shandarin, Sergei F
2014-01-01
A new computational paradigm for the analysis of substructure of the Cosmic Web in cosmological cold dark matter simulations is proposed. We introduce a new data-field --- the flip-flop field ---which carries wealth of information about the history and dynamics of the structure formation in the universe. The flip-flop field is an ordered data set in Lagrangian space representing the number of turns inside out sign reversals of an elementary volume of each collisionless fluid element represented by a computational particle in a N-body simulation. This field is computed using the Lagrangian submanifold, i.e. the three-dimensional dark matter sheet in the six-dimensional space formed by three Lagrangian and three Eulerian coordinates of the simulation particles. It is demonstrated that the very rich substructure of dark matter haloes and the void regions can be reliably and unambiguously recovered from the flip-flop field.
Predicting chaotic dispersion with Eulerian symmetry measures: Wavy Taylor-vortex flow
King, G. P.; Rowlands, G.; Rudman, Murray; Yannacopoulos, A. N.
2001-09-01
In a recent investigation of particle transport in numerically computed wavy Taylor-vortex flow, Rudman estimated an effective axial diffusion coefficient, Dz, to characterize the enhanced mixing due to chaotic advection [AIChE J. 44, 1015 (1998)]. We find that Dz is proportional to the product of two measures of symmetry deviation. The first is a measure of the average deviation of the flow from rotational symmetry, and the second is a measure of the average deviation from flexion-free flow (a flow where the curl of the vorticity is zero). Because these quantities are obtained directly from the velocity field, we call them Eulerian symmetry measures. Thus, we show that the macroscopic transport behavior in a flow can be quantified directly in terms of the velocity field and its gradients, and hence provides a connection between Eulerian and Lagrangian pictures of transport—a problem of fundamental and widespread interest.
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.
Lagrangian Hydrocode Simulations of Tsunamigenic, Subaerial Landslides
Schwaiger, H. F.; Parsons, J.; Higman, B.
2006-12-01
The interaction of debris flows, both subaqueous and subaerial, with bodies of water can produce tsunamis with a locally devastating impact. When debris flows begin above the water surface, the impact can produce a large air cavity, significantly increasing the effective volume of water displaced and complicating efforts to model the resulting tsunami. Because grid-based, Eulerian numerical methods have an inherent difficulty tracking material boundaries, we have implemented a particle-based, Lagrangian model (Smoothed Particle Hydrodynamics). The use of a particle model removes the common numerical difficulties associated with large deformation, multi-phase flows such as the numerical diffusion of material boundaries. We treat the debris flow as an incompressible, viscous fluid and the body of water as inviscid. Other rheologies of the debris flow (Mohr-Coulomb or Bingham plastic) can be included through the use of a non-linear viscosity. We apply this model to study the 1958 Lituya Bay landslide and resulting tsunami. Our simulation results compare favorably with field observations as well as a scaled laboratory experiment and a numerical study using an AMR Eulerian compressible fluid model.
Metriplectic Algebra for Dissipative Fluids in Lagrangian Formulation
Materassi, Massimo F D
2014-01-01
It is known that the dynamics of dissipative fluids in Eulerian variables can be derived from an algebra of Leibniz brackets of observables, the metriplectic algebra, that extends the Poisson algebra of the zero viscosity limit via a symmetric, semidefinite component. This metric bracket generates dissipative forces. The metriplectic algebra includes the conserved total Hamiltonian $H$, generating the non-dissipative part of dynamics, and the entropy $S$ of those microscopic degrees of freedom draining energy irreversibly, that generates dissipation. This $S$ is a Casimir of the Poisson algebra to which the metriplectic algebra reduces in the frictionless limit. In the present paper, the metriplectic framework for viscous fluids is re-written in the Lagrangian Formulation, where the system is described through material variables: this is a way to describe the continuum much closer to the discrete system dynamics than the Eulerian fields. Accordingly, the full metriplectic algebra is constructed in material va...
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.
COUNTING ROOTED NEAR-4-REGULAR EULERIAN MAPS ON SOME SURFACES
Institute of Scientific and Technical Information of China (English)
RenHan; LiuYanpei
1999-01-01
In this article the rooted planar near-4-regular Eulerian trails are enumerated and an explicit formula for such maps is presented. Further, the rooted near-4-regular Eulerian maps on the torus are counted in an exact way.
NUMERICAL SIMULATION OF WET STEAM CONDENSING FLOW WITH AN EULERIAN/EULERIAN MODEL
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Wet steam condensing flow in low-pressure steam turbine leads to efficiency losses and blade erosions.In order to investigate this problem by numerical approach, an Eulerian/Eulerian model has been developed, in which the wet steam is regarded as mixture comprising two coupled systems: the vapor phase and the liquid phase.These two systems are both described by conservation equations.High resolution TVD scheme is employed to capture condensing phenomena in wet steam flow.This model has been validated by numerical simulations of condensing flows in 1D and 2D nozzles.Compared with experimental data, a good agreement is observed.This Eulerian/Eulerian model can be extended to 3D calculation of condensing flow.
Equilibrium-eulerian les model for turbulent poly-dispersed particle-laden flow
Icardi, Matteo
2013-04-01
An efficient Eulerian method for poly-dispersed particles in turbulent flows is implemented, verified and validated for a channel flow. The approach couples a mixture model with a quadrature-based moment method for the particle size distribution in a LES framework, augmented by an approximate deconvolution method to reconstructs the unfiltered velocity. The particle velocity conditioned on particle size is calculated with an equilibrium model, valid for low Stokes numbers. A population balance equation is solved with the direct quadrature method of moments, that efficiently represents the continuous particle size distribution. In this first study particulate processes are not considered and the capability of the model to properly describe particle transport is investigated for a turbulent channel flow. First, single-phase LES are validated through comparison with DNS. Then predictions for the two-phase system, with particles characterised by Stokes numbers ranging from 0.2 to 5, are compared with Lagrangian DNS in terms of particle velocity and accumulation at the walls. Since this phenomenon (turbophoresis) is driven by turbulent fluctuations and depends strongly on the particle Stokes number, the approximation of the particle size distribution, the choice of the sub-grid scale model and the use of an approximate deconvolution method are important to obtain good results. Our method can be considered as a fast and efficient alternative to classical Lagrangian methods or Eulerian multi-fluid models in which poly-dispersity is usually neglected.
Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics.
Busse, Angela; Müller, Wolf-Christian; Gogoberidze, Grigol
2010-12-01
For the phenomenological description of magnetohydrodynamic turbulence competing models exist, e.g., Boldyrev [Phys. Rev. Lett. 96, 115002 (2006)] and Gogoberidze [Phys. Plasmas 14, 022304 (2007)], which predict the same Eulerian inertial-range scaling of the turbulent energy spectrum although they employ fundamentally different basic interaction mechanisms. A relation is found that links the Lagrangian frequency spectrum with the autocorrelation time scale of the turbulent fluctuations τ(ac) and the associated cascade time scale τ(cas). Thus, the Lagrangian energy spectrum can serve to identify weak (τ(ac) ≪ τ(cas)) and strong (τ(ac) ∼ τ(cas)) interaction mechanisms providing insight into the turbulent energy cascade. The new approach is illustrated by results from direct numerical simulations of two- and three-dimensional incompressible MHD turbulence.
The Lagrangian Deformation Structure of Three-Dimensional Steady Flow
Lester, Daniel R; Borgne, Tanguy Le; de Barros, Felipe P J
2016-01-01
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures (LCSs). To understand and model these processes it is necessary to quantify Lagrangian deformation in terms of Eulerian flow properties, currently an open problem. To elucidate this link we develop a Protean (streamline) coordinate transform for steady three-dimensional (3D) flows which renders both the velocity gradient and deformation gradient upper triangular. This frame not only simplifies computation of fluid deformation metrics such as fi?nite-time Lyapunov exponents (FTLEs) and elucidates the deformation structure of the flow, but moreover explicitly recovers kinematic and topological constraints upon deformation such as those related to helicity density and the Poincar\\'{e}-Bendixson theorem. We apply this transform to several classes of steady 3D flow, including helical ...
Eulerian bias and the galaxy density field
Mann, B M; Heavens, A F; Mann, Bob; Peacock, John; Heavens, Alan
1997-01-01
We investigate the effects on cosmological clustering statistics of empirical biasing, where the galaxy distribution is a local transformation of the present-day Eulerian density field. The effects of the suppression of galaxy numbers in voids, and their enhancement in regions of high density, are considered, independently and in combination. We compare results from numerical simulations with the predictions of simple analytic models. We find that the bias is generally scale-dependent, so that the shape of the galaxy power spectrum differs from that of the underlying mass distribution. The degree of bias is always a monotonic function of scale, tending to an asymptotic value on scales where the density fluctuations are linear. The scale dependence is often rather weak, with many reasonable prescriptions giving a bias which is nearly independent of scale. We have investigated whether such an Eulerian bias can reconcile a range of theoretical power spectra with the twin requirements of fitting the galaxy power ...
Directory of Open Access Journals (Sweden)
D. A. Belikov
2015-07-01
Full Text Available We present the development of the Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric (A-GELCA model that consists of the National Institute for Environmental Studies (NIES model as an Eulerian three-dimensional transport model (TM, and FLEXPART (FLEXible PARTicle dispersion model as the Lagrangian plume diffusion model (LPDM. The tangent and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving the performance of the computing, including MPI (Message Passing Interface. As results, the adjoint of Eulerian model is discrete. Construction of the adjoint of the Lagrangian component did not require any code modification, as LPDMs are able to track a significant number of particles back in time and thereby calculate the sensitivity of observations to the neighboring emissions areas. Eulerian and Lagrangian adjoint components were coupled at the time boundary in the global domain.The results are verified using a series of test experiments. The forward simulation shown the coupled model is effective in reproducing the seasonal cycle and short-term variability of CO2 even in the case of multiple limiting factors, such as high uncertainty of fluxes and the low resolution of the Eulerian model. The adjoint model demonstrates the high accuracy compared to direct forward sensitivity calculations and fast performance. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation.
Sepe, D.
2013-01-01
The obstruction to construct a Lagrangian bundle over a fixed integral affine manifold was constructed by Dazord and Delzant (J Differ Geom 26:223–251, 1987) and shown to be given by ‘twisted’ cup products in Sepe (Differ GeomAppl 29(6): 787–800, 2011). This paper uses the topology of universal Lagr
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Arbitrary spin conformal fields in (A)dS
Metsaev, R R
2014-01-01
Totally symmetric arbitrary conformal spin fields in (A)dS space of even dimension greater than or equal to four are studied. Ordinary-derivative and gauge invariant Lagrangian formulation for such fields is obtained. Gauge symmetries are realized by using auxiliary fields and Stueckelberg fields. We demonstrate explicitly that Lagrangian of conformal field is decomposed into a sum of gauge invariant Lagrangians for massless, partial-massless, and massive fields. We obtain a mass spectrum of the partial-massless and massive fields and confirm the conjecture about the mass spectrum made in the earlier literature. Explicit interrelation between Poincar\\'e basis conformal fields and (A)dS basis conformal fields is obtained. Covariant Lorentz-like and de-Donder like gauge conditions considerably simplifying the Lagrangian of conformal fields are proposed. Using such gauge conditions, we explain how the partition function of conformal field is obtained in the framework of our approach.
Symmetries in Lagrangian Field Theory
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
Symplectic Applicability of Lagrangian Surfaces
Directory of Open Access Journals (Sweden)
Lorenzo Nicolodi
2009-06-01
Full Text Available We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equations. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.
Energy Technology Data Exchange (ETDEWEB)
Buchbinder, I.L., E-mail: joseph@tspu.edu.ru [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation); National Research Tomsk State University (Russian Federation); Snegirev, T.V., E-mail: snegirev@tspu.edu.ru [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation); Zinoviev, Yu.M., E-mail: Yurii.Zinoviev@ihep.ru [Institute for High Energy Physics, Protvino, Moscow Region, 142280 (Russian Federation)
2014-11-10
We construct the frame-like gauge-invariant Lagrangian formulation for massive fermionic arbitrary spin fields in three-dimensional AdS space. The Lagrangian and complete set of gauge transformations are obtained. We also develop the formalism of gauge-invariant curvatures for the massive theory under consideration and show how the Lagrangian is formulated in their terms. The massive spin-5/2 field is discussed as an example.
Eulerian and Lagrangian views of a turbulent boundary layer flow using time-resolved tomographic PIV
Schröder, A.; Geisler, R.; Staack, K.; Elsinga, G.E.; Scarano, F.; Wieneke, B.; Henning, A.; Poelma, C.; Westerweel, J.
2010-01-01
Coherent structures and their time evolution in the logarithmic region of a turbulent boundary layer investigated by means of 3D space–time correlations and time-dependent conditional averaging techniques are the focuses of the present paper. Experiments have been performed in the water tunnel at TU
Eulerian vs. Lagrangian analyses of pedestrian dynamics asymmetries in a staircase landing
Corbetta, Alessandro; Muntean, Adrian; Toschi, Federico
2016-01-01
Real-life, out-of-laboratory, measurements of pedestrian movements allow extensive and fully-resolved statistical analyses. However, data acquisition in real-life is subjected to the wide heterogeneity that characterizes crowd flows over time. Disparate flow conditions, such as co-flows and counter-flows at low and at high pedestrian densities, typically follow randomly one another. When analysing the data in order to study the dynamics and behaviour of pedestrians it is crucial to be able disentangle and to properly select (query) data from statistically homogeneous flow conditions in order to avoid spurious statistics and to enable qualitative comparisons. In this paper we extend our previous analysis on the asymmetric pedestrian dynamics on a staircase landing, where we collected a large statistical database of measurements from ad hoc continuous recordings. This contribution has a two-fold aim: first, method-wise, we discuss two possible approaches to query experimental datasets for homogeneous flow condi...
A combined eulerian-lagrangian three-dimensional finite-element analysis of edge-rolling
Huisman, H.J.; Huetink, J.
1985-01-01
After edge-rolling (heavy width-reduction), the cross-section of a continuously-cast steel slab may be non-rectangular, whereas what is desired is that it should be exactly rectangular. The deformed shape results in an increased number of heavy width- and thickness-reductions having to be imposed on
LYNX: A Linked Eulerian and Lagrangian Code. Volume II. LYNX Computer Listing
1975-11-01
KMI-X0H(J,KM)«OLTH-XiJ*l .KZ) YM»YPlJtKH!»DVI J,KH|- TDH ( j|KM)»CLTM-r ( J*l . X Z > TXX4-TAXCJ*liKZ) TYY1-TYYIJ*l»*L) TXY4-TAY1J*liKZ) IF...VCUCÜT WC X XON XMSS XPLRHX T TDH YPLRUN TVINT | 00101 00103 S 00107 00126 00132 00133 00134 00135 00136 00137 00140 00141...White Sands Missile Range New Mexico 88002 President US Army Infantry Board Fort Benning, GA 31905 1 HQDA (DAMA, LTC Shelton) Washington, DC 20310
A combined eulerian-lagrangian three-dimensional finite-element analysis of edge-rolling
Huisman, H.J.; Huetink, Han
1985-01-01
After edge-rolling (heavy width-reduction), the cross-section of a continuously-cast steel slab may be non-rectangular, whereas what is desired is that it should be exactly rectangular. The deformed shape results in an increased number of heavy width- and thickness-reductions having to be imposed on
2014-11-01
temperature equation-of-state (EOS) [ Luscher et al., 2013] for the pressure. For isotropic (e.g., untextured polycrystalline) solids, nonlinear elasticity...elastoplasticity [ Luscher et al., 2013]. 1450048-12 2nd Reading October 15, 2014 11:4 WSPC-255-IJAM S1758-8251 1450048 Shock Compression of Metal Crystals...Clayton, 2011; Luscher et al., 2013] S̄ = ∂Ū ∂E = ∂Ψ̄ ∂E = JFE−1σFE−T, θ = ∂Ū/∂η, η = −∂Ψ̄/∂θ, χ̄ = −∂Ψ̄/∂ζ, (3.7) c̄θ̇ = ∑ α τ̄αγ̇α + θ ∂S̄ ∂θ : Ė
Papritz, Lukas; Schemm, Sebastian
2013-01-01
In this idealised modelling study, the development of a downstream cyclone, which closely follows the life-cycle of a Shapiro-Keyser cyclone, is addressed from a quasi-geostrophic kinetic energy perspective. To this end a simulation of a dry, highly idealised, dispersive baroclinic wave, developing a primary and a downstream cyclone, is performed. Kinetic energy and processes contributing to its tendency – in particular baroclinic conversion and ageostrophic geopotential fluxes – are investig...
Differential geometry based solvation model I: Eulerian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2010-11-01
This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to
Minimum Orders of Eulerian Oriented Digraphs with Given Diameter
Institute of Scientific and Technical Information of China (English)
Yoomi RHO; Byeong Moon KIM; Woonjae HWANG; Byung Chul SONG
2014-01-01
A digraph D is oriented if it does not contain 2-cycles. If an oriented digraph D has a directed eulerian path, it is an oriented eulerian digraph. In this paper, when an oriented eulerian digraph D has minimum out-degree 2 and a diameter d, we find the minimum order of D. In addition, when D is 2-regular with diameter 4m (m≥2), we classify the extremal cases.
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
Eulerian Dynamics with a Commutator Forcing
2017-01-09
not. The results below are stated over the torus, Ω = T1, for the purely technical reason of securing a uniform lower bound of the density away from...2.1. L∞-bound of the velocity. We assume that L satisfies the following monotonicity condition. Let x+ = arg max x g(x) and x− = arg min x g(x). Then...special case of the monotonicity condition (2.1) with (f, g) = (1, ρ) implies L(ρ)(x−) > L(1(x−))ρ− = 0. EULERIAN DYNAMICS WITH A COMMUTATOR FORCING 9 Here
Renormalization and effective lagrangians
Polchinski, Joseph
1984-01-01
There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional λø 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed.
Gravity, Time, and Lagrangians
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
Gravity, Time, and Lagrangians
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
2010-09-30
the vertical interpolation adjustment given by Equation 8 (SL OMT ), NOGAPS SL/SI with non-interpolation in the vertical (SL NIV), and the non semi...interpolation scheme (SL OMT ), the non-interpolating scheme in the vertical (SL NIV) and the non semi-Lagrangian NOGAPS (EULER). Figures 4 and...2009 comparing the control NOGAPS SL/SI with the adjusted vertical interpolation scheme (SL OMT ), the non-interpolating scheme in the vertical (SL NIV
Unambiguous formalism for higher order Lagrangian field theories
Energy Technology Data Exchange (ETDEWEB)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain); Vankerschaver, Joris [Control and Dynamical Systems, California Institute of Technology, CA (United States)], E-mail: cedricmc@imaff.cfmac.csic.es, E-mail: mdeleon@imaff.cfmac.csic.es, E-mail: d.martin@imaff.cfmac.csic.es, E-mail: jv@caltech.edu
2009-11-27
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Pressure-field extraction from Lagrangian flow measurements: first experiences with 4D-PTV data
Neeteson, N. J.; Bhattacharya, S.; Rival, D. E.; Michaelis, D.; Schanz, D.; Schröder, A.
2016-06-01
As a follow-up to a previous proof-of-principle study, a novel Lagrangian pressure-extraction technique is analytically evaluated, and experimentally validated using dense 4D-PTV data. The technique is analytically evaluated using the semi-three-dimensional Taylor-Green vortex, and it is found that the Lagrangian technique out-performs the standard Eulerian technique when Dirichlet boundary conditions are enforced. However, the Lagrangian technique produces worse estimates of the pressure field when Neumann boundary conditions are enforced on boundaries with strong pressure gradients. The technique is experimentally validated using flow data obtained for the case of a free-falling, index-matched sphere at Re=2100. The experimental data were collected using a four-camera particle tracking velocimetry measurement system, and processed using 4D-PTV. The pressure field is then extracted using both the Eulerian and Lagrangian techniques, and the resulting pressure fields are compared. Qualitatively, the pressure fields agree; however, quantitative differences are found with respect to the magnitude of the pressure minima on the side of the sphere. Finally, the pressure-drag coefficient is estimated using each technique, and the two techniques are found to be in very close agreement. A comparison to a reference value from literature confirms that the drag coefficient estimates are reasonable, demonstrating the validity of the technique.
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.
Does a Functional Integral Really Need a Lagrangian?
Directory of Open Access Journals (Sweden)
D. Kochan
2010-01-01
Full Text Available Path integral formulation of quantum mechanics (and also other equivalent formulations depends on a Lagrangian and/or Hamiltonian function that is chosen to describe the underlying classical system. The arbitrariness presented in this choice leads to a phenomenon called Quantization ambiguity. For example both L1 = ˙q2 and L2 = eq˙ are suitable Lagrangians on a classical level (δL1 = δL2, but quantum mechanically they are diverse. This paper presents a simple rearrangement of the path integral to a surface functional integral. It is shown that the surface functional integral formulation gives transition probability amplitude which is free of any Lagrangian/Hamiltonian and requires just the underlying classical equations of motion. A simple example examining the functionality of the proposed method is considered.
ESES: Software for Eulerian solvent excluded surface.
Liu, Beibei; Wang, Bao; Zhao, Rundong; Tong, Yiying; Wei, Guo-Wei
2017-03-15
Solvent excluded surface (SES) is one of the most popular surface definitions in biophysics and molecular biology. In addition to its usage in biomolecular visualization, it has been widely used in implicit solvent models, in which SES is usually immersed in a Cartesian mesh. Therefore, it is important to construct SESs in the Eulerian representation for biophysical modeling and computation. This work describes a software package called Eulerian solvent excluded surface (ESES) for the generation of accurate SESs in Cartesian grids. ESES offers the description of the solvent and solute domains by specifying all the intersection points between the SES and the Cartesian grid lines. Additionally, the interface normal at each intersection point is evaluated. Furthermore, for a given biomolecule, the ESES software not only provides the whole surface area, but also partitions the surface area according to atomic types. Homology theory is utilized to detect topological features, such as loops and cavities, on the complex formed by the SES. The sizes of loops and cavities are measured based on persistent homology with an evolutionary partial differential equation-based filtration. ESES is extensively validated by surface visualization, electrostatic solvation free energy computation, surface area and volume calculations, and loop and cavity detection and their size estimation. We used the Amber PBSA test set in our electrostatic solvation energy, area, and volume validations. Our results are either calibrated by analytical values or compared with those from the MSMS software. © 2017 Wiley Periodicals, Inc.
A lattice model for the Eulerian description of heavy particle suspensions
Laenen, François; Bec, Jérémie
2015-01-01
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is here introduced for simulating the dynamics of diffusive heavy inertial particles in turbulent flows. The approach is based on the position/velocity phase-space particle distribution. The discretization of velocities is inspired from lattice Boltzmann methods and is chosen to match discrete displacements between two time steps. For each spatial position, the time evolution of particles momentum is approximated by a finite-volume approach. The proposed method is tested for particles experiencing a Stokes viscous drag with a prescribed fluid velocity field in one dimension using a random flow, and in two dimensions with the solution to the forced incompressible Navier-Stokes equations. Results show good agreements between Lagrangian and Eulerian dynamics for both spatial cluster...
An Eulerian-based Bubble Dynamics Model for Computational Fluid Dynamics
Balu, Asish; Kinzel, Michael
2015-11-01
Cavitation dynamics of nuclei are largely governed by the Rayleigh-Plesset Equation (RPE). This research explores the implementation of a one-way coupling to the solution of the RPE to a computational fluid dynamics (CFD) simulation in an Eulerian-framework. In this work, we used transport equations (i.e., advection) of the bubble radius and bubble growth rate, both of which are governed by advection mechanisms and coupling to the RPE through the CFD pressure field. The method is validated in the context of hypothetical pressure fields by prescribing a temporally varying pressure. Then, it is extended to one-way coupling with cavitation development in three different flow situations: (1) flow over a cylinder, (2) bubble formation during a bottle collapse event, and (3) cavitation in a tip vortex. In the context of these flows, the CFD simulations replicate an equivalent MATLAB-based solution to the RPE, thus validating the model. Additionally, an analytical formulation for appropriate upper and lower bounds for the bubble's physical properties is presented. These boundary values allow the CFD solver to run at larger time steps, therefore increasing the rate of convergence as well as maintaining solution accuracy. The results from this work suggest that Eulerian-based RPE cavitation models are practical and have the potential to simulate large numbers of bubbles that challenge Lagrangian methods.
Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows
Innocenti, A; Chibbaro, S
2016-01-01
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves for a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided b...
Bounded fractional diffusion in geological media: Definition and Lagrangian approximation
Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang
2016-11-01
Spatiotemporal fractional-derivative models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and nonzero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing nonzero-value spatial-nonlocal boundary conditions with directional superdiffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eulerian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the nonlocal and nonsymmetric fractional diffusion. For a nonzero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite domains to those with any size and boundary conditions.
On manifolds admitting the consistent Lagrangian formulation for higher spin fields
Buchbinder, I L; Lavrov, P M
2011-01-01
We study a possibility of Lagrangian formulation for free higher spin bosonic totally symmetric tensor field on the background manifold characterizing by the arbitrary metric, vector and third rank tensor fields in framework of BRST approach. Assuming existence of massless and flat limits in the Lagrangian and using the most general form of the operators of constraints we show that the algebra generated by these operators will be closed only for constant curvature space with no nontrivial coupling to the third rank tensor and the strength of the vector fields. This result finally proves that the consistent Lagrangian formulation at the conditions under consideration is possible only in constant curvature Riemann space.
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.
Currents for Arbitrary Helicity
Dragon, Norbert
2016-01-01
Using Mackey's classification of unitary representations of the Poincar\\'e group on massles states of arbitrary helicity we disprove the claim that states with helicity |h|>=1 cannot couple to a conserved current by constructing such a current.
Topological Classification of Lagrangian Fibrations
Sepe, D
2009-01-01
We define topological invariants of regular Lagrangian fibrations using the integral affine structure on the base space and we show that these coincide with the classes known in the literature. We also classify all symplectic types of Lagrangian fibrations with base $\\rpr$ and fixed monodromy representation, generalising a construction due to Bates.
Lagrangian hydrocode simulations of the 1958 Lituya Bay tsunamigenic rockslide
Schwaiger, H. F.; Higman, B.
2007-07-01
The interaction of debris flows, whether subaqueous or subaerial, with bodies of water can produce tsunamis with a locally devastating impact. When debris flows begin above the water surface, the impact can produce a large air cavity, corresponding to a large effective volume of water displaced and complicating efforts to model the resulting tsunami. Because grid-based, Eulerian numerical methods have an inherent difficulty tracking material boundaries, we have implemented a particle-based, Lagrangian model (Smoothed Particle Hydrodynamics). We treat the debris flow as an incompressible, viscous fluid and the body of water as inviscid. We use this model to simulate the 1958 Lituya Bay rockslide and resulting tsunami. Our simulation results compare favorably with field observations as well as a scaled laboratory experiment and numerical studies.
Bailey, Brian N.
2017-01-01
When Lagrangian stochastic models for turbulent dispersion are applied to complex atmospheric flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behaviour in the numerical solution. Here we discuss numerical strategies for solving the non-linear Langevin-based particle velocity evolution equation that eliminate such unphysical behaviour in both Reynolds-averaged and large-eddy simulation applications. Extremely large or `rogue' particle velocities are caused when the numerical integration scheme becomes unstable. Such instabilities can be eliminated by using a sufficiently small integration timestep, or in cases where the required timestep is unrealistically small, an unconditionally stable implicit integration scheme can be used. When the generalized anisotropic turbulence model is used, it is critical that the input velocity covariance tensor be realizable, otherwise unphysical behaviour can become problematic regardless of the integration scheme or size of the timestep. A method is presented to ensure realizability, and thus eliminate such behaviour. It was also found that the numerical accuracy of the integration scheme determined the degree to which the second law of thermodynamics or `well-mixed condition' was satisfied. Perhaps more importantly, it also determined the degree to which modelled Eulerian particle velocity statistics matched the specified Eulerian distributions (which is the ultimate goal of the numerical solution). It is recommended that future models be verified by not only checking the well-mixed condition, but perhaps more importantly by checking that computed Eulerian statistics match the Eulerian statistics specified as inputs.
Metriplectic Algebra for Dissipative Fluids in Lagrangian Formulation
Directory of Open Access Journals (Sweden)
Massimo Materassi
2015-03-01
Full Text Available The dynamics of dissipative fluids in Eulerian variables may be derived from an algebra of Leibniz brackets of observables, the metriplectic algebra, that extends the Poisson algebra of the frictionless limit of the system via a symmetric semidefinite component, encoding dissipative forces. The metriplectic algebra includes the conserved total Hamiltonian H, generating the non-dissipative part of dynamics, and the entropy S of those microscopic degrees of freedom draining energy irreversibly, which generates dissipation. This S is a Casimir invariant of the Poisson algebra to which the metriplectic algebra reduces in the frictionless limit. The role of S is as paramount as that of H, but this fact may be underestimated in the Eulerian formulation because S is not the only Casimir of the symplectic non-canonical part of the algebra. Instead, when the dynamics of the non-ideal fluid is written through the parcel variables of the Lagrangian formulation, the fact that entropy is symplectically invariant clearly appears to be related to its dependence on the microscopic degrees of freedom of the fluid, that are themselves in involution with the position and momentum of the parcel.
Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion
Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas H.
2012-01-01
demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current
Lagrangian flows within reflecting internal waves at a horizontal free-slip surface
Energy Technology Data Exchange (ETDEWEB)
Zhou, Qi, E-mail: q.zhou@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA (United Kingdom); Diamessis, Peter J. [School of Civil and Environmental Engineering, Cornell University, Ithaca, New York 14853 (United States)
2015-12-15
In this paper sequel to Zhou and Diamessis [“Reflection of an internal gravity wave beam off a horizontal free-slip surface,” Phys. Fluids 25, 036601 (2013)], we consider Lagrangian flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking Lagrangian fluid particles in direct numerical simulation (DNS) datasets of the Eulerian flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that Eulerian mean flow due to wave-wave interaction and wave-induced Stokes drift cancels each other out completely at the second order in wave steepness A, i.e., O(A{sup 2}), implying zero Lagrangian mean flow up to that order. However, high-accuracy particle tracking in finite-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A{sup 2}) is not complete. This partial cancelation significantly weakens the mean Lagrangian flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean Lagrangian drifts on O(A{sup 2}) and thus particle dispersion on O(A{sup 4}). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.
Eulerian-Eulerian Simulation of Particle-Liquid Slurry Flow in Horizontal Pipe
Directory of Open Access Journals (Sweden)
Titus Ntow Ofei
2016-01-01
Full Text Available In this study, a computational fluid dynamics (CFD simulation which adopts the inhomogeneous Eulerian-Eulerian two-fluid model in ANSYS CFX-15 was used to examine the influence of particle size (90 μm to 270 μm and in situ particle volume fraction (10% to 40% on the radial distribution of particle concentration and velocity and frictional pressure loss. The robustness of various turbulence models such as the k-epsilon (k-ε, k-omega (k-ω, SSG Reynolds stress, shear stress transport, and eddy viscosity transport was tested in predicting experimental data of particle concentration profiles. The k-epsilon model closely matched the experimental data better than the other turbulence models. Results showed a decrease in frictional pressure loss as particle size increased at constant particle volume fraction. Furthermore, for a constant particle volume fraction, the radial distribution of particle concentration increased with increasing particle size, where high concentration of particles occurred at the bottom of the pipe. Particles of size 90 μm were nearly buoyant especially for high particle volume fraction of 40%. The CFD study shows that knowledge of the variation of these parameters with pipe position is very crucial if the understanding of pipeline wear, particle attrition, or agglomeration is to be advanced.
CFD simulation of an industrial hydrocyclone with Eulerian-Eulerian approach:A case study
Institute of Scientific and Technical Information of China (English)
Safa Raziyeh; Soltani Goharrizi Ataallah⇑
2014-01-01
In the present study, a three-dimensional computational fluid dynamics simulation together with exper-imental field measurements was applied to optimize the performance of an industrial hydrocyclone at Sarcheshmeh copper complex. In the simulation, the Eulerian-Eulerian approach was used for solid and liquid phases, the latter being water. In this approach, nine continuous phases were considered for the solid particles with different sizes and one continuous phase for water. The continuity and momen-tum equations with inclusion of buoyancy and drag forces were solved by the finite volume method. The k-e RNG turbulence model was used for modeling of turbulency. There was a good agreement between the simulation results and the experimental data. After validation of the model accuracy, the effect of inlet solid percentage, pulp inlet velocity, rod inserting in the middle of the hydrocyclone and apex diam-eter on hydrocyclone performance was investigated. The results showed that by decreasing the inlet solid percentage and increasing the pulp inlet velocity, the efficiency of hydrocyclone increased. Decreasing the apex diameter caused an increase in the hydrocyclone efficiency.
Lagrangian Modeling of the Atmosphere
Schultz, Colin
2013-08-01
Like watching a balloon borne by the breeze, a Lagrangian model tracks a parcel of air as it flows through the atmosphere. Whether running forward or backward in time, Lagrangian models offer a powerful tool for tracking and understanding the fates, or origins, of atmospheric flows. In the AGU monograph Lagrangian Modeling of the Atmosphere, editors John Lin, Dominik Brunner, Christoph Gerbig, Andreas Stohl, Ashok Luhar, and Peter Webley explore the nuances of the modeling technique. In this interview Eos talks to Lin about the growing importance of Lagrangian modeling as the world settles on climate change mitigation strategies, the societal value of operational modeling, and how recent advances are making it possible to run these complex calculations at home.
The Lagrangian in Quantum Mechanics
Dirac, P. A. M.
Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue, as a result of which the whole of the classical Hamiltonian theory, which is just a structure built up on this notion, could be taken over in all its details into quantum mechanics. Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. In the first place the Lagrangian method allows one to collect together all the equations of motion and express them as the stationary property of a certain action function. (This action function is just the time-integral of the Lagrangian.) There is no corresponding action principle in terms of the coordinates and momenta of the Hamiltonian theory. Secondly the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially non-relativistic in form, since it marks out a particular time variable as the canonical conjugate of the Hamiltonian function. For these reasons it would seem desirable to take up the question of what corresponds in the quantum theory to the Lagrangian method of the classical theory. A little consideration shows, however, that one cannot expect to be able to take over the classical Lagrangian equations in any very direct way. These equations involve partial derivatives of the Lagrangian with respect to the coordinates and velocities and no meaning can be given to such derivatives in quantum mechanics. The only differentiation process that can be carried out with respect to the dynamical variables of
Presymplectic structures and intrinsic Lagrangians
Grigoriev, Maxim
2016-01-01
It is well-known that a Lagrangian induces a compatible presymplectic form on the equation manifold (stationary surface, understood as a submanifold of the respective jet-space). Given an equation manifold and a compatible presymplectic form therein, we define the first-order Lagrangian system which is formulated in terms of the intrinsic geometry of the equation manifold. It has a structure of a presymplectic AKSZ sigma model for which the equation manifold, equipped with the presymplectic form and the horizontal differential, serves as the target space. For a wide class of systems (but not all) we show that if the presymplectic structure originates from a given Lagrangian, the proposed first-order Lagrangian is equivalent to the initial one and hence the Lagrangian per se can be entirely encoded in terms of the intrinsic geometry of its stationary surface. If the compatible presymplectic structure is generic, the proposed Lagrangian is only a partial one in the sense that its stationary surface contains the...
Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
Ruiz, D E
2015-01-01
Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Both phenomena are governed by an effective gauge Hamiltonian, which vanishes in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of $N$ resonant modes, where $N$ is arbitrary, and lead to equations for the wave spin, which happens to be a $(N^2-1)$-dimensional spin vector. As a special case, classical equations for a Dirac particle $(N=2)$ are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangi...
Chiral Lagrangian and chiral quark model from confinement in QCD
Simonov, Yu A
2015-01-01
The effective chiral Lagrangian in both nonlocal form $L_{ECCL}$ and standard local form $L_{ECL}$ are derived in QCD using the confining kernel, obtained in the vacuum correlator formalism. As a result all coefficients of $L_{ECL}$ can be computed via $q\\bar q$ Green's functions. In the $p^2$ order of $L_{ECL}$ one obtains GOR relations and quark decay constants $f_a$ are calculated $a=1,...8$, while in the $p^4$ order the coefficients $L_1, L_2, L_3,L_4, L_5, L_6$ are obtained in good agreement with the values given by data. The chiral quark model is shown to be a simple consequence of $L_{ECCL}$ with defined coefficients. It is demonstrated that $L_{ECCL}$ gives an extension of the limiting low-energy Lagrangian $L_{ECL}$ to arbitrary momenta.
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.
Lagrangian velocity auto-correlations in statistically-steady rotating turbulence
Del Castello, Lorenzo
2013-01-01
Lagrangian statistics of passive tracers in rotating turbulence is investigated by Particle Tracking Velocimetry. A confined and steadily-forced turbulent flow is subjected to five different rotation rates. The PDFs of the velocity components clearly reveal the anisotropy induced by background rotation. Although the statistical properties of the horizontal turbulent flow field are approximately isotropic, in agreement with previously reported results by van Bokhoven and coworkers [Phys. Fluids 21, 096601 (2009)], the velocity component parallel to the (vertical) rotation axis gets strongly reduced (compared to the horizontal ones) while the rotation is increased. The auto-correlation coefficients of all three components are progressively enhanced for increasing rotation rates, although the vertical one shows a tendency to decrease for slow rotation rates. The decorrelation is approximately exponential. Lagrangian data compare favourably with previously reported Eulerian data for horizontal velocity components...
Eulerian frequency analysis of structural vibrations from high-speed video
Venanzoni, Andrea; De Ryck, Laurent; Cuenca, Jacques
2016-06-01
An approach for the analysis of the frequency content of structural vibrations from high-speed video recordings is proposed. The techniques and tools proposed rely on an Eulerian approach, that is, using the time history of pixels independently to analyse structural motion, as opposed to Lagrangian approaches, where the motion of the structure is tracked in time. The starting point is an existing Eulerian motion magnification method, which consists in decomposing the video frames into a set of spatial scales through a so-called Laplacian pyramid [1]. Each scale - or level - can be amplified independently to reconstruct a magnified motion of the observed structure. The approach proposed here provides two analysis tools or pre-amplification steps. The first tool provides a representation of the global frequency content of a video per pyramid level. This may be further enhanced by applying an angular filter in the spatial frequency domain to each frame of the video before the Laplacian pyramid decomposition, which allows for the identification of the frequency content of the structural vibrations in a particular direction of space. This proposed tool complements the existing Eulerian magnification method by amplifying selectively the levels containing relevant motion information with respect to their frequency content. This magnifies the displacement while limiting the noise contribution. The second tool is a holographic representation of the frequency content of a vibrating structure, yielding a map of the predominant frequency components across the structure. In contrast to the global frequency content representation of the video, this tool provides a local analysis of the periodic gray scale intensity changes of the frame in order to identify the vibrating parts of the structure and their main frequencies. Validation cases are provided and the advantages and limits of the approaches are discussed. The first validation case consists of the frequency content
Attraction-Based Computation of Hyperbolic Lagrangian Coherent Structures
Karrasch, Daniel; Haller, George
2014-01-01
Recent advances enable the simultaneous computation of both attracting and repelling families of Lagrangian Coherent Structures (LCS) at the same initial or final time of interest. Obtaining LCS positions at intermediate times, however, has been problematic, because either the repelling or the attracting family is unstable with respect to numerical advection in a given time direction. Here we develop a new approach to compute arbitrary positions of hyperbolic LCS in a numerically robust fashion. Our approach only involves the advection of attracting material surfaces, thereby providing accurate LCS tracking at low computational cost. We illustrate the advantages of this approach on a simple model and on a turbulent velocity data set.
Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics.
Ilinskii, Yurii A; Hamilton, Mark F; Zabolotskaya, Evgenia A
2007-02-01
Two models of interacting bubble dynamics are presented, a coupled system of second-order differential equations based on Lagrangian mechanics, and a first-order system based on Hamiltonian mechanics. Both account for pulsation and translation of an arbitrary number of spherical bubbles. For large numbers of interacting bubbles, numerical solution of the Hamiltonian equations provides greater stability. The presence of external acoustic sources is taken into account explicitly in the derivation of both sets of equations. In addition to the acoustic pressure and its gradient, it is found that the particle velocity associated with external sources appears in the dynamical equations.
On Problems of the Lagrangian Quantization of W3-gravity
Geyer, B; Lavrov, P M; Moshin, P Y
2003-01-01
We consider the two-dimensional model of W3-gravity within Lagrangian quantization methods for general gauge theories. We use the Batalin-Vilkovisky formalism to study the arbitrariness in the realization of the gauge algebra. We obtain a one-parametric non-analytic extension of the gauge algebra, and a corresponding solution of the classical master equation, related via an anticanonical transformation to a solution corresponding to an analytic realization. We investigate the possibility of closed solutions of the classical master equation in the Sp(2)-covariant formalism and show that such solutions do not exist in the approximation up to the third order in ghost and auxiliary fields.
Arbitrary Spin Galilean Oscillator
Hagen, C R
2014-01-01
The so-called Dirac oscillator was proposed as a modification of the free Dirac equation which reproduces many of the properties of the simple harmonic oscillator but accompanied by a strong spin-orbit coupling term. It has yet to be extended successfully to the arbitrary spin S case primarily because of the unwieldiness of general spin Lorentz invariant wave equations. It is shown here using the formalism of totally symmetric multispinors that the Dirac oscillator can, however, be made to accommodate spin by incorporating it into the framework of Galilean relativity. This is done explicitly for spin zero and spin one as special cases of the arbitrary spin result. For the general case it is shown that the coefficient of the spin-orbit term has a 1/S behavior by techniques which are virtually identical to those employed in the derivation of the g-factor carried out over four decades ago.
Griffin, Maurice; Sugawara, Glen
1995-02-01
A system for storing an arbitrary waveform on nonvolatile random access memory (NVRAM) device and generating an analog signal using the NVRAM device is described. A central processing unit is used to synthesize an arbitrary waveform and create a digital representation of the waveform and transfer the digital representation to a microprocessor which, in turn, writes the digital data into an NVRAM device which has been mapped into a portion of the microprocessor address space. The NVRAM device is removed from address space and placed into an independent waveform generation unit. In the waveform generation unit, an address clock provides an address timing signal and a cycle clock provides a transmit signal. Both signals are applied to an address generator. When both signals are present, the address generator generates and transmits to the NVRAM device a new address for each cycle of the address timing signal. In response to each new address generated, the NVRAM devices provides a digital output which is applied to a digital to analog converter. The converter produces a continuous analog output which is smoothed by a filter to produce the arbitrary waveform.
Innocenti, Alessio; Marchioli, Cristian; Chibbaro, Sergio
2016-11-01
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study particle-laden turbulent flows, when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGSs) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided by LES and then used to advance the SDEs in time. The model consistency is assessed in the limit of particles with zero inertia, when "duplicate fields" are available from both the Eulerian LES and the Lagrangian tracking. Tests with inertial particles were performed to examine the capability of the model to capture the particle preferential concentration and near-wall segregation. Upon comparison with DNS-based statistics, our results show improved accuracy and considerably reduced errors with respect to the case in which no SGS model is used in the equations of particle motion.
Covering-Based Rough Sets on Eulerian Matroids
Directory of Open Access Journals (Sweden)
Bin Yang
2013-01-01
Full Text Available Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids.
Generalized Radar 4-COORDINATES and Equal-Time Cauchy Surfaces for Arbitrary Accelerated Observers
Alba, David; Lusanna, Luca
All existing 4-coordinate systems centered on the world-line of an accelerated observer are only locally defined, as for Fermi coordinates both in special and general relativity. As a consequence, it is not known how non-inertial observers can build equal-time surfaces which (a) correspond to a conventional observer-dependent definition of synchronization of distant clocks, and (b) are good Cauchy surfaces for Maxwell equations. Another type of coordinate singularities generating the same problems are those connected to the relativistic rotating coordinate systems used in the treatment of the rotating disk and the Sagnac effect. We show that the use of Hamiltonian methods based on 3+1 splittings of space-time allows one to define as many observer-dependent globally defined radar 4-coordinate systems as nice foliations of space-time with space-like hyper-surfaces admissible according to Møller (for instance, only the differentially rotating relativistic coordinate system, but not the rigidly rotating ones of non-relativistic physics, are allowed). All these conventional notions of an instantaneous 3-space for an arbitrary observer can be empirically defined by introducing generalizations of the Einstein ½ convention for clock synchronization in inertial frames. Each admissible 3+1 splitting has two naturally associated congruences of time-like observers: as a consequence every 3+1 splitting gives rise to non-rigid non-inertial frames centered on any one of these observers. Only for Eulerian observers are the simultaneity leaves orthogonal to the observer world-line. When there is a Lagrangian description of an isolated relativistic system, its reformulation as a parametrized Minkowski theory allows one to show that all the admissible synchronization conventions are gauge equivalent, as also happens in the canonical metric and tetrad gravity, where, however, the chrono-geometrical structure of space-time is dynamically determined. The framework developed in this
About non standard Lagrangians in cosmology
Energy Technology Data Exchange (ETDEWEB)
Dimitrijevic, Dragoljub D.; Milosevic, Milan [Department of Physics, Faculty of Science and Mathematics, University of Nis, Visegradska 33, P.O. Box 224, 18000 Nis (Serbia)
2012-08-17
A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.
Furuichi, M.; Kameyama, M.; Kageyama, A.
2007-12-01
Reproducing a realistic plate tectonics with mantle convection simulation is one of the greatest challenges in computational geophysics. We have developed a three dimensional Eulerian numerical procedure toward plate-mantle simulation, which includes a finite deformation of the plate in the mantle convection. Our method, combined with CIP-CSLR (Constrained Interpolation Profile method-Conservative Semi-Lagrangian advection scheme with Rational function) and ACuTE method, enables us to solve advection and force balance equations even with a large and sharp viscosity jump, which marks the interface between the plates and surrounding upper mantle materials. One of the typical phenomena represented by our method is a fluid rope coiling event, where a stream of viscous fluid is poured onto the bottom plane from a certain height. This coiling motion is due to delicate balances between bending, twisting and stretching motions of fluid rope. In the framework of the Eulerian scheme, the fluid rope and surrounding air are treated as a viscosity profile which differs by several orders of magnitude. Our method solves the complex force balances of the fluid rope and air, by a multigrid iteration technique of ACuTE algorithm. In addition, the CIP-CSLR advection scheme allows us to obtain a deforming shape of the fluid rope, as a low diffusive solution in the Eulerian frame of reference. In this presentation, we will show the simulation result of the fluid rope coiling as an accuracy test for our simulation scheme, by comparing with the simplified numerical solution for thin viscous jet.
Lagrangian perturbations and the matter bispectrum I: fourth-order model for non-linear clustering
Energy Technology Data Exchange (ETDEWEB)
Rampf, Cornelius [Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen, Physikzentrum RWTH-Melaten, D-52056 Aachen (Germany); Buchert, Thomas, E-mail: rampf@physik.rwth-aachen.de, E-mail: buchert@obs.univ-lyon1.fr [Université de Lyon, Observatoire de Lyon, Centre de Recherche Astrophysique de Lyon, CNRS UMR 5574: Université Lyon 1 and École Normale Supérieure de Lyon, 9 avenue Charles André, F-69230 Saint-Genis-Laval (France)
2012-06-01
We investigate the Lagrangian perturbation theory of a homogeneous and isotropic universe in the non-relativistic limit, and derive the solutions up to the fourth order. These solutions are needed for example for the next-to-leading order correction of the (resummed) Lagrangian matter bispectrum, which we study in an accompanying paper. We focus on flat cosmologies with a vanishing cosmological constant, and provide an in-depth description of two complementary approaches used in the current literature. Both approaches are solved with two different sets of initial conditions — both appropriate for modelling the large-scale structure. Afterwards we consider only the fastest growing mode solution, which is not affected by either of these choices of initial conditions. Under the reasonable approximation that the linear density contrast is evaluated at the initial Lagrangian position of the fluid particle, we obtain the nth-order displacement field in the so-called initial position limit: the nth order displacement field consists of 3(n-1) integrals over n linear density contrasts, and obeys self-similarity. Then, we find exact relations between the series in Lagrangian and Eulerian perturbation theory, leading to identical predictions for the density contrast and the peculiar-velocity divergence up to the fourth order.
Transport Induced by Mean-Eddy Interaction: I. Theory, and Relation to Lagrangian Lobe Dynamics
Ide, Kayo
2011-01-01
In this paper we develop a method for the estimation of {\\bf T}ransport {\\bf I}nduced by the {\\bf M}ean-{\\bf E}ddy interaction (TIME) in two-dimensional unsteady flows. The method is built on the dynamical systems approach and can be viewed as a hybrid combination of Lagrangian and Eulerian methods. The (Eulerian) boundaries across which we consider (Lagrangian) transport are kinematically defined by appropriately chosen streamlines of the mean flow. By evaluating the impact of the mean-eddy interaction on transport, the TIME method can be used as a diagnostic tool for transport processes that occur during a specified time interval along a specified boundary segment. We introduce two types of TIME functions: one that quantifies the accumulation of flow properties and another that measures the displacement of the transport geometry. The spatial geometry of transport is described by the so-called pseudo-lobes, and temporal evolution of transport by their dynamics. In the case where the TIME functions are evalua...
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.)
High Order Semi-Lagrangian Advection Scheme
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2014-11-01
In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
A Student's Guide to Lagrangians and Hamiltonians
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Direct numerical simulation of a compressible multiphase flow through the fast Eulerian approach
Cerminara, Matteo; Ongaro, Tomaso Esposti; Salvetti, Maria Vittoria
2014-01-01
Our work is motivated by the analysis of ash plume dynamics, arising in the study of volcanic eruptions. Such phenomena are characterized by large Reynolds number (exceeding $10^7$) and a large number of polydispersed particles~[1]. Thus, the choice of the methodology to be used is straightforward: we need LES of a multiphase gas-particles flow. Since the simulation of the behavior of a large number of dispersed particles is very difficult with Lagrangian methods, we model the particles as a continuum, Eulerian fluid (dust), by using reduced models involving two fluids, as proposed in Ref.~[2,3,4]. Moreover, we need a robust numerical scheme to simultaneously treat compressibility, buoyancy effects and turbulent dispersal dynamics. We analyze the turbulence properties of such models in a homogeneous and isotropic setting, with the aim of formulating a LES model. In particular, we examine the development of freely decaying homogeneous and isotropic turbulence in subsonic regime (the r.m.s. Mach number either 0...
Implementation of the TEPLA Damage Model in a 3D Eulerian Hydrocode
Holian, Kathleen S.; Clancy, Sean P.; Maudlin, Paul J.
2007-06-01
A sophisticated damage model (TEPLA) has been implemented into a three-dimensional (Cartesian) computer code (Pagosa) used here at Los Alamos National Laboratory. TEPLA was originally an isotropic damage model based upon the Gurson flow surface (a potential function used in conjunction with the associated flow law) that models damage due to both porosity growth and plastic strain. It has since been modified to model anisotropic elastoplastic material strength as well. Pagosa is an Eulerian hydrodynamics code that has the following special features: a predictor-corrector Lagrangian step that advances the state variables in time, a high-order advection algorithm that remaps the problem back to the original mesh every time step, and a material interface tracking scheme with van Leer monotonic advection. It also includes a variety of equation of state, strength, fracture, and high explosive burn models. We will describe the physics of the TEPLA model (that models both strength and damage) and will show preliminary results of test problems that are used to validate the model. The four test problems (simple shear, stretching rod, Taylor anvil, and plate impact) can be compared with either analytic solutions or with experimental data.
Lagrangian multi-particle statistics
DEFF Research Database (Denmark)
Lüthi, Beat; Berg, Jacob; Ott, Søren
2007-01-01
Combined measurements of the Lagrangian evolution of particle constellations and the coarse-grained velocity derivative tensor. partial derivative(u) over tilde (i) /partial derivative x(j) are presented. The data are obtained from three-dimensional particle tracking measurements in a quasi isotr...
Galilean invariance in Lagrangian mechanics
Mohallem, J. R.
2015-10-01
The troublesome topic of Galilean invariance in Lagrangian mechanics is discussed in two situations: (i) A particular case involving a rheonomic constraint in uniform motion and (ii) the general translation of an entire system and the constants of motion involved. A widespread impropriety in most textbooks is corrected, concerning a condition for the equality h = E to hold.
Data Assimilation With Regional Lagrangian Models
1999-09-30
Journal of Marine Systems . RESULTS We are able to fit the inviscid Lagrangian model with synthetic Lagrangian data for short periods of time (1-2 days...Mead and A.F. Bennett, 1999. Towards regional assimilation of data: The Lagrangian form of the reduced gravity model and its inverse, (submitted), Journal of Marine Systems .
Anchored Lagrangian submanifolds and their Floer theory
Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru
2009-01-01
We introduce the notion of (graded) anchored Lagrangian submanifolds and use it to study the filtration of Floer' s chain complex. We then obtain an anchored version of Lagrangian Floer homology and its (higher) product structures. They are somewhat different from the more standard non-anchored version. The anchored version discussed in this paper is more naturally related to the variational picture of Lagrangian Floer theory and so to the likes of spectral invariants. We also discuss rationality of Lagrangian submanifold and reduction of the coefficient ring of Lagrangian Floer cohomology of thereof.
Massive "spin-2" theories in arbitrary $D \\ge 3$ dimensions
Dalmazi, D; Mendonça, E L
2014-01-01
Here we show that in arbitrary dimensions $D\\ge 3$ there are two families of second order Lagrangians describing massive "spin-2" particles via a nonsymmetric rank-2 tensor. They differ from the usual Fierz-Pauli theory in general. At zero mass one of the families is Weyl invariant. Such massless theory has no particle content in $D=3$ and gives rise, via master action, to a dual higher order (in derivatives) description of massive spin-2 particles in $D=3$ where both the second and the fourth order terms are Weyl invariant, contrary to the linearized New Massive Gravity. However, only the fourth order term is invariant under arbitrary antisymmetric shifts. Consequently, the antisymmetric part of the tensor $e_{[\\mu\
Effective Lagrangian for Nonrelativistic Systems
Directory of Open Access Journals (Sweden)
Haruki Watanabe
2014-09-01
Full Text Available The effective Lagrangian for Nambu-Goldstone bosons (NGBs in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing 1 dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in 1+1 dimensions.
Complex Lagrangians and phantom cosmology
Andrianov, A A; Kamenshchik, A Yu
2006-01-01
Motivated by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with PT symmetry, we show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. The model is based on a classical complex Lagrangian of a scalar field. Specific symmetry properties analogous to PT in non-Hermitian quantum mechanics lead to purely real equation of motion.
BRST-BFV Lagrangian Formulations for Higher Spin Fields subject to two-column Young Tableaux
Reshetnyak, Alexander A
2014-01-01
The details of Lagrangian description of irreducible integer higher-spin representations of the Poincare group with an Young tableaux $Y[\\hat{s}_1,\\hat{s}_2]$ having $2$ columns are considered for Bose particles propagated on an arbitrary dimensional Minkowski space-time. The procedure is based, first, on using of an auxiliary Fock space generated by Fermi oscillators (antisymmetric basis), second, on construction of the Verma module and finding auxiliary oscillator realization for $sl(2)\\oplus sl(2)$ algebra which encodes the second-class operator constraints subsystem in the HS symmetry superalgebra. Application of an BRST-BFV receipt permits to reproduce gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive mixed-antisymmetric bosonic fields of any spin with appropriate number of gauge and Stueckelberg fields. The general prescription possesses by the possibility to derive constrained Lagrangians with only BRST-invariant extended algebraic con...
Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space
Buchbinder, I L; Lavrov, P M
2006-01-01
We develop the BRST approach to Lagrangian construction for the massive integer higher spin fields in an arbitrary dimensional AdS space. The theory is formulated in terms of auxiliary Fock space. Closed nonlinear symmetry algebra of higher spin bosonic theory in AdS space is found and method of deriving the BRST operator for such an algebra is proposed. General procedure of Lagrangian construction describing the dynamics of bosonic field with any spin is given on the base of the BRST operator. No off-shell constraints on the fields and the gauge parameters are used from the very beginning. As an example of general procedure, we derive the Lagrangians for massive bosonic fields with spin 0, 1 and 2 containing total set of auxiliary fields and gauge symmetries.
Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space
Energy Technology Data Exchange (ETDEWEB)
Buchbinder, I.L. [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634041 (Russian Federation)]. E-mail: joseph@tspu.edu.ru; Krykhtin, V.A. [Laboratory of Mathematical Physics, Tomsk Polytechnic University, Tomsk 634034 (Russian Federation)]. E-mail: krykhtin@mph.phtd.tpu.edu.ru; Lavrov, P.M. [Department of Mathematical Analysis, Tomsk State Pedagogical University, Tomsk 634041 (Russian Federation)]. E-mail: lavrov@tspu.edu.ru
2007-02-05
In this work we develop the BRST approach to Lagrangian construction for the massive integer higher spin fields in an arbitrary dimensional AdS space. The theory is formulated in terms of auxiliary Fock space. Closed nonlinear symmetry algebra of higher spin bosonic theory in AdS space is found and a method of deriving the BRST operator for such an algebra is proposed. A general procedure of Lagrangian construction, describing the dynamics of a bosonic field with any spin is given on the base of the BRST operator. No off-shell constraints on the fields and the gauge parameters are used from the very beginning. As an example of general procedure, we derive the Lagrangians for massive bosonic fields with spin 0, 1 and 2, containing the total set of auxiliary fields and gauge symmetries.
On the notion of gauge symmetries of generic Lagrangian field theory
Giachetta, G; Sardanashvily, G
2008-01-01
Treating gauge theories in a general setting, one meets the following problems: (i) any Lagrangian possesses gauge symmetries which therefore should be separated into the trivial and non-trivial ones, (ii) there is no intrinsic definition of higher-stage gauge symmetries, (iii) gauge and higher-stage gauge symmetries need not form an algebra. We define gauge symmetries as those associated to the Noether identities. Generic Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Under certain conditions, its non-trivial Noether and higher-stage Noether identities are well defined by constructing the antifield Koszul--Tate complex. The inverse second Noether theorem associates to this complex the cochain sequence of ghosts whose ascent operator provides all non-trivial gauge and higher-stage gauge symmetries of Lagrangian theory. This ascent operator, called the gauge operator, is not nilpotent, unless gauge symmetries are abelian. We replace a condition that gauge symmetries for...
Accurate direct Eulerian simulation of dynamic elastic-plastic flow
Energy Technology Data Exchange (ETDEWEB)
Kamm, James R [Los Alamos National Laboratory; Walter, John W [Los Alamos National Laboratory
2009-01-01
The simulation of dynamic, large strain deformation is an important, difficult, and unsolved computational challenge. Existing Eulerian schemes for dynamic material response are plagued by unresolved issues. We present a new scheme for the first-order system of elasto-plasticity equations in the Eulerian frame. This system has an intrinsic constraint on the inverse deformation gradient. Standard Godunov schemes do not satisfy this constraint. The method of Flux Distributions (FD) was devised to discretely enforce such constraints for numerical schemes with cell-centered variables. We describe a Flux Distribution approach that enforces the inverse deformation gradient constraint. As this approach is new and novel, we do not yet have numerical results to validate our claims. This paper is the first installment of our program to develop this new method.
2013-01-01
第4回極域科学シンポジウム横断セッション：[IA] 「急変する北極気候システム及びその全球的な影響の総合的解明」―GRENE北極気候変動研究事業研究成果報告2013―11月12日（火） 国立極地研究所 ２階大会議室
Canepa, Edward S.
2014-01-01
This article describes a new approach to urban traffic flow sensing using decentralized traffic state estimation. Traffic sensor data is generated both by fixed traffic flow sensor nodes and by probe vehicles equipped with a short range transceiver. The data generated by these sensors is sent to a local coordinator node, that poses the problem of estimating the local state of traffic as a mixed integer linear program (MILP). The resulting optimization program is then solved by the nodes in a distributed manner, using branch-and-bound methods. An optimal amount of noise is then added to the maps before dissemination to a central database. Unlike existing probe-based traffic monitoring systems, this system does not transmit user generated location tracks nor any user presence information to a centralized server, effectively preventing privacy attacks. A simulation of the system performance on computer-generated traffic data shows that the system can be implemented with currently available technology. © 2014 Springer International Publishing Switzerland.
Violato, D.; Moore, P.; Scarano, F.
2010-01-01
This work investigates the rod-airfoil air flow by time-resolved Tomographic Particle Image Velocimetry (TR-TOMO PIV) in thin-light volume configuration. Experiments are performed at the region close to the leading edge of a NACA0012 airfoil embedded in the von Karman wake of a cylindrical rod. The
Lagrangian simulation of mixing and reactions in complex geochemical systems
Engdahl, Nicholas B.; Benson, David A.; Bolster, Diogo
2017-04-01
Simulations of detailed geochemical systems have traditionally been restricted to Eulerian reactive transport algorithms. This note introduces a Lagrangian method for modeling multicomponent reaction systems. The approach uses standard random walk-based methods for the particle motion steps but allows the particles to interact with each other by exchanging mass of their various chemical species. The colocation density of each particle pair is used to calculate the mass transfer rate, which creates a local disequilibrium that is then relaxed back toward equilibrium using the reaction engine PhreeqcRM. The mass exchange is the only step where the particles interact and the remaining transport and reaction steps are entirely independent for each particle. Several validation examples are presented, which reproduce well-known analytical solutions. These are followed by two demonstration examples of a competitive decay chain and an acid-mine drainage system. The source code, entitled Complex Reaction on Particles (CRP), and files needed to run these examples are hosted openly on GitHub (https://github.com/nbengdahl/CRP), so as to enable interested readers to readily apply this approach with minimal modifications.
The life cycle of a coherent Lagrangian Agulhas ring
Wang, Y; Olascoaga, M J
2016-01-01
We document the long-term evolution of an Agulhas ring detected from satellite altimetry using a technique from nonlinear dynamical systems that enables objective (i.e., observer-independent) eddy framing. Such objectively detected eddies have Lagrangian (material) boundaries that remain coherent (unfilamented) over the detection period. The ring preserves a quite compact material entity for a period of about 2 years even after most initial coherence is lost within 5 months after detection. We attribute this to the successive development of short-term coherent material boundaries around the ring. These boundaries provide effective short-term shielding for the ring, which prevents a large fraction of the ring's interior from being mixed with the ambient turbulent flow. We show that such coherence regain events cannot be inferred from Eulerian analysis. This process is terminated by a ring-splitting event which marks the ring demise, near the South American coast. The genesis of the ring is characterized by a r...
A semi-Lagrangian gas-kinetic scheme for smooth flows
Wang, Peng
2014-01-01
In this paper, a semi-Lagrangian gas-kinetic scheme is developed for smooth flows based on the Bhatnagar-Gross-Krook (BGK) equation. As a finite-volume scheme, the evolution of the average flow variables in a control volume is under the Eulerian framework, whereas the construction of the numerical flux across the cell interface comes from the Lagrangian perspective. The adoption of the Lagrangian aspect makes the collision and the transport mechanisms intrinsically coupled together in the flux evaluation. As a result, the time step is independent of the particle collision time and solely determined by the Courant-Friedrichs-Lewy (CFL) conditions. A set of simulations are carried out to validate the performance of the new scheme. The results show that with second-order spatial accuracy, the scheme exhibits low numerical dissipation, and can accurately capture the Navier-Stokers solutions for the smooth flows with viscous heat dissipation from the low-speed incompressible to hypersonic compressible regimes.
Hegarty, J. D.; Draxler, R.; Stein, A. F.; Brioude, J.; Eluszkiewicz, J.; Mountain, M.; Nehrkorn, T.; Andrews, A. E.
2012-12-01
The accuracy of greenhouse gas (GHG) fluxes estimated using inverse methods is highly dependent on the fidelity of the atmospheric transport model employed. Lagrangian particle dispersion models (LPDMs) driven by customized meteorological output from mesoscale models have emerged as a powerful tool in inverse GHG estimates at policy-relevant regional and urban scales, for several reasons: 1) Mesoscale meteorology can be available at higher resolution than in most global models, and therefore has the potential to be more realistic, 2) the Lagrangian approach minimizes numerical diffusion present in Eulerian models and is thus better able to represent transport in the near-field of measurement locations, and 3) the Lagrangian approach offers an efficient way to compute the grid-scale adjoint of the transport model ("footprints") by running transport backwards in time. Motivated by these considerations, we intercompare three widely used LPDMs (HYSPLIT, STILT, and FLEXPART) driven by identical meteorological input from the Weather Research and Forecasting (WRF) model against measurements from the controlled tracer release experiments (ready-testbed.arl.noaa.gov/HYSPLIT_datem.php). Our analysis includes statistical assessments of each LPDM in terms of its ability to simulate the observed tracer concentrations, reversibility, and sensitivity to the WRF configuration, particularly with regard to the simulation of the planetary boundary layer.
Alternative expression for the electromagnetic Lagrangian
Saldanha, Pablo L
2015-01-01
We propose an alternative expression for the Lagrangian density that governs the interaction of a charged particle with external electromagnetic fields. The proposed Lagrangian is written in terms of the local superposition of the particle fields with the applied electromagnetic fields, not in terms of the particle charge and of the electromagnetic potentials as is usual. The total Lagrangian for a set of charged particles assumes a simple elegant form with the alternative formulation, giving an aesthetic support for it. The proposed Lagrangian is equivalent to the traditional one in their domain of validity and provides an interesting description of the Aharonov-Bohm effect.
On necessary and sufficient conditions of the BV quantization of a generic Lagrangian field system
Bashkirov, D; Mangiarotti, L; Sardanashvily, G
2005-01-01
We address the problem of extending an original field Lagrangian to ghosts and antifields in order to satisfy the master equation in the framework of the BV quantization of Lagrangian field systems. This extension essentially depends on the degeneracy of an original Lagrangian. A generic Lagrangian system of even and odd fields on an arbitrary smooth manifold is examined in the algebraic terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys the Noether identities which need not be independent, but satisfy the first-stage Noether identities, and so on. We state the necessary and sufficient condition of the existence of the exact antifield Koszul-tate complex with the boundary operator whose nilpotency property provides all the Noether and higher-stage Noether identities of an original Lagrangian system. The Noether inverse second theorem that we prove associates to this Koszul-Tate complex the sequence graded in ghosts whose ascent operator provides the gauge and higher-stage g...
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper, a theoretical and numerical as-sessment of the validity of Eulerian truncation in stochastic modeling is presented. Specifically, we analyze and compare theoretically various existing Eulerian-based first-order tech-niques with and without invoking "Eulerian truncation" and quantify the terms truncated and retained in the stochastic per-turbation equations using high resolution Monte Carlo simula-tions. We also analyze and compare numerically various exist-ing Eulerian-based first-order techniques and Monte Carlo simulation. The obtained results have demonstrated theoreti-cally and numerically that existing Eulerian-based stochastic perturbation techniques are equivalent. The terms truncated are indeed one order higher than those retained. Therefore,we conclude that "Eulerian truncation" is mathematically con-sistent and asymptotic.
Poisson structures in BRST-antiBRST invariant Lagrangian formalism
Geyer, B; Nersessian, A P; Geyer, Bodo; Lavrov, Petr; Nersessian, Armen
2001-01-01
We show that the specific operators V^a appearing in the triplectic formalism can be viewed as the anti-Hamiltonian vector fields generated by a second rank irreducible Sp(2) tensor. This allows for an explicit realization of the triplectic algebra being constructed from an arbitrary Poisson bracket on the space of the fields only. We show that the whole space of fields and antifields can be equipped with an even supersymplectic structure when this Poisson bracket is non-degenerate. This observation opens the possibility to provide the BRST/antiBRST path integral by a well-defined integration measure, as well as to establish a direct link between the Sp(2) symmetric Lagrangian and Hamiltonian BRST quantization schemes.
MEDSLIK-II, a Lagrangian marine oil spill model for short-term forecasting – Part 1: Theory
Directory of Open Access Journals (Sweden)
M. De Dominicis
2013-03-01
Full Text Available 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 oil slick numerical model and re-writes the constitutive equations in a modern mathematical framework. The Lagrangian numerical representation of the oil slick requires three different state variables: the slick, the particle and the structural state variables. Transformation processes (evaporation, spreading, dispersion and coastal adhesion act on the slick state variables, while particles variables are used to model the transport and diffusion processes. The slick and particle variables are recombined together to compute the oil concentration in water, a structural state variable. The mathematical and numerical formulation of oil transport, diffusion and transformation processes described in this paper, together with the many simplifying hypothesis and parameterizations, form the basis of a new, open source Lagrangian surface oil spill model, so-called MEDSLIK-II. Part 2 of this paper describes the applications of MEDSLIK-II to oil spill simulations that allow the validation of the model results and the study of the sensitivity of the simulated oil slick to different model numerical parameterizations.
Linear wave equations and effective lagrangians for Wigner supermultiplets
Dahm, R
1995-01-01
The relevance of the contracted SU(4) group as a symmetry group of the pion nucleon scattering amplitudes in the large N_c limit of QCD raises the problem on the construction of effective Lagrangians for SU(4) supermultiplets. In the present study we suggest effective Lagrangians for selfconjugate representations of SU(4) in exploiting isomorphism between so(6) and ist universal covering su(4). The model can be viewed as an extension of the linear \\sigma model with SO(6) symmetry in place of SO(4) and generalizes the concept of the linear wave equations for particles with arbitrary spin. We show that the vector representation of SU(4) reduces on the SO(4) level to a complexified quaternion. Its real part gives rise to the standard linear \\sigma model with a hedgehog configuration for the pion field, whereas the imaginary part describes vector meson degrees of freedom via purely transversal \\rho mesons for which a helical field configuration is predicted. As a minimal model, baryonic states are suggested to ap...
Vital sign monitoring utilizing Eulerian video magnification and thermography.
Aubakir, Bauyrzhan; Nurimbetov, Birzhan; Tursynbek, Iliyas; Varol, Huseyin Atakan
2016-08-01
In this paper we present a proof of concept for non-contact extraction of vital signs using RGB and thermal images obtained from a smart phone. Using our method, heart rate, respiratory rate and forehead temperature can be measured concurrently. Face detection and tracking is leveraged in order to allow natural motion of patients. Heart rate is estimated via processing of visible band RGB video using Eulerian Video Magnification technique. Respiratory rate and the temperature is measured using thermal video. Experiments conducted with 11 healthy subjects indicate that heart rate and respiration rate can be measured with 92 and 94 percent accuracy, respectively.
An example of special Lagrangian fibration
Institute of Scientific and Technical Information of China (English)
FU Jixiang
2005-01-01
On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4directions.
Electroweak Chiral Lagrangian for Neutral Higgs Boson
Institute of Scientific and Technical Information of China (English)
WANG Shun-Zhi; WANG Qing
2008-01-01
A neutral Higgs boson is added into the traditional electroweak chiral Lagrangian by writing down all possible high dimension operators. The matter part of the Lagrangian is investigated in detail. We find that if Higgs field dependence of Yukawa couplings can be factorized out, there will be no flavour changing neutral couplings; neutral Higgs can induce coupling between light and heavy neutrinos.
A functional LMO invariant for Lagrangian cobordisms
DEFF Research Database (Denmark)
Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël
2008-01-01
Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le–Murakami–Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category...
Anomalous effective lagrangians and vector resonance models
Pallante, E.; Petronzio, R.
1993-01-01
Chiral lagrangians including vector resonances have been shown to saturate the finite part of some of the counterterms needed to regularize ordinary one-loop effective lagrangians of pseudoscalar interactions with external currents. The equivalence between different models has been discussed in the
Pisso, Ignacio; Patra, Prabir; Breivik, Knut
2015-04-01
Lagrangian transport models based on times series of Eulerian fields provide a computationally affordable way of achieving very high resolution for limited areas and time periods. This makes them especially suitable for the analysis of point-wise measurements of atmospheric tracers. We present an application illustrated with examples of greenhouse gases from anthropogenic emissions in urban areas and biogenic emissions in Japan and of pollutants in the Arctic. We asses the algorithmic complexity of the numerical implementation as well as the use of non-procedural techniques such as Object-Oriented programming. We discuss aspects related to the quantification of uncertainty from prior information in the presence of model error and limited number of observations. The case of non-linear constraints is explored using direct numerical optimisation methods.
A Lagrangian approach to classical thermodynamics
Stokes, A.
2017-02-01
The specification of microstates of interacting dynamical systems is different in Lagrangian and Hamiltonian approaches whenever the interaction Lagrangian depends on generalised velocities. In almost all cases of physical interest however, velocity-dependent interaction Lagrangians do not couple velocities belonging to different subsystems. For these cases we define reduced system and bath Lagrangian macrostates, which like the underlying microstates differ from their Hamiltonian counterparts. We then derive exact first and second laws of thermodynamics without any modification of the original system and bath quantities. This approach yields manifestly gauge-invariant definitions of work and free energy, and a gauge-invariant Jarzynski equality is derived. The formalism is applied in deriving the thermodynamic laws for a material system within the radiation reservoir. The Lagrangian partition of the total energy is manifestly gauge-invariant and is in accordance with Poynting's theorem.
On Attracting Lagrangian Coherent Structures
Karrasch, Daniel
2013-01-01
In this note, we show that in the autonomous, two-dimensional incompressible saddle flow, contrary to common intuition, also attracting Lagrangian Coherent Structures (LCSs) can show up as ridges of the forward finite-time Lyapunov exponent (FTLE) field. This raises the issue of characterization of attracting LCSs from forward time FTLE analysis. First, we extend recent results of Haller & Sapsis (2011) [11] on the relation between forward and backward maximal and minimal stretching rates to the whole finite-time Lyapunov spectrum and to stretching directions by considering the singular value decomposition (SVD) of the deformation gradient. We show two significant advantages of the SVD compared to the usual eigendecomposition of the Cauchy-Green strain tensor: (1) one gains theoretical insight into local deformation under a finite-time dynamical system, and (2) one obtains both complete forward and backward strain information from a single grid advection. Furthermore, we give a short and direct proof of t...
Time-Dependent Lagrangian Biomechanics
Ivancevic, Tijana T
2009-01-01
In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. On this extended configuration space we develop time-dependent biomechanical Lagrangian dynamics, using derived jet spaces of velocities and accelerations, as well as the underlying geometric evolution of the mass-inertia matrix. Keywords: Human time-dependent biomechanics, configuration manifold, jet spaces, geometric evolution
Eulerian hydrocode modeling of a dynamic tensile extrusion experiment (u)
Energy Technology Data Exchange (ETDEWEB)
Burkett, Michael W [Los Alamos National Laboratory; Clancy, Sean P [Los Alamos National Laboratory
2009-01-01
Eulerian hydrocode simulations utilizing the Mechanical Threshold Stress flow stress model were performed to provide insight into a dynamic extrusion experiment. The dynamic extrusion response of copper (three different grain sizes) and tantalum spheres were simulated with MESA, an explicit, 2-D Eulerian continuum mechanics hydrocode and compared with experimental data. The experimental data consisted of high-speed images of the extrusion process, recovered extruded samples, and post test metallography. The hydrocode was developed to predict large-strain and high-strain-rate loading problems. Some of the features of the features of MESA include a high-order advection algorithm, a material interface tracking scheme and a van Leer monotonic advection-limiting. The Mechanical Threshold Stress (MTS) model was utilized to evolve the flow stress as a function of strain, strain rate and temperature for copper and tantalum. Plastic strains exceeding 300% were predicted in the extrusion of copper at 400 m/s, while plastic strains exceeding 800% were predicted for Ta. Quantitative comparisons between the predicted and measured deformation topologies and extrusion rate were made. Additionally, predictions of the texture evolution (based upon the deformation rate history and the rigid body rotations experienced by the copper during the extrusion process) were compared with the orientation imaging microscopy measurements. Finally, comparisons between the calculated and measured influence of the initial texture on the dynamic extrusion response of tantalum was performed.
The Shock and Vibration Digest. Volume 12, Number 11,
1980-11-01
used ture During a HCDA exclusively, whereas for the fluid transient, Lagrangian, R.F. Kulak Eulerian, and arbitrary Lagrangian-Eulerian (quasi-Eulerian...13, 1979, 19 pp (1979) action problems in HCDA analysis. CON F-790802-70 42 -4, Key Words: Interaction: structure-fluid, Nuclear reactors, T. Ikushima...July 1978) ruptive Accident ( HCDA ) is presented. During this accident the sodium above the core is propelled upward until it im- Key Words: Columns
An Investigation on Generalized Eulerian Polynomials and Fractions%关于广义Euler多项式和分式的讨论
Institute of Scientific and Technical Information of China (English)
孙佳宁
2006-01-01
This note establishes a pair of exponential generating functions for generalized Eulerian polynomials and Eulerian fractions, respectively. A kind of recurrence relation is obtained for the Eulerian fractions. Finally, a short proof of a certain summation formula is given.
The Interpretation of Saussure’s Arbitrariness
Institute of Scientific and Technical Information of China (English)
王艳
2015-01-01
According to Saussure,The arbitrary nature of language is"first principle of linguistic".With the development of cognitive science,some exaggerate the importance of iconicity;some even suggest iconicity should replace arbitrariness.What leads to this extreme view is the misunderstanding of arbitrariness.The paper aims at advocating an overall and objective view towards the arbitrary nature of language,putting forward that arbitrariness and iconicity are not incompatible but complementary.
Critical Point Theory for Lagrangian Systems
Mazzucchelli, Marco
2012-01-01
Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange's reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more spec
An Augmented Lagrangian Approach for Scheduling Problems
Nishi, Tatsushi; Konishi, Masami
The paper describes an augmented Lagrangian decomposition and coordination approach for solving single machine scheduling problems to minimize the total weighted tardiness. The problem belongs to the class of NP-hard combinatorial optimization problem. We propose an augmented Lagrangian decomposition and coordination approach, which is commonly used for continuous optimization problems, for solving scheduling problems despite the fact that the problem is nonconvex and non-differentiable. The proposed method shows a good convergence to a feasible solution without heuristically constructing a feasible solution. The performance of the proposed method is compared with that of an ordinary Lagrangian relaxation.
Energy Technology Data Exchange (ETDEWEB)
Wong, Michael K. W.; Summers, Randall M.; Petney, Sharon Joy Victor; Luchini, Christopher Bernard; Drake, Richard Roy; Carroll, Susan K.; Hensinger, David M.; Garasi, Christopher Joseph; Robinson, Allen Conrad; Voth, Thomas Eugene; Haill, Thomas A.; Mehlhorn, Thomas Alan; Robbins, Joshua H.; Brunner, Thomas A.
2005-01-01
ALEGRA is an arbitrary Lagrangian-Eulerian multi-material finite element code used for modeling solid dynamics problems involving large distortion and shock propagation. This document describes the basic user input language and instructions for using the software.
Energy Technology Data Exchange (ETDEWEB)
Garasi, Christopher Joseph; Haill, Thomas A.; Robinson, Allen Conrad
2003-11-01
ALEGRA is an arbitrary Lagrangian-Eulerian finite element code that emphasizes large distortion and shock propagation in inviscid fluids and solids. This document describes user options for modeling magnetohydrodynamic, thermal conduction, and radiation emission effects.
Energy Technology Data Exchange (ETDEWEB)
Garasi, Christopher Joseph; Cochrane, Kyle Robert; Mehlhorn, Thomas Alan; Haill, Thomas A.; Summers, Randall M.; Robinson, Allen Conrad
2005-01-01
ALEGRA is an arbitrary Lagrangian-Eulerian finite element code that emphasizes large distortion and shock propagation in inviscid fluids and solids. This document describes user options for modeling resistive magnetohydrodynamic, thermal conduction, and radiation emission effects.
Representing Arbitrary Boosts for Undergraduates.
Frahm, Charles P.
1979-01-01
Presented is a derivation for the matrix representation of an arbitrary boost, a Lorentz transformation without rotation, suitable for undergraduate students with modest backgrounds in mathematics and relativity. The derivation uses standard vector and matrix techniques along with the well-known form for a special Lorentz transformation. (BT)
Gyrokinetic theory for arbitrary wavelength electromagnetic modes in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Qin, H.; Tang, W.M.; Rewoldt, G.
1997-10-15
A linear gyrokinetic system for arbitrary wavelength electromagnetic modes is developed. A wide range of modes in inhomogeneous plasmas, such as the internal kink modes, the toroidal Alfven eigenmode (TAE) modes, and the drift modes, can be recovered from this system. The inclusion of most of the interesting physical factors into a single framework enables one to look at many familiar modes simultaneously and thus to study the modifications of and the interactions between them in a systematic way. Especially, the authors are able to investigate self-consistently the kinetic MHD phenomena entirely from the kinetic side. Phase space Lagrangian Lie perturbation methods and a newly developed computer algebra package for vector analysis in general coordinate system are utilized in the analytical derivation. In tokamak geometries, a 2D finite element code has been developed and tested. In this paper, they present the basic theoretical formalism and some of the preliminary results.
Frenkel electron on an arbitrary electromagnetic background and magnetic Zitterbewegung
Deriglazov, Alexei A
2014-01-01
We present Lagrangian which implies both necessary constraints and dynamical equations for position and spin of relativistic spin one-half particle. The model is consistent for any value of magnetic moment $\\mu$ and for arbitrary electromagnetic background. Our equations coincide with those of Frenkel in the approximation in which the latter have been obtained by Frenkel. Transition from approximate to exact equations yields two structural modifications of the theory. First, Frenkel condition on spin-tensor turns into the Pirani condition. Second, canonical momentum is no more proportional to velocity. Due to this, even when $\\mu=1$ (Frenkel case), the complete and approximate equations predict different behavior of spinning particle. The difference of momentum from velocity means extra contribution into spin-orbit interaction. To estimate the contribution, we found exact solution to complete equations for the case of uniform magnetic field. While BMT electron moves around the circle, our particle experiences...
Classical resolution of black hole singularities in arbitrary dimension
Bazeia, D; Olmo, Gonzalo J; Rubiera-Garcia, D; Sanchez-Puente, A
2015-01-01
A metric-affine approach is employed to study higher-dimensional modified gravity theories involving different powers and contractions of the Ricci tensor. It is shown that the field equations are \\emph{always} second-order, as opposed to the standard metric approach, where this is only achieved for Lagrangians of the Lovelock type. We point out that this property might have relevant implications for the AdS/CFT correspondence in black hole scenarios. We illustrate these aspects by considering the case of Born-Infeld gravity in $d$ dimensions, where we work out exact solutions for electrovacuum configurations. Our results put forward that black hole singularities in arbitrary dimensions can be cured in a purely classical geometric scenario governed by second-order field equations.
An Energy Preserving Monolithic Eulerian Fluid-Structure Numerical Scheme
Pironneau, Olivier
2016-01-01
The conservation laws of continuum mechanic written in an Eulerian frame make no difference between fluids and solids except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials of energy for hyperelastic solids. By taking the velocities as unknown , monolithic methods for fluid structure interactions (FSI) are built. In this article such a formulation is analyzed when the fluid is compressible and the fluid is incompressible. The idea is not new but the progress of mesh generators and numerical schemes like the Characteristics-Galerkin method render this approach feasible and reasonably robust. In this article the method and its discretization are presented, stability is discussed by through an energy estimate. A numerical section discusses implementation issues and presents a few simple tests.
Full Eulerian lattice Boltzmann model for conjugate heat transfer.
Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong
2015-12-01
In this paper a full Eulerian lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results.
Eulerian simulations of collisional effects on electrostatic plasma waves
Pezzi, Oreste; Perrone, Denise; Veltri, Pierluigi
2013-01-01
The problem of collisions in a plasma is a wide subject with a huge historical literature. In fact, the description of realistic plasmas is a tough problem to attach, both from the theoretical and the numerical point of view, and which requires in general to approximate the original collisional Landau integral by simplified differential operators in reduced dimensionality. In this paper, a Eulerian time-splitting algorithm for the study of the propagation of electrostatic waves in collisional plasmas is presented. Collisions are modeled through one-dimensional operators of the Fokker-Planck type, both in linear and nonlinear form. The accuracy of the numerical code is discussed by comparing the numerical results to the analytical predictions obtained in some limit cases when trying to evaluate the effects of collisions in the phenomenon of wave plasma echo and collisional dissipation of Bernstein-Greene-Kruskal waves. Particular attention is devoted to the study of the nonlinear Dougherty collisional operator...
Noninvasive Free Flap Monitoring Using Eulerian Video Magnification
Directory of Open Access Journals (Sweden)
Yuan Fang Liu
2016-01-01
Full Text Available Eulerian Video Magnification (EVM can enhance subtle changes in videos to reveal what was once invisible to the naked eye. In this proof of concept study, we investigated using EVM as a novel form of free flap monitoring. Free flaps with skin paddles were filmed in the operating room with manipulation of their pedicles. In a representative 77-year-old female who received a latissimus dorsi-serratus-rib composite free flap, EVM was able to detect blockage of arterial or venous supply instantaneously, providing a visible representation through degree of color change in videos. EVM has the potential to serve as a powerful free flap monitoring tool with the benefit of being noninvasive, sensitive, easy-to-use, and nearly cost-free.
FULLY NONLINEAR WAVE COMPUTATIONS FOR ARBITRARY FLOATING BODIES USING THE DELTA METHOD
Institute of Scientific and Technical Information of China (English)
Lee Tzung-hang
2003-01-01
Fully nonlinear water wave problems are solved using Eulerian-Lagrangian time stepping methods in conjunction with a desingularized approach to solve the mixed boundary value problem that arises at each time step. In the desingularized approach, the singularities generating the flow field are outside the fluid domain. This allows the singularity distribution to be replaced by isolated Rankine sources with the corresponding reduction in computational complexity and computer time. A moving boundary technique is applied to eliminate the reflection waves from limited computational boundaries. Examples of the use of the method in three-dimensions are given for the exciting forces acting on a modified wigley hull and Series 60 are presented. The numerical results show good agreements with those of experiments.
Development and deployment of constitutive softening routines in Eulerian hydrocodes.
Energy Technology Data Exchange (ETDEWEB)
Fuller, Timothy Jesse; Dewers, Thomas A.; Swan, Matthew Scot
2013-03-01
The state of the art in failure modeling enables assessment of crack nucleation, propagation, and progression to fragmentation due to high velocity impact. Vulnerability assessments suggest a need to track material behavior through failure, to the point of fragmentation and beyond. This eld of research is particularly challenging for structures made of porous quasi-brittle materials, such as ceramics used in modern armor systems, due to the complex material response when loading exceeds the quasi-brittle material's elastic limit. Further complications arise when incorporating the quasi-brittle material response in multi-material Eulerian hydrocode simulations. In this report, recent e orts in coupling a ceramic materials response in the post-failure regime with an Eulerian hydro code are described. Material behavior is modeled by the Kayenta material model [2] and Alegra as the host nite element code [14]. Kayenta, a three invariant phenomenological plasticity model originally developed for modeling the stress response of geologic materials, has in recent years been used with some success in the modeling of ceramic and other quasi-brittle materials to high velocity impact. Due to the granular nature of ceramic materials, Kayenta allows for signi cant pressures to develop due to dilatant plastic ow, even in shear dominated loading where traditional equations of state predict little or no pressure response. When a material's ability to carry further load is compromised, Kayenta allows the material's strength and sti ness to progressively degrade through the evolution of damage to the point of material failure. As material dilatation and damage progress, accommodations are made within Alegra to treat in a consistent manner the evolving state.
Measuring And Explaining The Supersymmetric Lagrangian
Wang, L
2002-01-01
The issues of measuring the supersymmetric Lagrangian once data is available, and making the connections between the low energy effective Lagrangian and fundamental theory, are considered. After a brief introduction to the fundamentals of supersymmetry and overview of Minimal Supersymmetric Standard Model (MSSM), case studies in ways of measuring different parameters in the low energy MSSM Lagrangian are presented. They include: measuring CP violation phases and LSP masses in gluino decay; Higgs production and detection; flavor and CP violation in b → sγ processes; signature of cold dark matter in the cosmic rays. Potential ambiguities in the process of recovering the high energy effective Lagrangian from low energy data are discussed. A new basis, which is explicitly independent of unphysical parameters, is proposed to write the renormalization group equations. After a brief survey of some basic issues of string theory phenomenology, a string theory motivated Pati-Salam like model is const...
Multi-Lagrangians for Integrable Systems
Nutku, Y
2001-01-01
We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit $N$-fold first order local Hamiltonian structure can be cast into variational form with $2N-1$ Lagrangians which will be local functionals of Clebsch potentials. Furthermore we construct a new Lagrangian for polytropic gas dynamics in 1+1 dimensions which is a {\\it local} functional of the physical field variables, namely density and velocity.
Effective Lagrangians and Light Gravitino Phenomenology
Luty, M A; Luty, Markus A.; Ponton, Eduardo
1998-01-01
We construct the low-energy effective lagrangian for supersymmetry breaking models with a light gravitino. Our effective lagrangian is written in terms of the spin-1/2 Goldstino (the longitudinal component of the gravitino) transforming under a non-linear realization of supersymmetry. The Goldstino is derivatively coupled. We use this lagrangian to place bounds on the supersymmetry breaking scale \\sqrt{F} from Goldstino phenomenology. The most stringent bounds come from the coupling of a single photon to Goldstino pairs. For gauge-mediated models, this coupling arises at one loop in the effective lagrangian, and supernova cooling allows \\sqrt{F} > 610 GeV or \\sqrt{F} 140 GeV for tan\\beta = 2.
Detecting Lagrangian fronts with favourable fishery conditions
Prants, S V; Uleysky, M Yu
2012-01-01
Lagrangian fronts in the ocean delineate boundaries between surface waters with different Lagrangian properties. They can be accurately detected in a given velocity field by computing synoptic maps of the drift of synthetic tracers, their Lyapunov exponents, and other Lagrangian indicators. Using Russian ship's catch and location data for a number of commercial fishing seasons in the region of the northwest Pacific with one of the richest fishery in the world, it is shown that the saury fishing grounds with maximal catches are located mainly along those Lagrangian fronts where productive cold waters of the Oyashio Current, warmer waters of the southern branch of the Soya Current, and waters of warm-core Kuroshio rings converge. Computation of those fronts with the altimetric geostrophic velocity fields both in the years with the First and Second Oyashio Intrusions shows that in spite of different oceanographic conditions in both the cases the front locations may serve good indicators of potential fishing grou...
On invariant sets in Lagrangian graphs
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this exposition, we show that the Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are sufficiently smooth. We also provide some counterexamples to show that if the Hamiltonian function is not smooth enough, then it may be non-constant on a compact invariant connected subset which lies in a Lagrangian graph.
Lagrangian Formulation of Todorov-Komar Model
Gomis, J.; Kamimura, K.; Pons, J. M.
1984-05-01
The multi-temporal Hamiltonian model of relativistic particle interaction (Todorov-Komar model) is studied from the viewpoint of the Lagrangian formalism. The action is constructed and the gauge structure is clarified.The mathematical coordinates used to describe the Lagrangian are not gauge invariant and are disqualified as the physical coordinates of the interacting particles. The position of the particles is defined as the function of the canonical variables so that the world lines are invariant under the gauge transformations.
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.
Bird impact at aircraft structure - Damage analysis using Coupled Euler Lagrangian Approach
Smojver, I.; Ivancevic, D.
2010-06-01
Numerical bird strike damage prediction procedure has been applied on the very detailed large airplane secondary structure consisting of sandwich, composite and metallic structural items. The impacted inboard flap finite element model is modelled using 3D, shell and continuum shell elements, coupled with appropriate kinematic constraints. The bird has been modelled using Coupled Euler Lagrangian approach, in order to avoid the numerical difficulties connected with mesh distortion. Various failure modes, such as Carbon Fibre Reinforced Plastics (CFRP) face layer rupture, failure of composite matrix, damage initiation / evolution in the sandwich structure Nomex core and elastoplastic failure of a metallic structure have been investigated. Besides, general contact has been applied as to efficiently capture the contact between Eulerian bird material and the structure, as well as large deformations of the different structural components. Compared to the classic Lagrangian modelling of the bird, the analysis has proven to be more stable, and the results, such as damage areas, physically more realistic. The impact has been applied in the area that is the most probably subjected to the impact damage during exploitation.
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.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding
Energy Technology Data Exchange (ETDEWEB)
Krause, Katharina; Klopper, Wim, E-mail: klopper@kit.edu [Karlsruhe Institute of Technology (KIT), Institute of Physical Chemistry, Theoretical Chemistry Group, KIT Campus South, P.O. Box 6980, 76049 Karlsruhe (Germany)
2016-01-28
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.
Solomenko, Z; Fourati, Manel; Larachi, Faical; Boyer, Christophe; Augier, Frédéric
2015-01-01
Liquid spreading in gas-liquid concurrent trickle-bed reactors is simulated using an Eulerian twofluid CFD approach. In order to propose a model that describes exhaustively all interaction forces acting on each fluid phase with an emphasis on dispersion mechanisms, a discussion of closure laws available in the literature is proposed. Liquid dispersion is recognized to result from two main mechanisms: capillary and mechanical (Attou and Ferschneider, 2000; Lappalainen et al., 2009- The proposed model is then implemented in two trickle-bed configurations matching with two experimental set ups: In the first configuration, simulations on a 2D axisymmetric geometry are considered and the model is validated upon a new set of experimental data. Overall pressure drop and liquid distribution obtained from $\\gamma$-ray tomography are provided for different geometrical and operating conditions. In the second configuration, a 3D simulation is considered and the model is compared to experimental liquid flux patterns at th...
Wilson loops with arbitrary charges
Korcyl, Piotr; Wosiek, Jacek
2014-01-01
We discuss how to implement, in lattice gauge theories, external charges which are not commensurate with an elementary gauge coupling. It is shown that an arbitrary, real power of a standard Wilson loop (or Polyakov line) can be defined and consistently computed in lattice formulation of non-abelian, two dimensional gauge theories. However, such an observable can excite quantum states with integer fluxes only. Since the non-integer fluxes are not in the spectrum of the theory they cannot be created, no matter which observable is chosen. Also the continuum limit of above averages does not exist unless the powers in question are in fact integer. On the other hand, a new continuum limit exists, which is rather intuitive, and where above observables make perfect sense and lead to the string tension proportional to the square of arbitrary (non necessary commensurate with gauge coupling) charge.
Arbitrary bending plasmonic light waves.
Epstein, Itai; Arie, Ady
2014-01-17
We demonstrate the generation of self-accelerating surface plasmon beams along arbitrary caustic curvatures. These plasmonic beams are excited by free-space beams through a two-dimensional binary plasmonic phase mask, which provides the missing momentum between the two beams in the direction of propagation and sets the required phase for the plasmonic beam in the transverse direction. We examine the cases of paraxial and nonparaxial curvatures and show that this highly versatile scheme can be designed to produce arbitrary plasmonic self-accelerating beams. Several different plasmonic beams, which accelerate along polynomial and exponential trajectories, are demonstrated both numerically and experimentally, with a direct measurement of the plasmonic light intensity using a near-field scanning optical microscope.
Arbitrary Bending Plasmonic Light Waves
Epstein, Itai
2013-01-01
We demonstrate the generation of self-accelerating surface plasmon beams along arbitrary caustic curvatures. These plasmonic beams are excited by free-space beams through a two-dimensional binary plasmonic phase mask, which provides the missing momentum between the two beams in the direction of propagation, and sets the required phase for the plasmonic beam in the transverse direction. We examine the cases of paraxial and non-paraxial curvatures and show that this highly versatile scheme can be designed to produce arbitrary plasmonic self-accelerating beams. Several different plasmonic beams, which accelerate along polynomial and exponential trajectories, are demonstrated both numerically and experimentally, with a direct measurement of the plasmonic light intensity using a near-field-scanning-optical-microscope.
Wavefunctions for Particles with Arbitrary Spin
Institute of Scientific and Technical Information of China (English)
HUANG Shi-Zhong; RUAN Tu-Nan; WU Ning; ZHENG Zhi-Peng
2002-01-01
By solving rigorously the relativistic wave equations derived bom Bargmann-Wigner equation for arbitrary spin, the relativistic w avefunctions in momentum representation for particles with arbitrary spin are deduced.
Lifshitz black holes with arbitrary dynamical exponent in Horndeski theory
Bravo-Gaete, Moises
2013-01-01
In arbitrary dimensions, we consider a particular Horndeski action given by the Einstein-Hilbert Lagrangian with a cosmological constant term, while the source part is described by a real scalar field with its usual kinetic term together with a nonminimal kinetic coupling. For this model, whose field equations are of second-order, we report a class of Lifshitz black hole solutions with arbitrary dynamical exponents z. The solutions depend on a unique constant of integration with a scalar field that can not be switched off, and the signs of the coupling constants must be fixed in a precise way. In the second part, we show that this model also supports Lifshitz black hole solutions with a time-dependent scalar field only for a special value of the dynamical exponent z=1/3. In this case, the configuration has an additional constant of integration which allows to leave free the signs of the coupling constants. Remarkably, in three dimensions, there are no restrictions on the dynamical exponent, and Lifshitz black...
Eulerian Air Traffic Flow Management Agent for the ACES Software Project
National Aeronautics and Space Administration — The development of an Eulerian model based en route traffic flow management agent for the ACES software is proposed. The proposed research will use a...
Eulerian simulation of sedimentation flows in vertical and inclined vessels
Institute of Scientific and Technical Information of China (English)
Wu Chun-Liang; Zhan Jie-Min
2005-01-01
Sedimentation of particles in inclined and vertical vessels in numerically simulated using a finite volume method where the Eulerian multiphase model is applied. The particulate phase as well as the fluid phase is regarded as a continuum while the viscosity and solid stress of the particulate phase are modelled by the kinetic theory of granular flows. The numerical results show an interesting phenomenon of the emergence of two circulation vortices of the sedimentation flow in a vertical vessel but only one in the inclined vessel. Several sensitivity tests are simulated to understand the factors that influence the dual-vortex flow structure in vertical sedimentation. Result show that a larger fluid viscosity makes the two vortex centres much closer to each other and the boundary layer effect at lateral walls is the key factor to induce this phenomenon. In the fluid boundary layer particles settle down more rapidly and drag the local carrier fluid to flow downward near the lateral walls and thus form the dual-vortex flow pattern.
Micro Expression Recognition Using the Eulerian Video Magnification Method
Directory of Open Access Journals (Sweden)
Elham Zarezadeh
2016-08-01
Full Text Available In this paper we propose a new approach for facial micro expressions recognition. For this purpose the Eulerian Video Magnification (EVM method is used to retrieve the subtle motions of the face. The results of this method are obtained as in the magnified images sequence. In this study the numerical tests are performed on two databases: Spontaneous Micro expression (SMIC and Category and Sourcing Managers Executive (CASME. We evaluate our proposed method in two phases using the eigenface method. In phase 1 we recognize the type of a micro expression, for example emotional versus unemotional in SMIC database. Phase 2 classifies the recognized micro expression as negative versus positive in SMIC database and happiness versus disgust in CASME database. The results show that the eigenface method by the EVM method for the retrieval of subtle motions of the face increases the performance of micro expression recognition. Moreover, the proposed approach is more accurate and promising than the previous works in micro expressions recognition.
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
Lagrangian Methods Of Cosmic Web Classification
Fisher, J D; Johnson, M S T
2015-01-01
The cosmic web defines the large scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. (2012) is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or halos) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian nature admits a straight forward inclusion of the Hubble flow negating the necessity of a visually defined thresh...
Lagrangians for the W-Algebra Models
Gaite, J C
1994-01-01
The field algebra of the minimal models of W-algebras is amenable to a very simple description as a polynomial algebra generated by few elementary fields, corresponding to order parameters. Using this description, the complete Landau-Ginzburg lagrangians for these models are obtained. Perturbing these lagrangians we can explore their phase diagrams, which correspond to multicritical points with $D_n$ symmetry. In particular, it is shown that there is a perturbation for which the phase structure coincides with that of the IRF models of Jimbo et al.
Effective Lagrangian in de Sitter Spacetime
Kitamoto, Hiroyuki
2016-01-01
Scale invariant fluctuations of metric are universal feature of quantum gravity in de Sitter spacetime. We construct an effective Lagrangian which summarizes their implications on local physics by integrating super-horizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective Lagrangian as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.
The Mather problem for lower semicontinuous Lagrangians
Gomes, Diogo A.
2013-08-01
In this paper we develop the Aubry-Mather theory for Lagrangians in which the potential energy can be discontinuous. Namely we assume that the Lagrangian is lower semicontinuous in the state variable, piecewise smooth with a (smooth) discontinuity surface, as well as coercive and convex in the velocity. We establish existence of Mather measures, various approximation results, partial regularity of viscosity solutions away from the singularity, invariance by the Euler-Lagrange flow away from the singular set, and further jump conditions that correspond to conservation of energy and tangential momentum across the discontinuity. © 2013 Springer Basel.
Learn the Lagrangian: A Vector-Valued RKHS Approach to Identifying Lagrangian Systems.
Cheng, Ching-An; Huang, Han-Pang
2016-12-01
We study the modeling of Lagrangian systems with multiple degrees of freedom. Based on system dynamics, canonical parametric models require ad hoc derivations and sometimes simplification for a computable solution; on the other hand, due to the lack of prior knowledge in the system's structure, modern nonparametric models in machine learning face the curse of dimensionality, especially in learning large systems. In this paper, we bridge this gap by unifying the theories of Lagrangian systems and vector-valued reproducing kernel Hilbert space. We reformulate Lagrangian systems with kernels that embed the governing Euler-Lagrange equation-the Lagrangian kernels-and show that these kernels span a subspace capturing the Lagrangian's projection as inverse dynamics. By such property, our model uses only inputs and outputs as in machine learning and inherits the structured form as in system dynamics, thereby removing the need for the mundane derivations for new systems as well as the generalization problem in learning from scratches. In effect, it learns the system's Lagrangian, a simpler task than directly learning the dynamics. To demonstrate, we applied the proposed kernel to identify the robot inverse dynamics in simulations and experiments. Our results present a competitive novel approach to identifying Lagrangian systems, despite using only inputs and outputs.
Directory of Open Access Journals (Sweden)
I. Wohltmann
2010-06-01
Full Text Available ATLAS is a new global Lagrangian Chemistry and Transport Model (CTM, which includes a stratospheric chemistry scheme with 46 active species, 171 reactions, heterogeneous chemistry on polar stratospheric clouds and a Lagrangian denitrification module. Lagrangian (trajectory-based models have several important advantages over conventional Eulerian models, including the absence of spurious numerical diffusion, efficient code parallelization and no limitation of the largest time step by the Courant-Friedrichs-Lewy criterion. This work describes and validates the stratospheric chemistry scheme of the model. Stratospheric chemistry is simulated with ATLAS for the Arctic winter 1999/2000, with a focus on polar ozone depletion and denitrification. The simulations are used to validate the chemistry module in comparison with measurements of the SOLVE/THESEO 2000 campaign. A Lagrangian denitrification module, which is based on the simulation of the nucleation, sedimentation and growth of a large number of polar stratospheric cloud particles, is used to model the substantial denitrification that occured in this winter.
Directory of Open Access Journals (Sweden)
I. Wohltmann
2010-11-01
Full Text Available ATLAS is a new global Lagrangian Chemistry and Transport Model (CTM, which includes a stratospheric chemistry scheme with 46 active species, 171 reactions, heterogeneous chemistry on polar stratospheric clouds and a Lagrangian denitrification module. Lagrangian (trajectory-based models have several important advantages over conventional Eulerian models, including the absence of spurious numerical diffusion, efficient code parallelization and no limitation of the largest time step by the Courant-Friedrichs-Lewy criterion. This work describes and validates the stratospheric chemistry scheme of the model. Stratospheric chemistry is simulated with ATLAS for the Arctic winter 1999/2000, with a focus on polar ozone depletion and denitrification. The simulations are used to validate the chemistry module in comparison with measurements of the SOLVE/THESEO 2000 campaign. A Lagrangian denitrification module, which is based on the simulation of the nucleation, sedimentation and growth of a large number of polar stratospheric cloud particles, is used to model the substantial denitrification that occured in this winter.
Finite BRST–antiBRST transformations in Lagrangian formalism
Energy Technology Data Exchange (ETDEWEB)
Moshin, Pavel Yu., E-mail: moshin@rambler.ru [Department of Physics, Tomsk State University, 634050 (Russian Federation); Reshetnyak, Alexander A., E-mail: reshet@ispms.tsc.ru [Institute of Strength Physics and Materials Science, Siberian Branch of Russian Academy of Sciences, 634021, Tomsk (Russian Federation); Tomsk State Pedagogical University, 634061 (Russian Federation)
2014-12-12
We continue the study of finite BRST–antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [1], with a doublet λ{sub a}, a=1,2, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant λ{sub a}. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian (proved to be correct in [31]) for finite field-dependent BRST–antiBRST transformations with functionally-dependent parameters, λ{sub a}=s{sub a}Λ, induced by a finite even-valued functional Λ(ϕ,π,λ) and by the generators s{sub a} of BRST–antiBRST transformations, acting in the space of fields ϕ, antifields ϕ{sub a}{sup *},ϕ{sup ¯} and auxiliary variables π{sup a},λ. On the basis of this Jacobian, we present and solve a compensation equation for Λ, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities, containing the parameters λ{sub a}, and study the problem of gauge-dependence. The general approach is exemplified by the Freedman–Townsend model of a non-Abelian antisymmetric tensor field.
Finite BRST–antiBRST transformations in Lagrangian formalism
Directory of Open Access Journals (Sweden)
Pavel Yu. Moshin
2014-12-01
Full Text Available We continue the study of finite BRST–antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [1], with a doublet λa, a=1,2, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant λa. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian (proved to be correct in [31] for finite field-dependent BRST–antiBRST transformations with functionally-dependent parameters, λa=saΛ, induced by a finite even-valued functional Λ(ϕ,π,λ and by the generators sa of BRST–antiBRST transformations, acting in the space of fields ϕ, antifields ϕa⁎,ϕ¯ and auxiliary variables πa,λ. On the basis of this Jacobian, we present and solve a compensation equation for Λ, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities, containing the parameters λa, and study the problem of gauge-dependence. The general approach is exemplified by the Freedman–Townsend model of a non-Abelian antisymmetric tensor field.
Lagrangian theoretical framework of dynamics of nonholonomic systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
@@ By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.
Lagrangian theoretical framework of dynamics of nonholonomic systems
Institute of Scientific and Technical Information of China (English)
LIANG; LiFu
2007-01-01
By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right. ……
On Stability of the Mechanical Lagrangian Systems
Directory of Open Access Journals (Sweden)
Valer Niminet
2011-12-01
Full Text Available
We consider MLS (mechanical Lagrangian systems with
external forces. We give some conditions of stability and dissipativity and show that the energy of the system decreases on the integral curves.
Key words: LMS, stability, dissipative system.
Lagrangian tetragons and instabilities in Hamiltonian dynamics
Entov, Michael; Polterovich, Leonid
2017-01-01
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.
Experimental design for drifting buoy Lagrangian test
Saunders, P. M.
1975-01-01
A test of instrumentation fabricated to measure the performance of a free drifting buoy as a (Lagrangian) current meter is described. Specifically it is proposed to distinguish between the trajectory of a drogued buoy and the trajectory of the water at the level of the drogue by measuring the flow relative to the drogue.
Towards effective Lagrangians for adelic strings
Dragovich, Branko
2009-01-01
p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By this way, one can consider adelic strings as a very useful instrument in the further investigation of modern string theory. It is remarkable that for some scalar p-adic strings exist effective Lagrangians, which are based on real instead of p-adic numbers and describe not only four-point scattering amplitudes but also all higher ones at the tree level. In this work, starting from p-adic Lagrangians, we consider some approaches to construction of effective field Lagrangians for p-adic sector of adelic strings. It yields Lagrangians for nonlinear and nonlocal scalar field theory, where spacetime nonlocality is determined by an infinite number of derivatives contained in the operator-valued Riemann zeta function. Owing to the Riemann zeta function in the dynamics of these sca...
A new semi-Lagrangian difference scheme
Institute of Scientific and Technical Information of China (English)
季仲贞; 陈嘉滨
2001-01-01
A new completely energy-conserving semi-Lagrangian scheme is constructed. The numerical solution of shallow water equation shows that this conservative scheme preserves the total energy in twelve significant digits, while the traditional scheme does only in five significant digits.
Lagrangian duality and cone convexlike functions
J.B.G. Frenk (Hans); G. Kassay
2005-01-01
textabstractIn this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation s
Lagrangian duality and cone convexlike functions
J.B.G. Frenk (Hans); G. Kassay
2005-01-01
textabstractIn this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation
Doisneau, François; Arienti, Marco; Oefelein, Joseph C.
2017-01-01
For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier-Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle-particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.
Energy Technology Data Exchange (ETDEWEB)
Doisneau, François, E-mail: fdoisne@sandia.gov; Arienti, Marco, E-mail: marient@sandia.gov; Oefelein, Joseph C., E-mail: oefelei@sandia.gov
2017-01-15
For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier–Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle–particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.
Target Lagrangian kinematic simulation for particle-laden flows
Murray, S.; Lightstone, M. F.; Tullis, S.
2016-09-01
The target Lagrangian kinematic simulation method was motivated as a stochastic Lagrangian particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target Lagrangian integral timescale. In addition to recovering the expected Lagrangian properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark.
Arbitrary Inequality in Reputation Systems
Frey, Vincenz; van de Rijt, Arnout
2016-12-01
Trust is an essential condition for exchange. Large societies must substitute the trust traditionally provided through kinship and sanctions in small groups to make exchange possible. The rise of internet-supported reputation systems has been celebrated for providing trust at a global scale, enabling the massive volumes of transactions between distant strangers that are characteristic of modern human societies. Here we problematize an overlooked side-effect of reputation systems: Equally trustworthy individuals may realize highly unequal exchange volumes. We report the results of a laboratory experiment that shows emergent differentiation between ex ante equivalent individuals when information on performance in past exchanges is shared. This arbitrary inequality results from cumulative advantage in the reputation-building process: Random initial distinctions grow as parties of good repute are chosen over those lacking a reputation. We conjecture that reputation systems produce artificial concentration in a wide range of markets and leave superior but untried exchange alternatives unexploited.
electrode of an arbitrary shape
Directory of Open Access Journals (Sweden)
P. A. Krutitskii
1999-01-01
Full Text Available A problem on electric current in a semiconductor film from an electrode of an arbitrary shape is studied in the presence of a magnetic field. This situation describes the Hall effect, which indicates the deflection of electric, current from electric field in a semiconductor. From mathematical standpoint we consider the skew derivative problem for harmonic functions in the exterior of an open arc in a plane. By means of potential theory the problem is reduced to the Cauchy singular integral equation and next to the Fredholm equation of the 2nd kind which is uniquely solvable. The solution of the integral equation can be computed by standard codes by discretization and inversion of the matrix. The uniqueness and existence theorems are formulated.
Classification of Lagrangian Fibrations over a Klein Bottle
Sepe, D
2009-01-01
This paper completes the classification of regular Lagrangian fibratiopns over compact surfaces. \\cite{misha} classifies regular Lagrangian fibrations over $\\mathbb{T}^2$. The main theorem in \\cite{hirsch} is used in order to classify integral affine structures on the Klein bottle $K^2$ and, hence, regular Lagrangian fibrations over this space.
Lagrangian multiplier and massive Yang-Mills fields
Energy Technology Data Exchange (ETDEWEB)
Li, Z.P.
1982-09-01
If we give appropriate constraint to the gauge invariant Lagrangian, the variation principle of the action convert to the variational problems with subsidiary condition. The effective Lagrangian which contains Lagrangian multiplier may have the mass term of the mesons. In that case we obtain naturally the massive Yang-Mills fields which was discussed by Nakanishi.
Lagrangian statistics in turbulent channel flow: implications for Lagrangian stochastic models
Stelzenmuller, Nickolas; Polanco, Juan Igancio; Vinkovic, Ivana; Mordant, Nicolas
2016-11-01
Lagrangian acceleration and velocity correlations in statistically one-dimesional turbulence are presented in the context of the development of Lagrangian stochastic models of inhomogeneous turbulent flows. These correlations are measured experimentally by 3D PTV in a high aspect ratio water channel at Reτ = 1450 , and numerically from DNS performed at the same Reynolds number. Lagrangian timescales, key components of Lagrangian stochastic models, are extracted from acceleration and velocity autocorrelations. The evolution of these timescales as a function of distance to the wall is presented, and compared to similar quantities measured in homogeneous isotropic turbulence. A strong dependance of all Lagrangian timescales on wall distance is present across the width of the channel. Significant cross-correlations are observed between the streamwise and wall-normal components of both acceleration and velocity. Lagrangian stochastic models of this flow must therefore retain dependance on the wall-normal coordinate and the components of acceleration and velocity, resulting in significantly more complex models than those used for homogeneous isotropic turbulence. We gratefully acknowledge funding from the Agence Nationale de la Recherche, LabEx Tec 21, and CONICYT Becas Chile.
Classification of Flat Lagrangian Surfaces in Complex Lorentzian Plane
Institute of Scientific and Technical Information of China (English)
Bang-Yen CHEN; Johan FASTENAKELS
2007-01-01
One of the most fundamental problems in the study of Lagrangian submanifolds fromRiemannian geometric point of view is to classify Lagrangian immersions of real space forms intocomplex space forms. The main purpose of this paper is thus to classify flat Lagrangian surfaces inthe Lorentzian complex plane C12. Our main result states that there are thirty-eight families of flatLagrangian surfaces in C12. Conversely, every flat Lagrangian surface in C12 is locally congruent to oneof the thirty-eight families.
Directory of Open Access Journals (Sweden)
M. De Dominicis
2013-03-01
Full Text Available In this paper we use MEDSLIK-II, a Lagrangian marine oil spill model described in Part 1 of this paper (De Dominicis et al., 2013, to simulate oil slick transport and transformation processes for realistic oceanic cases where satellite or drifting buoys data are available for verification. The model is coupled with operational oceanographic currents, atmospheric analyses winds and remote-sensing data for initialization. The sensitivity of the oil spill simulations to several model parameterizations is analyzed and the results are validated using surface drifters and SAR (Synthetic Aperture Radar images in different regions of the Mediterranean Sea. It is found that the forecast skill of Lagrangian trajectories largely depends on the accuracy of the Eulerian ocean currents: the operational models give useful estimates of currents, but high-frequency (hourly and high spatial resolution is required, and the Stokes drift velocity has to be often added, especially in coastal areas. From a numerical point of view, it is found that a realistic oil concentration reconstruction is obtained using an oil tracer grid resolution of about 100 m, with at least 100 000 Lagrangian particles. Moreover, sensitivity experiments to uncertain model parameters show that the knowledge of oil type and slick thickness are, among all the others, key model parameters affecting the simulation results. Considering acceptable for the simulated trajectories a maximum spatial error of the order of three times the horizontal resolution of the Eulerian ocean currents, the predictability skill for particle trajectories is from 1 to 2.5 days depending on the specific current regime. This suggests that re-initialization of the simulations is required every day.
Testing of a new dense gas approach in the Lagrangian Dispersion Model SPRAY.
Mortarini, Luca; Alessandrini, Stefano; Ferrero, Enrico; Anfossi, Domenico; Manfrin, Massimiliano
2013-04-01
A new original method for the dispersion of a positively and negatively buoyant plume is proposed. The buoyant pollutant movement is treated introducing a fictitious scalar inside the Lagrangian Stochastic Particle Model SPRAY. The method is based on the same idea of Alessandrini and Ferrero (Phys. A 388:1375-1387, 2009) for the treatment of a background substance entrainment into the plume. In this application, the fictitious scalar is the density and momentum difference between the plume portions and the environment air that naturally takes into account the interaction between the plume and the environment. As a consequence, no more particles than those inside the plume have to be released to simulate the entrainment of the background air temperature. In this way the entrainment is properly simulated and the plume sink is calculated from the local property of the flow. This new approach is wholly Lagrangian in the sense that the Eulerian grid is only used to compute the propriety of a portion of the plume from the particles contained in every cell. No equation of the bulk plume is solved on a fixed grid. To thoroughly test the turbulent velocity field calculated by the model, the latter is compared with a water tank experiment carried out in the TURLAB laboratory in Turin (Italy). A vertical density driven current was created releasing a saline solution (salt and water) in a water tank with no mean flow. The experiment reproduces in physical similarity, based on the density Froud number, the release of a dense gas in the planetary boundary layer and the Particle Image Velocimetry technique has been used to analyze the buoyancy generated velocity field. The high temporal and spatial resolution of the measurements gives a deep insight to the problems of the bouncing of the dense gas and of the creation of the outflow velocity at the ground.
Synchronous Lagrangian variational principles in General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in relativistic classical field theory which are either asynchronous or synchronous. The historical Einstein-Hilbert and Palatini variational formulations are found to belong to the first category. Nevertheless, it is shown that an alternative route exists which permits one to cast these principles in terms of equivalent synchronous Lagrangian variational formulations. The advantage is twofold. First, synchronous approaches allow one to overcome the lack of gauge symmetry of the asynchronous principles. Second, the property of manifest covariance of the theory is also restored at all levels, including the symbolic Euler-Lagrange equations, with the variational Lagrangian density being now identified with a $4-$scalar. As an application, a joint synchronous variational principle...
A Lagrangian particle level set method
Hieber, Simone E.; Koumoutsakos, Petros
2005-11-01
We present a novel particle level set method for capturing interfaces. The level set equation is solved in a Lagrangian frame using particles that carry the level set information. A key aspect of the method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field. The Lagrangian description of the level set method is inherently adaptive and exact in the case of solid body motions. The efficiency and accuracy of the method is demonstrated in several benchmark problems in two and three dimensions involving pure advection and curvature induced motion of the interface. The simplicity of the particle description is shown to be well suited for real time simulations of surfaces involving cutting and reconnection as in virtual surgery environments.
Multiloop Information from the QED Effective Lagrangian
Dunne, G V; Dunne, Gerald V.; Schubert, Christian
2006-01-01
We obtain information on the QED photon amplitudes at high orders in perturbation theory starting from known results on the QED effective Lagrangian in a constant electric field. A closed-form all-order result for the weak field limit of the imaginary part of this Lagrangian has been given years ago by Affleck, Alvarez and Manton (for scalar QED) and by Lebedev and Ritus (for spinor QED). We discuss the evidence for its correctness, and conjecture an analogous formula for the case of a self-dual field. From this extension we then obtain, using Borel analysis, the leading asymptotic growth for large N of the maximally helicity violating component of the L - loop N - photon amplitude in the low energy limit. The result leads us to conjecture that the perturbation series converges for the on-shell renormalized QED N - photon amplitudes in the quenched approximation.
Lagrangian Vortices in Developing Tropical Cyclones
2015-06-25
cyclones B. Rutherford,a* T. J. Dunkertona and M. T. Montgomeryb aNorthwest Research Associates, Redmond, WA, USA bNaval Postgraduate School, Monterey...article has been contributed to by a US Government employee and his work is in the public domain in the USA. Tracking pre-genesis tropical cyclones is...season. All of the Lagrangian coherent structures that can be identified by this field are shown for developing disturbances and mature cyclones . The
Equivalent Lagrangians: Generalization, Transformation Maps, and Applications
Directory of Open Access Journals (Sweden)
N. Wilson
2012-01-01
Full Text Available Equivalent Lagrangians are used to find, via transformations, solutions and conservation laws of a given differential equation by exploiting the possible existence of an isomorphic algebra of Lie point symmetries and, more particularly, an isomorphic Noether point symmetry algebra. Applications include ordinary differential equations such as the Kummer equation and the combined gravity-inertial-Rossbywave equation and certain classes of partial differential equations related to multidimensional wave equations.
Ocean Model Assessment with Lagrangian Metrics
2016-06-07
Ocean Model Assessment With Lagrangian Metrics” Pearn P. Niiler Scripps Institution of Oceanography 9500 Gilman Drive MC 0213 La Jolla, CA...project are to aid in the development of accurate modeling of upper ocean circulation by using data on circulation observations to test models . These tests...or metrics, will be statistical measures of model and data comparisons. It is believed that having accurate models of upper ocean currents will
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.
Optical arbitrary waveform characterization using linear spectrograms.
Jiang, Zhi; Leaird, Daniel E; Long, Christopher M; Boppart, Stephen A; Weiner, Andrew M
2010-08-01
We demonstrate the first application of linear spectrogram methods based on electro-optic phase modulation to characterize optical arbitrary waveforms generated under spectral line-by-line control. This approach offers both superior sensitivity and self-referencing capability for retrieval of periodic high repetition rate optical arbitrary waveforms.
Lagrangian methods of cosmic web classification
Fisher, J. D.; Faltenbacher, A.; Johnson, M. S. T.
2016-05-01
The cosmic web defines the large-scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid-based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or haloes) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian nature admits a straightforward inclusion of the Hubble flow negating the necessity of a visually defined threshold value which is commonly employed by grid-based classification methods.
Inverse Variational Problem for Nonstandard Lagrangians
Saha, A.; Talukdar, B.
2014-06-01
In the mathematical physics literature the nonstandard Lagrangians (NSLs) were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of the equation of motion and solve the associated inverse problem to obtain some of the existing results for NSLs. In addition, we provide a number of alternative Lagrangian representations. The case studies envisaged by us include (i) the usual modified Emden-type equation, (ii) Emden-type equation with dissipative term quadratic in velocity, (iii) Lotka-Volterra model and (vi) a number of the generic equations for dissipative-like dynamical systems. Our method works for nonstandard Lagrangians corresponding to the usual action integral of mechanical systems but requires modification for those associated with the modified actions like S =∫abe L(x ,x˙ , t) dt and S =∫abL 1 - γ(x ,x˙ , t) dt because in the latter case one cannot construct expressions for the Jacobi integrals.
Lagrangian approach and dissipative magnetic systems
Energy Technology Data Exchange (ETDEWEB)
Bose, Thomas, E-mail: thomas.bose@physik.uni-halle.de [Martin-Luther-University, Physics Department, Von-Seckendorff-Platz 1, 06114 Halle (Germany); Trimper, Steffen, E-mail: steffen.trimper@physik.uni-halle.de [Martin-Luther-University, Physics Department, Von-Seckendorff-Platz 1, 06114 Halle (Germany)
2011-06-13
A Lagrangian is introduced which includes the coupling between magnetic moments m and the degrees of freedom σ of a reservoir. In case the system-reservoir coupling breaks the time reversal symmetry the magnetic moments perform a damped precession around an effective field which is self-organized by the mutual interaction of the moments. The resulting evolution equation has the form of the Landau-Lifshitz-Gilbert equation. In case the bath variables are constant vector fields the moments m fulfill the reversible Landau-Lifshitz equation. Applying Noether's theorem we find conserved quantities under rotation in space and within the configuration space of the moments. -- Highlights: → We propose a new approach for describing magnetic systems with dissipation on a mesoscopic scale. → The Lagrangian consists of an active magnetic system and a bath. → The coupling between both subsystems breaks the time reversal symmetry. → The suggested Lagrangian leads to the Landau-Lifshitz equation with damping. → We consider symmetry operations by means of Noether's theorem.
Applications the Lagrangian description in aperiodic flows
Mendoza, Carolina; Mancho, Ana Maria
2012-11-01
We use several recently developed Lagrangian tools for describing transport in general aperiodic flows. In our approach the first step is based in a Lagrangian descriptor (the so called function M). It measures the length of particle trajectories on the ocean surface over a given interval of time. We describe its output over satellite altimetry data on the Kuroshio current. The technique is combined with the direct computation of manifolds of Distinguished Hyperbolic trajectories and a very detailed description of transport is achieved across an eddy and a jet on the Kuroshio current,. A second velocity data set is examined with the M function tool. These are obtained from the HYCOM project on the Gulf of Mexico during the time of the oil-spill. We have identified underlying Lagrangian structures and dynamics. We acknowledge to the hospitality of the university of Delaware and the assistance of Bruce Lipphardt and Helga Huntley in accessing the model data sets. We acknowledge to the grants: UPM-AL12-PAC-09, Becas de Movilidad de Caja Madrid 2011, MTM2011-26696 and ILINK-0145.
A Lagrangian-Lagrangian Model for Two-Phase Bubbly Flow around Circular Cylinder
Directory of Open Access Journals (Sweden)
M. Shademan
2014-06-01
Full Text Available A Lagrangian-Lagrangian model is developed using an in-house code to simulate bubble trajectory in two-phase bubbly flow around circular cylinder. Random Vortex Method (RVM which is a Lagrangian approach is used for solving the liquid phase. The significance of RVM relative to other RANS/LES methods is its capability in directly modelling the turbulence. In RVM, turbulence is modeled by solving the vorticity transport equation and there is no need to use turbulence closure models. Another advantage of RVM relative to other CFD approaches is its independence from mesh generation. For the bubbles trajectory, equation of motion of bubbles which takes into account effect of different forces are coupled with the RVM. Comparison of the results obtained from current model with the experimental data confirms the validity of the model. Effect of different parameters including flow Reynolds number, bubble diameter and injection point on the bubbles' trajectory are investigated. Results show that increase in the Reynolds number reduces the rising velocity of the bubbles. Similar behavior is observed for the bubbles when their diameter was decreased. According to the analysis carried out, present Lagrangian-Lagrangian model solves the issues of mesh generation and turbulence modelling which exist in common two phase flow modelling schemes.
Fisher, R.; Lamb, D.; Kadanoff, L.; Cattaneo, F.; Constantin, P.; Plewa, T.
2006-11-01
When simulating turbulence with complex or embedded geometries, or which transitions from incompressible to weakly-compressible, it is desirable to have a robust numerical method which is equally capable of handling these regimes without significant loss of accuracy. The FLASH 2006 turbulence simulation is a driven, weakly-compressible, homogeneous, isotropic simulation which explores this concept in detail. It was performed at 1856^3 resolution with 16.7 million Lagrangian tracer particles at a (1D) RMS velocity of 0.17. The simulation was performed by special invitation on the LLNL BG/L machine shortly before it was permanently placed inside their secure network earlier this year. Approximately one week of CPU time on 65,536 processors were used. We will present results including both Eulerian and Lagrangian properties of the simulation, and compare these to previous experiments and theories. We will also discuss a systematic error in the determination of the higher-order structure functions due to finite statistics and address this issue for our dataset.
A small 50 K cooling device for a quarter-circle Eulerian cradle diffractometer
Energy Technology Data Exchange (ETDEWEB)
Zobel, D.; Luger, P. (Freie Univ. Berlin (Germany, F.R.). Inst. fuer Kristallographie)
1990-06-01
A one-stage He refrigerator (Displex CS1003) has been modified and installed on a quarter-circle Eulerian cradle of 250 mm diameter (AED Siemens) and has been operated down to 50 K. The mechanical interface, which can easily be mounted, is described as well as some alignment problems. The device is suitable for any Eulerian cradle 250 mm or larger. Structure redeterminations of two organic compounds were carried out at 52 K. R values of 2.2 and 3.6% were obtained and proved the quality of this set up. (orig.).
Dynamics of Multibody Systems Near Lagrangian Points
Wong, Brian
This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the Lagrangian points of a Circular Restricted Three-Body System. The spacecraft system is arranged in a wheel-spoke configuration with smaller and less massive satellites connected to a central hub using truss/beams or tether connectors. The kinematics of the system is first defined, and the kinetic, gravitational potential energy and elastic potential energy of the system are derived. The Assumed Modes Method is used to discretize the continuous variables of the system, and a general set of ordinary differential equations describing the dynamics of the connectors and the central hub are obtained using the Lagrangian method. The flexible body dynamics of the tethered and truss connected systems are examined using numerical simulations. The results show that these systems experienced only small elastic deflections when they are naturally librating or rotating at moderate angular velocities, and these deflections have relatively small effect on the attitude dynamics of the systems. Based on these results, it is determined that the connectors can be modeled as rigid when only the attitude dynamics of the system is of interest. The equations of motion of rigid satellites stationed at the Lagrangian points are linearized, and the stability conditions of the satellite are obtained from the linear equations. The required conditions are shown to be similar to those of geocentric satellites. Study of the linear equations also revealed the resonant conditions of rigid Lagrangian point satellites, when a librational natural frequency of the satellite matches the frequency of its station-keeping orbit leading to large attitude motions. For tethered satellites, the linear analysis shows that the tethers are in stable equilibrium when they lie along a line joining the two primary celestial bodies of the Three-Body System. Numerical simulations are used to study the long term
Comparison of Semi-Lagrangian Algorithms for Solving Vlasov-type Equations
Brunner, Stephan
2005-10-01
In view of pursuing CRPP's effort in carrying out gyrokinetic simulations using an Eulerian-type approach [M. Brunetti et. al, Comp. Phys. Comm. 163, 1 (2004)], different alternative algorithms have been considered. The issue is to identify the most appropriate time-stepping scheme, both from a point of view of numerical accuracy and numerical efficiency. Our efforts have concentrated on two semi-Lagrangian approaches: The widely used cubic B-spline interpolation scheme, based on the original work of Cheng and Knorr [C. Z. Cheng and G. Knorr, J. Comp. Phys. 22, 330 (1976)], as well as the Cubic Interpolation Propagation (CIP) scheme, based on cubic Hermite interpolation, which has only more recently been applied for solving Vlasov-type equations [T. Nakamura and T. Yabe, Comp. Phys. Comm. 120, 122 (1999)]. The systematic comparison of these algorithms with respect to their basic spectral (diffusion/dispersion) properties, as well as their ability to avoid the overshoot (Gibbs) problem, is first presented. Results from solving a guiding-center model of the two-dimensional Kelvin-Helmholtz instability are then compared. This test problem enables to address some of the key technical issues also met with the more complex gyrokinetic-type equations.
Lagrangian Approach to Jet Mixing and Optimization of the Reactor for Production of Carbon Nanotubes
Povitsky, Alex; Salas, Manuel D.
2001-01-01
This study was motivated by an attempt to optimize the High Pressure carbon oxide (HiPco) process for the production of carbon nanotubes from gaseous carbon oxide, The goal is to achieve rapid and uniform heating of catalyst particles by an optimal arrangement of jets. A mixed Eulerian and Lagrangian approach is implemented to track the temperature of catalyst particles along their trajectories as a function of time. The FLUENT CFD software with second-order upwind approximation of convective terms and an algebraic multigrid-based solver is used. The poor performance of the original reactor configuration is explained in terms of features of particle trajectories. The trajectories most exposed to the hot jets appear to be the most problematic for heating because they either bend towards the cold jet interior or rotate upwind of the mixing zone. To reduce undesirable slow and/or oscillatory heating of catalyst particles, a reactor configuration with three central jets is proposed and the optimal location of the central and peripheral nozzles is determined.
Numerical Simulation of Friction Stir Welding by Natural Element Methods
Alfaro, I.; Fratini, L.; CUETO, Elias; Chinesta, Francisco
2009-01-01
International audience; In this work we address the problem of numerically simulating the Friction Stir Welding process. Due to the special characteristics of this welding method (i.e., high speed of the rotating pin, very large deformations, etc.) finite element methods (FEM) encounter several difficulties. While Lagrangian simulations suffer from mesh distortion, Eulerian or Arbitrary Lagrangian Eulerian (ALE) ones still have difficulties due to the treatment of convective terms, the treatm...
Spherical Gravitating Systems of Arbitrary Dimension
Das, A
2001-01-01
We study spherically symmetric solutions to the Einstein field equations under the assumption that the space-time may possess an arbitrary number of spatial dimensions. The general solution of Synge is extended to describe systems of any dimension. Arbitrary dimension analogues of known four dimensional solutions are also presented, derived using the above scheme. Finally, we discuss the requirements for the existence of Birkhoff's theorems in space-times of arbitrary dimension with or without matter fields present. Cases are discussed where the assumptions of the theorem are considerably weakened yet the theorem still holds. We also discuss where the weakening of certain conditions may cause the theorem to fail.
Numerical uncertainty at mesoscale in a Lagrangian model in complex terrain
Brioude, Jerome; Angevine, Wayne; McKeen, Stuart; Hsie, Eirh Yu
2013-04-01
Recently, it has been shown that mass conservation in Lagrangian models is improved by using time-average winds out of Eulerian models. In this study, we evaluate the mass conservation and trajectory uncertainties in complex terrain at mesoscale using the FLEXPART Lagrangian particle dispersion model coupled with the WRF mesoscale model. The specific form of vertical wind used is found to have a large effect. Time average wind with time average sigma dot, instantaneous wind with geometric cartesian vertical wind (w) and instantaneous wind with sigma dot are used to simulate mixing ratios of a passive tracer in forward and backward runs using different time interval outputs and horizontal resolutions in California. Mass conservation in the FLEXPART model was not an issue when using time-average wind or instantaneous wind with sigma dot. However, mass was poorly conserved using instantaneous wind with w, with a typical variation of 25% within 24 h. Uncertainties in surface residence time (a backtrajectory product commonly used in source receptor studies or inverse modeling) calculated for each backtrajectory run were also analyzed. The smallest uncertainties were systematically found when using time-average wind. Uncertainties using instantaneous wind with sigma dot were slightly larger, as long as the time interval of output was sufficiently small. The largest uncertainties were found when using instantaneous wind with w. Those uncertainties were found to be linearly correlated with the local average gradient of orography. Differences in uncertainty were much smaller when trajectories were calculated over flat terrain. For a typical run at mesoscale in complex terrain, 4 km horizontal resolution and 1 h time interval output, the average uncertainty and bias in surface residence time is, respectively, 8.4% and -2.5% using time-average wind, and 13% and -3.7% using instantaneous wind with sigma dot in complex terrain. The corresponding values for instantaneous wind
Eulerian simulation of the perforation of aluminum plates by nondeforming projectiles
Energy Technology Data Exchange (ETDEWEB)
Silling, S.A.
1992-03-01
A new algorithm for the treatment of sliding interfaces between solids with or without friction in an Eulerian wavecode is described. The algorithm has been implemented in the two-dimensional version of the CTH code. The code was used to simulate penetration and perforation of aluminum plates by rigid, conical-nosed tungsten projectiles. Comparison with experimental data is provided.
Modelling of Non-Spherical Particle Evolution for Ice Crystals Simulation with an Eulerian Approach
Iuliano, E.; Montreuil, E.; Norde, Ellen; van der Weide, Edwin Theodorus Antonius; Hoeijmakers, Hendrik Willem Marie
2015-01-01
In this study a comparison is made between results from three Eulerian-based computational methods that predict the ice crystal trajectories and impingement on a NACA-0012 airfoil. The computational methods are being developed within CIRA (Imp2D/3D), ONERA (CEDRE/Spiree) and University of Twente
A Geometrical Way to Sum Powers by Means of Tetrahedrons and Eulerian Numbers
Barra, Mario
2011-01-01
We geometrically prove that in a d-dimensional cube with edges of length n, the number of particular d-dimensional tetrahedrons are given by Eulerian numbers. These tetrahedrons tassellate the cube, In this way the sum of the cubes are the sums of the tetrahedrons, whose calculation is trivial.
Lagrangian Coherent Structures in the Trieste Gulf
Besio, G.; Enrile, F.; Magaldi, M. G.; Mantovani, C.; Cosoli, S.; Gerin, R.; Poulain, P. M.
2013-12-01
One serious issue in Environmental Science and Engineering concerns the prediction of the fate of contaminants released in a water body. A possible way to tackle this problem consists in forecasting pollutant trajectories from velocity-field data sets obtained by measurements or numerical simulations. A shortcoming of such a traditional approach is the high sensitivity to initial conditions. Another way to understand transport in complex fluid flows comes from a new mathematical tool: Lagrangian Coherent Structures (LCS). The idea of using Lagrangian Structures rose as a meeting point between non-linear dynamics and fluid mechanics. It provides the means to identify material lines that shape trajectory patterns, dividing the flow field into regions with different dynamical behaviours. The objective of this study is the detection of Lagrangian Coherent Structures in the Gulf of Trieste. LCS are calculated from the 2D surface velocity field measured by the coastal radars of the TOSCA (Tracking Oil Spills & Coastal Awareness network) project. Blobs of simulated particles are subjected to chaotic stirring (transport and stretching) that is in agreement with the detected LCS. In the TOSCA project drifters were deployed, too. Therefore, a simple simulation of some of these drifters was carried out. The trajectory of the simulated drifters diverge from the real one: this result is due to the chaotic transport of passive tracers. However, the separation becomes more evident when velocity fields are less accurate because of lack of measurements, previously filled with nearest neighbourhood interpolation. In the light of such results, the use of LCS could be helpful in understanding the trajectory followed by drifters and passive tracers in general, because they can point out the directions along which transport is likely to develop.
Lagrangian form of Schrödinger equation
Arsenović, D.; Burić, N.; Davidović, D. M.; Prvanović, S.
2014-07-01
Lagrangian formulation of quantum mechanical Schrödinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein-Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schrödinger equation.
Webs of Lagrangian Tori in Projective Symplectic Manifolds
Hwang, Jun-Muk
2012-01-01
For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.
New Terms for Compact Form of Electroweak Chiral Lagrangian
Institute of Scientific and Technical Information of China (English)
YE Wei; ZHANG Hong-Hao; YANG Hong-Wei; YAN Wen-Bin; CHEN Na; J.K. Parry; LI Xue-Song
2008-01-01
The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add several new chiral invariant terms to it and discuss the contributions of these terms to the original electroweak chiral Lagrangian.
Towards Lagrangian approach to quantum computations
Vlasov, A Yu
2003-01-01
In this work is discussed possibility and actuality of Lagrangian approach to quantum computations. Finite-dimensional Hilbert spaces used in this area provide some challenge for such consideration. The model discussed here can be considered as an analogue of Weyl quantization of field theory via path integral in L. D. Faddeev's approach. Weyl quantization is possible to use also in finite-dimensional case, and some formulas may be simply rewritten with change of integrals to finite sums. On the other hand, there are specific difficulties relevant to finite case. This work has some allusions with phase space models of quantum computations developed last time by different authors.
Hamiltonian and Lagrangian theory of viscoelasticity
Hanyga, A.; Seredyńska, M.
2008-03-01
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
Trivial Lagrangians in the Causal Approach
Grigore, Dan-Radu
2015-01-01
We prove the non-uniqueness theorem for the chronological products of a gauge model. We use a cohomological language where the cochains are chronological products, gauge invariance means a cocycle restriction and coboundaries are expressions producing zero sandwiched between physical states. Suppose that we have gauge invariance up to order n of the perturbation theory and we modify the first-order chronological products by a coboundary (a trivial Lagrangian). Then the chronological products up to order n get modified by a coboundary also.
THE EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES
Institute of Scientific and Technical Information of China (English)
Wen Li; Jian-xin Chen
2006-01-01
In this paper we present some new absolute and relative perturbation bounds for the eigenvalue for arbitrary matrices, which improves some recent results. The eigenvalue inclusion region is also discussed.
Arbitrary orbital angular momentum of photons
Pan, Yue; Ren, Zhi-Cheng; Wang, Xi-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2015-01-01
Orbital angular momentum (OAM) of photons, as a new fundamental degree of freedom, has excited a great diversity of interest, because of a variety of emerging applications. Arbitrarily tunable OAM has gained much attention, but its creation remains still a tremendous challenge. We demonstrate the realization of well-controlled arbitrary OAM in both theory and experiment. We present the concept of general OAM, which extends the OAM carried by the scalar vortex field to the OAM carried by the azimuthally varying polarized vector field. The arbitrary OAM has the same characteristics as the well-defined integer OAM: intrinsic OAM, uniform local OAM and intensity ring, and propagation stability. The arbitrary OAM has unique natures: it is allowed to be flexibly tailored and the radius of the focusing ring can have various choices for a desired OAM, which are of great significance to the benefit of surprising applications of the arbitrary OAM.
Positive Gravitattional Energy in Arbitrary Dimensions
Choquet-Bruhat, Yvonne
2011-01-01
We present a streamlined, complete proof, valid in arbitrary space dimension $n$, and using only spinors on the oriented Riemannian space $(M^{n};g),$ of the positive energy theorem in General Relativity.
Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs
Institute of Scientific and Technical Information of China (English)
X. X. HUANG; K. L. TEO; X. Q. YANG
2006-01-01
In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.
The Dirac Conjecture and the Non-uniqueness of Lagrangian
Wang, Yong-Long; Jiang, Hua; Lu, Wei-Tao; Pan, Hong-Zhe
2013-01-01
We prove the validity of the Dirac conjecture generally by adding the total time derivatives of all constraints to the Lagrangian step by step. It is worthy to state that the total time derivatives added to the original Lagrangian can turn up some constraints, and discover the symmetries hidden in the original Lagrangian. For a constrained system, the extended Hamiltonian $H_E$ contains more constraints, and shows more symmetries. We discuss the Cawley's counterexample, and prove it not a real one to the Dirac conjecture. And we offer an example, its extended Hamiltonian is better that its total Hamiltonian for its Lagrangian.
Energy Technology Data Exchange (ETDEWEB)
Gwo, J.P.; Jardine, P.M. [Oak Ridge National Lab., TN (United States); Yeh, G.T. [Pennsylvania State Univ., University Park, PA (United States) Department of Civil and Environmental Engineering; Wilson, G.V. [Tennessee Univ., Knoxville, TN (United States). Dept. of Plant and Soil Science
1995-04-01
Matrix diffusion, a diffusive mass transfer process,in the structured soils and geologic units at ORNL, is believe to be an important subsurface mass transfer mechanism; it may affect off-site movement of radioactive wastes and remediation of waste disposal sites by locally exchanging wastes between soil/rock matrix and macropores/fractures. Advective mass transfer also contributes to waste movement but is largely neglected by researchers. This report presents the first documented 2-D multiregion solute transport code (MURT) that incorporates not only diffusive but also advective mass transfer and can be applied to heterogeneous porous media under transient flow conditions. In this report, theoretical background is reviewed and the derivation of multiregion solute transport equations is presented. Similar to MURF (Gwo et al. 1994), a multiregion subsurface flow code, multiplepore domains as suggested by previous investigators (eg, Wilson and Luxmoore 1988) can be implemented in MURT. Transient or steady-state flow fields of the pore domains can be either calculated by MURF or by modelers. The mass transfer process is briefly discussed through a three-pore-region multiregion solute transport mechanism. Mass transfer equations that describe mass flux across pore region interfaces are also presented and parameters needed to calculate mass transfer coefficients detailed. Three applications of MURT (tracer injection problem, sensitivity analysis of advective and diffusive mass transfer, hillslope ponding infiltration and secondary source problem) were simulated and results discussed. Program structure of MURT and functions of MURT subroutiness are discussed so that users can adapt the code; guides for input data preparation are provided in appendices.
Variational Contact Symmetries of Constraint Lagrangians
Terzis, Petros A; Christodoulakis, T; Paliathanasis, A; Tsamparlis, M
2015-01-01
The investigation of contact symmetries of re--parametrization invariant Lagrangians of finite degrees of freedom and quadratic in the velocities is presented. The main concern of the paper is those symmetry generators which depend linearly in the velocities. A natural extension of the symmetry generator along the lapse function $N(t)$, with the appropriate extension of the dependence in $\\dot{N}(t)$ of the gauge function, is assumed; this action yields new results. The central finding is that the integrals of motion are either linear or quadratic in velocities and are generated, respectively by the conformal Killing vector fields and the conformal Killing tensors of the configuration space metric deduced from the kinetic part of the Lagrangian (with appropriate conformal factors). The freedom of re--parametrization allows one to appropriately scale $N(t)$, so that the potential becomes constant; in this case the integrals of motion can be constructed from the Killing fields and Killing tensors of the scaled ...
Sigma decomposition: the CP-odd Lagrangian
Hierro, I. M.; Merlo, L.; Rigolin, S.
2016-04-01
In Alonso et al., JHEP 12 (2014) 034, the CP-even sector of the effective chiral Lagrangian for a generic composite Higgs model with a symmetric coset has been constructed, up to four momenta. In this paper, the CP-odd couplings are studied within the same context. If only the Standard Model bosonic sources of custodial symmetry breaking are considered, then at most six independent operators form a basis. One of them is the weak- θ term linked to non-perturbative sources of CP violation, while the others describe CP-odd perturbative couplings between the Standard Model gauge bosons and an Higgs-like scalar belonging to the Goldstone boson sector. The procedure is then applied to three distinct exemplifying frameworks: the original SU(5)/SO(5) Georgi-Kaplan model, the minimal custodial-preserving SO(5)/SO(4) model and the minimal SU(3)/(SU(2) × U(1)) model, which intrinsically breaks custodial symmetry. Moreover, the projection of the high-energy electroweak effective theory to the low-energy chiral effective Lagrangian for a dynamical Higgs is performed, uncovering strong relations between the operator coefficients and pinpointing the differences with the elementary Higgs scenario.
Generating functionals and Lagrangian partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)
2013-08-15
The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.
Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids
Energy Technology Data Exchange (ETDEWEB)
Sambasivan, Shiv Kumar [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory; Burton, Donald E. [Los Alamos National Laboratory; Christon, Mark A. [Los Alamos National Laboratory
2012-07-19
A finite volume cell-centered Lagrangian scheme for solving large deformation problems is constructed based on the hypo-elastic model and using the mimetic theory. Rigorous analysis in the context of gas and solid dynamics, and arbitrary polygonal meshes, is presented to demonstrate the ability of cell-centered schemes in mimicking the continuum properties and principles at the discrete level. A new mimetic formulation based gradient evaluation technique and physics-based, frame independent and symmetry preserving slope limiters are proposed. Furthermore, a physically consistent dissipation model is employed which is both robust and inexpensive to implement. The cell-centered scheme along with these additional new features are applied to solve solids undergoing elasto-plastic deformation.
Lagrangian relative equilibria for a gyrostat in the three-body problem: bifurcations and stability
Energy Technology Data Exchange (ETDEWEB)
Guirao, Juan L G; Vera, Juan A, E-mail: juan.garcia@upct.e, E-mail: juanantonio.vera@upct.e [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203 Cartagena, Region de Murcia (Spain)
2010-05-14
In this paper we consider the non-canonical Hamiltonian dynamics of a gyrostat in the frame of the three-body problem. Using geometric/mechanic methods we study the approximate dynamics of the truncated Legendre series representation of the potential of an arbitrary order. Working in the reduced problem, we study the existence of relative equilibria that we refer to as Lagrange type following the analogy with the standard techniques. We provide necessary and sufficient conditions for the linear stability of Lagrangian relative equilibria if the gyrostat morphology form is close to a sphere. Thus, we generalize the classical results on equilibria of the three-body problem and many results on them obtained by the classic approach for the case of rigid bodies.
Lagrangian for Frenkel electron and position's non-commutativity due to spin
Deriglazov, Alexei A
2014-01-01
We construct relativistic-invariant spinning-particle Lagrangian without auxiliary variables. Spin is considered as a composed quantity constructed on the base of non-Grassmann vector-like variable. The variational problem guarantees both fixed value of spin and Frenkel condition on spin-tensor. Taking into account the Frenkel condition, we obtain, inevitably, relativistic corrections to the algebra of position variables: their classical brackets became noncommutative, with the "parameter of non-commutativity" proportional to the spin-tensor. This leads to a number of interesting consequences in quantum theory. We construct the relativistic quantum mechanics in canonical formalism (in physical-time parametrization) and in covariant formalism (in arbitrary parametrization). We show how state-vectors and operators of covariant formulation can be used to compute mean values of physical operators of position and spin. This proves relativistic covariance of canonical formalism. Various candidates for position and ...
Directory of Open Access Journals (Sweden)
C. Mendoza
2012-08-01
Full Text Available This article reviews several recently developed Lagrangian tools and shows how their combined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the climate impact of ocean transport processes, we illustrate a 2-D application on altimeter data sets over the area of the Kuroshio Current, although the proposed techniques are general and applicable to arbitrary time dependent aperiodic flows. The first challenge for describing transport in aperiodical time dependent flows is obtaining a representation of the phase portrait where the most relevant dynamical features may be identified. areas that are related to confinement regions. This representation is accomplished by using global Lagrangian descriptors that when applied for instance to the altimeter data sets retrieve over the ocean surface a phase portrait where the geometry of interconnected dynamical systems is visible. The phase portrait picture is essential because it evinces which transport routes are acting on the whole flow. Once these routes are roughly recognised, it is possible to complete a detailed description by the direct computation of the finite time stable and unstable manifolds of special hyperbolic trajectories that act as organising centres of the flow.
Lagrangian for Frenkel electron and position's non-commutativity due to spin
Energy Technology Data Exchange (ETDEWEB)
Deriglazov, Alexei A. [Universidade Federal de Juiz de Fora, Depto. de Matematica, ICE, Juiz de Fora, MG (Brazil); Tomsk Polytechnic University, Laboratory of Mathematical Physics, Tomsk (Russian Federation); Pupasov-Maksimov, Andrey M. [Universidade Federal de Juiz de Fora, Depto. de Matematica, ICE, Juiz de Fora, MG (Brazil)
2014-10-15
We construct a relativistic spinning-particle Lagrangian where spin is considered as a composite quantity constructed on the base of a non-Grassmann vector-like variable. The variational problem guarantees both a fixed value of the spin and the Frenkel condition on the spin-tensor. The Frenkel condition inevitably leads to relativistic corrections of the Poisson algebra of the position variables: their classical brackets became noncommutative. We construct the relativistic quantum mechanics in the canonical formalism (in the physical-time parametrization) and in the covariant formalism (in an arbitrary parametrization). We show how state vectors and operators of the covariant formulation can be used to compute the mean values of physical operators in the canonical formalism, thus proving its relativistic covariance. We establish relations between the Frenkel electron and positive-energy sector of the Dirac equation. Various candidates for the position and spin operators of an electron acquire clear meaning and interpretation in the Lagrangian model of the Frenkel electron. Our results argue in favor of Pryce's (d)-type operators as the spin and position operators of Dirac theory. This implies that the effects of non-commutativity could be expected already at the Compton wavelength. We also present the manifestly covariant form of the spin and position operators of the Dirac equation. (orig.)
Evaluation of the Lagrangian Marker Method in CTH: Taylor Impact
2015-03-01
ARL-TR-7235•MAR 2015 US Army Research Laboratory Evaluation of the Lagrangian Marker Method in CTH: Taylor Impact by Stephen Schraml Approved for...Research Laboratory Evaluation of the Lagrangian Marker Method in CTH: Taylor Impact by Stephen Schraml Weapons and Materials Research Directorate, ARL...
Deformations of log-Lagrangian submanifolds of Poisson manifolds
2013-01-01
We consider Lagrangian-like submanifolds in certain even-dimensional 'symplectic-like' Poisson manifolds. We show, under suitable transversality hypotheses, that the pair consisting of the ambient Poisson manifold and the submanifold has unobstructed deformations and that the deformations automatically preserve the Lagrangian-like property.
Parallel Lagrangian models for turbulent transport and chemistry
Crone, Gilia Cornelia
1997-01-01
In this thesis we give an overview of recent stochastic Lagrangian models and present a new particle model for turbulent dispersion and chemical reactions. Our purpose is to investigate and assess the feasibility of the Lagrangian approach for modelling the turbulent dispersion and chemistry
Flux form Semi-Lagrangian methods for parabolic problems
Bonaventura, Luca
2015-01-01
A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and convergence analysis are proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection--diffusion and nonlinear parabolic problems.
Geometric Lagrangians for massive higher-spin fields
Francia, D
2007-01-01
Lagrangians for massive, unconstrained, higher-spin bosons and fermions are proposed. The idea is to modify the geometric, gauge invariant Lagrangians describing the corresponding massless theories by the addition of suitable quadratic polynomials. These polynomials provide generalisations of the Fierz-Pauli mass term containing all possible traces of the basic field. No auxiliary fields are needed.
Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics
Miron, Radu
2012-01-01
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries. More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author. The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order. For short, in this text we aim to solve some difficult problems: The problem of geometrization of classical non conservative mechanical systems; The foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;To determine the evolution equations of the classical mechanical systems for whose external forces depend on the hig...
Lagrangian and Hamiltonian two-scale reduction
Giannoulis, Johannes; Mielke, Alexander
2008-01-01
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave...
Lagrangian coherent structures and plasma transport processes
Falessi, M V; Schep, T J
2015-01-01
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\\'e map provides a splitting of the phase space into regions where particles have different kinds of motion: periodic, quasi-periodic or chaotic. The boundaries of these regions are transport barriers; i.e., a trajectory cannot cross such boundaries during the whole evolution of the system. Lagrangian Coherent Structure (LCS) generalize this method to systems with the most general time dependence, splitting the phase space into regions with different qualitative behaviours. This leads to the definition of finite-time transport barriers, i.e. trajectories cannot cross the barrier for a finite amount of time. This methodology can be used to identify fast recirculating regions in the dynamical system and to characterize the transport between them.
Instantons in a Lagrangian model of turbulence
Grigorio, Leonardo S; Pereira, Rodrigo M; Chevillard, Laurent
2016-01-01
The role of instantons is investigated in the Lagrangian model for the velocity gradient evolution known as the Recent Fluid Deformation approximation. After recasting the model into the path-integral formalism, the probability distribution function is computed along with the most probable path in the weak noise limit through the saddle-point approximation. Evaluation of the instanton solution is implemented numerically by means of the iteratively Chernykh-Stepanov method. In the case of the longitudinal velocity gradient statistics, due to symmetry reasons, the number of degrees of freedom can be reduced to one, allowing the pdf to be evaluated analytically as well, thereby enabling a prediction of the scaling of the moments as a function of Reynolds number. It is also shown that the instanton solution lies on the Vieillefosse line concerning the RQ-plane. We illustrate how instantons can be unveiled in the stochastic dynamics performing a conditional statistics.
Holography, chiral Lagrangian and form factor relations
Zuo, Fen
2013-01-01
We perform a detailed study of mesonic properties in a class of holographic models of QCD, which is described by the Yang-Mills plus Chern-Simons action. By decomposing the 5 dimensional gauge field into resonances and integrating out the massive ones, we reproduce the Chiral Perturbative Theory Lagrangian up to ${\\cal O}(p^6)$ and obtain all the relevant low energy constants (LECs). The numerical predictions of the LECs show minor model dependence, and agree reasonably with the determinations from other approaches. Interestingly, various model-independent relations appear among them. Some of these relations are found to be the large-distance limits of universal relations between form factors of the anomalous and even-parity sectors of QCD.
Non-Lagrangian theories from brane junctions
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.
A perturbative approach to Lagrangian flow networks
Fujiwara, Naoya; Donges, Jonathan F; Donner, Reik V
2016-01-01
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (a...
Lagrangian Coherent Structures: Introduction and Applications
Haller, George
2008-11-01
Lagrangian Coherent Structures (LCS) are distinguished material surfaces that organize the global mixing and transport of fluid particles. While these surfaces define a skeleton that governs all mixing events even in turbulent flows, LCS remain hidden to traditional coherent structure detecting methods based on vorticity, pressure, streamlines, or other frame-dependent quantities. Here we review the mathematical foundations of LCS and discuss how they can be located in an objective (frame-independent) way in complex flows. We also highlight applications to experimental and numerical flow data analysis. Examples include two-dimensional rotating turbulence, hairpin vortices in three-dimensional numerical simulations, passive ocean pollution control and atmospheric clear-air turbulence detection. Some of these examples will be discussed in more detail in later talks within this minisymposium.
Lagrangian mixing in an axisymmetric hurricane model
Directory of Open Access Journals (Sweden)
B. Rutherford
2009-09-01
Full Text Available This paper discusses the extension of established Lagrangian mixing measures to make them applicable to data extracted from a 2-D axisymmetric hurricane simulation. Because of the non-steady and unbounded characteristics of the simulation, the previous measures are extended to a moving frame approach to create time-dependent mixing rates that are dependent upon the initial time of particle integration, and are computed for nonlocal regions. The global measures of mixing derived from finite-time Lyapunov exponents, relative dispersion, and a measured mixing rate are applied to distinct regions representing different characteristic feautures within the model. It is shown that these time-dependent mixing rates exhibit correlations with maximal tangential winds during a quasi-steady state, establishing a connection between mixing and hurricane intensity.
On Active Current Selection for Lagrangian Profilers
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.
Spin in an arbitrary gravitational field
Obukhov, Yuri N; Teryaev, Oleg V
2013-01-01
We study the quantum mechanics of a Dirac fermion on a curved spacetime manifold. The metric of the spacetime is completely arbitrary, allowing for the discussion of all possible inertial and gravitational field configurations. In this framework, we find the Hermitian Dirac Hamiltonian for an arbitrary classical external field (including the gravitational and electromagnetic ones). In order to discuss the physical content of the quantum-mechanical model, we further apply the Foldy-Wouthuysen transformation, and derive the quantum equations of motion for the spin and position operators. We analyse the semiclassical limit of these equations and compare the results with the dynamics of a classical particle with spin in the framework of the standard Mathisson-Papapetrou theory and in the classical canonical theory. The comparison of the quantum mechanical and classical equations of motion of a spinning particle in an arbitrary gravitational field shows their complete agreement.
Comparison of Direct Eulerian Godunov and Lagrange Plus Remap, Artificial Viscosity Schemes
Energy Technology Data Exchange (ETDEWEB)
Pember, R B; Anderson, R W
2001-03-30
The authors compare two algorithms for solving the equations of unsteady inviscid compressible flow in an Eulerian frame: a staggered grid, Lagrange plus remap artificial viscosity scheme and a cell-centered, direct Eulerian higher-order Godunov scheme. They use the two methods to compute solutions to a number of one- and two-dimensional problems. The results show the accuracy of the two schemes to be generally equivalent. In a 1984 survey paper by Woodward and Colella, the Lagrange plus remap approach did not compare favorably with the higher-order Godunov methodology. They examine, therefore, how certain features of the staggered grid scheme considered here contribute to its improved accuracy. The critical features are shown to be the use of a monotonic artificial viscosity in the Lagrange step and, in the remap step, the use of a corner transport upwind scheme with van Leer limiters in conjunction with separate advection of internal and kinetic energies.
A Full Eulerian Vlasov-Maxwell Study of Turbulent Dynamics and Dissipation
TenBarge, J. M.; Juno, J.; Hakim, A.
2016-12-01
The development of a detailed understanding of turbulence in magnetized plasmas has been a long standing goal of the broader scientific community, both as a fundamental physics process and because of its applicability to a wide variety of phenomena. Turbulence in a magnetized plasma is the primary mechanism responsible for transforming energy at large injection scales into small-scale motions, which are ultimately dissipated as heat in systems such as the solar corona and wind. At large scales, the turbulence is well described by fluid models of the plasma; however, understanding the processes responsible for heating a weakly collisional plasma such as the solar wind requires a kinetic description. We present the first fully kinetic Eulerian Vlasov-Maxwell study of turbulence using the Gkeyll simulation code. We focus on the pristine distribution function dynamics that are possible with the Eulerian approach. We also present the signatures and form of dissipation as diagnosed via field-particle correlation functions.
Eulerian method for fluid-structure interaction and submerged solid-solid contact problems
Valkov, Boris; Kamrin, Ken
2014-01-01
We present a fully Eulerian, blurred-interface numerical method for fluid-structure interaction (FSI) with extension to the case of fluid-immersed solids interacting through contact. The method uses the Eulerian-frame Reference Map Technique (RMT) to represent the solid phase(s), permitting simulation of large-deformation constitutive behaviors. We demonstrate the method with multiple examples involving a compressible Navier-Stokes fluid coupled to a neo-Hookean solid. We verify the method's convergence. The algorithm is faster and more stable than previous methods based on RMT. It is easily appended with a contact subroutine for multiple solids interacting within fluid, which we introduce and demonstrate with two examples.
Eulerian identities on matrix rings%矩阵环的欧拉恒等式
Institute of Scientific and Technical Information of China (English)
曹明; 冯怡君; 魏亚萍; 游松发
2013-01-01
A class of multilinear called Eulerian polynomials were constructed from extremely simple Eulerian graphs . The conditions of these polynomial identities on matrix ring were investigated .Famous Amitsur-Levitzki theorem and Chang-Giambruno-Sehgal theroem in PI-theory were the immediate consequences of the conclusion .%由简单的欧拉图构造一类多重线性多项式，称作欧拉多项式，并探讨这些多项式成为矩阵环的恒等式的条件，PI-理论中著名的Amitsur-Levitzki定理和Chang-Giambruno-Sehgal定理是本文结果的直接推论。
Mass transport in a thin layer of power-law fluid in an Eulerian coordinate system
Institute of Scientific and Technical Information of China (English)
刘洁; 白玉川
2016-01-01
The mass transport velocity in a thin layer of muddy fluid is studied theoretically. The mud motion is driven by a periodic pressure load on the free surface, and the mud is described by a power-law model. Based on the key assumptions of the shallowness and the small deformation, a perturbation analysis is conducted up to the second order to find the mean Eulerian velocity in an Eulerian coordinate system. The numerical iteration method is adopted to solve these non-linear equations of the leading order. From the numerical results, both the first-order flow fields and the second-order mass transport velocities are examined. The verifications are made by comparing the numerical results with experimental results in the literature, and a good agreement is confirmed.
Two new triangles of $q$-integers via $q$-Eulerian polynomials of type $A$ and $B$
Han, Guoniu; Zeng, Jiang
2012-01-01
The classical Eulerian polynomials can be expanded in the basis $t^{k-1}(1+t)^{n+1-2k}$ ($1\\leq k\\leq\\lfloor (n+1)/2\\rfloor$) with positive integral coefficients. This formula implies both the symmetry and the unimodality of the Eulerian polynomials. In this paper, we prove a $q$-analogue of this expansion for Carlitz's $q$-Eulerian polynomials as well as a similar formula for Chow-Gessel's $q$-Eulerian polynomials of type $B$. We shall give some applications of these two formulae, which involve two new sequences of polynomials in the variable $q$ with positive integral coefficients. An open problem is to give a combinatorial interpretation for these polynomials.
Influence of Diesel Nozzle Geometry on Cavitation Using Eulerian Multi-Fluid Method
Institute of Scientific and Technical Information of China (English)
张军; 杜青; 杨延相
2010-01-01
Dependent on automatically generated unstructured grids, a comprehensive computational fluid dynamics(CFD)numerical simulation is performed to analyze the influence of nozzle geometry on the internal flow characteristics of a multi-hole diesel injector with the multi-phase flow model based on Eulerian multi-fluid method.The diesel components in nozzle are considered as two continuous phases, diesel liquid and diesel vapor respectively.Considering that both of them are fully coupled and interpenetrated, sepa...
Fuel Effects on Nozzle Flow and Spray Using Fully Coupled Eulerian Simulations
2015-09-01
atomization and mixing characteristics of non-reacting isothermal diesel engine sprays. An Eulerian modeling approach was adopted to simulate both the...of single and multi-component surrogate fuel mixtures on the atomization and mixing characteristics of non-reacting isothermal diesel engine sprays...simulations and has shown the suitability of several multi-component kerosene surrogates at diesel engine conditions. The measurements were validated
Implementation and Development of an Eulerian Spray Model for CFD simulations of diesel Sprays
2016-01-01
[EN] The main objective of this work is the modeling of diesel sprays under engine conditions, including the atomization, transport and evaporation processes pivotal in the diesel spray formation and its development. For this purpose, an Eulerian single fluid model, embedded in a RANS environment, is implemented in the CFD platform OpenFOAM. The modeling approach implemented here is based on the ⅀-Y model. The model is founded on the assumption of flow scales separation. In actual i...
1978-09-01
and move across the Eulerian mesh with the local velocity field. A damage region is formed when material in an Eulerian cell first satisfies the...parameters of the added material with those of the region before it was enlarged. The tracer strings of the modified regions are rede - fined by making use...deletes the damage tracers that were interior to the cell. PURDMR rede - fines the mass of the reduced region. 85 i» mmm To enlarge a region
Eulerian Simulation of Acoustic Waves Over Long Range in Realistic Environments
Chitta, Subhashini; Steinhoff, John
2015-11-01
In this paper, we describe a new method for computation of long-range acoustics. The approach is a hybrid of near and far-field methods, and is unique in its Eulerian treatment of the far-field propagation. The near-field generated by any existing method to project an acoustic solution onto a spherical surface that surrounds a source. The acoustic field on this source surface is then extended to an arbitrarily large distance in an inhomogeneous far-field. This would normally require an Eulerian solution of the wave equation. However, conventional Eulerian methods have prohibitive grid requirements. This problem is overcome by using a new method, ``Wave Confinement'' (WC) that propagates wave-identifying phase fronts as nonlinear solitary waves that live on grid indefinitely. This involves modification of wave equation by the addition of a nonlinear term without changing the basic conservation properties of the equation. These solitary waves can then be used to ``carry'' the essential integrals of the acoustic wave. For example, arrival time, centroid position and other properties that are invariant as the wave passes a grid point. Because of this property the grid can be made as coarse as necessary, consistent with overall accuracy to resolve atmospheric/ground variations. This work is being funded by the U.S. Army under a Small Business Innovation Research (SBIR) program (contract number: # W911W6-12-C-0036). The authors would like to thank Dr. Frank Caradonna and Dr. Ben W. Sim for this support.
Impact of the Eulerian chaos of magnetic field lines in magnetic reconnection
Firpo, M.-C.; Ettoumi, W.; Lifschitz, A. F.; Retinò, A.; Farengo, R.; Ferrari, H. E.; García-Martínez, P. L.
2016-12-01
Stochasticity is an ingredient that may allow the breaking of the frozen-in law in the reconnection process. It will first be argued that the non-ideal effects may be considered as an implicit way to introduce stochasticity. Yet there also exists an explicit stochasticity that does not require the invocation of non-ideal effects. This comes from the spatial (or Eulerian) chaos of magnetic field lines that can show up only in a truly three-dimensional description of magnetic reconnection since the two-dimensional models impose the integrability of the magnetic field lines. Some implications of this magnetic braiding, such as the increased particle finite-time Lyapunov exponents and increased acceleration of charged particles, are discussed in the frame of tokamak sawteeth that forms a laboratory prototype of spontaneous magnetic reconnection. A justification for an increased reconnection rate with chaotic vs. the integrable magnetic field lines is proposed. Moreover, in 3D, the Eulerian chaos of the magnetic field lines may coexist with the Eulerian chaos of velocity field lines, that is more commonly named the turbulence.
Unit physics performance of a mix model in Eulerian fluid computations
Energy Technology Data Exchange (ETDEWEB)
Vold, Erik [Los Alamos National Laboratory; Douglass, Rod [Los Alamos National Laboratory
2011-01-25
In this report, we evaluate the performance of a K-L drag-buoyancy mix model, described in a reference study by Dimonte-Tipton [1] hereafter denoted as [D-T]. The model was implemented in an Eulerian multi-material AMR code, and the results are discussed here for a series of unit physics tests. The tests were chosen to calibrate the model coefficients against empirical data, principally from RT (Rayleigh-Taylor) and RM (Richtmyer-Meshkov) experiments, and the present results are compared to experiments and to results reported in [D-T]. Results show the Eulerian implementation of the mix model agrees well with expectations for test problems in which there is no convective flow of the mass averaged fluid, i.e., in RT mix or in the decay of homogeneous isotropic turbulence (HIT). In RM shock-driven mix, the mix layer moves through the Eulerian computational grid, and there are differences with the previous results computed in a Lagrange frame [D-T]. The differences are attributed to the mass averaged fluid motion and examined in detail. Shock and re-shock mix are not well matched simultaneously. Results are also presented and discussed regarding model sensitivity to coefficient values and to initial conditions (IC), grid convergence, and the generation of atomically mixed volume fractions.
Monadic Maps and Folds for Arbitrary Datatypes
Fokkinga, Maarten
1994-01-01
Each datatype constructor comes equiped not only with a so-called map and fold (catamorphism), as is widely known, but, under some condition, also with a kind of map and fold that are related to an arbitrary given monad. This result follows from the preservation of initiality under lifting
On the Distance between Three Arbitrary Points
Directory of Open Access Journals (Sweden)
Parin Chaipunya
2013-01-01
Full Text Available We point out some equivalence between the results in (Sedghi et al., 2012 and (Khamsi, 2010. Then, we introduce the notion of a general distance between three arbitrary points and study some of its properties. In the final section, some fixed point results are proposed.
Guala, Michele; Liberzon, Alexander; Tsinober, Arkady; Kinzelbach, Wolfgang
Lagrangian auto- and cross-correlation functions of the rate of strain s(2) , enstrophy omega (2) , their respective production terms -s_{ij}s_{jk}s_{ki} and omega_{i}omega_{j}s_{ij}, and material derivatives, Ds s(2/Ds) t and Dsomega(2/Ds) t are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Re_{lambda} {=} 50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity omega and the rate of strain tensor s_{ij}, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of omega(2) to the relatively shorter time scales of s(2) , omega_{i}omega_{j}s_{ij} and -s_{ij}s_{jk}s_{ki}. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes of s(2) and omega(2) . In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between -s_{ij}s_{jk}s_{ki} and s(2) and between -s_{ij}s_{jk}s_{ki} and Ds s(2) /Ds t, in addition to a marked anti-correlation between omega_{i}omega_{j}s_{ij} and Ds s(2) /Ds t. Vorticity dampening in high-enstrophy regions is thus related to the decay of s(2) and its production term, -s_{ij}s_{jk}s_{ki}.
Shake-The-Box: Lagrangian particle tracking at high particle image densities
Schanz, Daniel; Gesemann, Sebastian; Schröder, Andreas
2016-05-01
particles. Processing an experimental data set on a transitional jet in water demonstrates the benefits of advanced Lagrangian evaluation in describing flow details—both on small scales (by the individual tracks) and on larger structures (using an interpolation onto an Eulerian grid). Comparisons to standard TOMO-PIV processing for synthetic and experimental evaluations show distinct benefits in local accuracy, completeness of the solution, ghost particle occurrence, spatial resolution, temporal coherence and computational effort.
Maric, Tomislav; Bothe, Dieter
2013-01-01
A new parallelized unsplit geometrical Volume of Fluid (VoF) algorithm with support for arbitrary unstructured meshes and dynamic local Adaptive Mesh Refinement (AMR), as well as for two and three dimensional computation is developed. The geometrical VoF algorithm supports arbitrary unstructured meshes in order to enable computations involving flow domains of arbitrary geometrical complexity. The implementation of the method is done within the framework of the OpenFOAM library for Computational Continuum Mechanics (CCM) using the C++ programming language with modern policy based design for high program code modularity. The development of the geometrical VoF algorithm significantly extends the method base of the OpenFOAM library by geometrical volumetric flux computation for two-phase flow simulations. For the volume fraction advection, a novel unsplit geometrical algorithm is developed, which inherently sustains volume conservation utilizing unique Lagrangian discrete trajectories located in the mesh points. ...
A reduction of order two for infinite-order Lagrangians
Jaén, X.; Llosa, J.; Molina, A.
1986-10-01
Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.
In defence of naivete The conceptual status of Lagrangian QFT
Wallace, D
2001-01-01
I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the "naive" quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work.
Lagrangian Volume Deformations around Simulated Galaxies
Robles, S; Oñorbe, J; Martínez-Serrano, F J
2015-01-01
We present a detailed analysis of the local evolution of 206 Lagrangian Volumes (LVs) selected at high redshift around galaxy seeds, identified in a large-volume $\\Lambda$CDM hydrodynamical simulation. The LVs have a mass range of $1 - 1500 \\times 10^{10} M_\\odot$. We follow the dynamical evolution of the density field inside these initially spherical LVs from $z=10$ up to $z_{\\rm low}= 0.05$, witnessing highly non-linear, anisotropic mass rearrangements within them, leading to the emergence of the local cosmic web (CW). These mass arrangements have been analysed in terms of the reduced inertia tensor $I_{ij}^r$, focusing on the evolution of the principal axes of inertia and their corresponding eigen directions, and paying particular attention to the times when the evolution of these two structural elements declines. In addition, mass and component effects along this process have also been investigated. We have found that deformations are led by DM dynamics and they transform most of the initially spherical L...
Lagrangian based methods for coherent structure detection
Energy Technology Data Exchange (ETDEWEB)
Allshouse, Michael R., E-mail: mallshouse@chaos.utexas.edu [Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, Texas 78712 (United States); Peacock, Thomas, E-mail: tomp@mit.edu [Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2015-09-15
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.
Sigma Decomposition: The CP-Odd Lagrangian
Hierro, I M; Rigolin, and S
2015-01-01
In Alonso et al., JHEP 12 (2014) 034, the CP-even sector of the effective chiral Lagrangian for a generic composite Higgs model with a symmetric coset has been constructed, up to four momenta. In this paper, the CP-odd couplings are studied within the same context. If only the Standard Model bosonic sources of custodial symmetry breaking are considered, then at most six independent operators form a basis. One of them is the weak-$\\theta$ term linked to non-perturbative sources of CP viola- tion, while the others describe CP-odd perturbative couplings between the Standard Model gauge bosons and an Higgs-like scalar belonging to the Goldstone boson sector. The procedure is then applied to three distinct exemplifying frameworks: the original $SU(5)/SO(5)$ Georgi-Kaplan model, the minimal custodial-preserving $SO(5)/SO(4)$ model and the minimal $SU(3)/(SU(2)\\times U(1))$ model, which intrinsically breaks cus- todial symmetry. Moreover, the projection of the high-energy electroweak effective theory to the low-ener...
Sea Fog Forecasting with Lagrangian Models
Lewis, J. M.
2014-12-01
In 1913, G. I. Taylor introduced us to a Lagrangian view of sea fog formation. He conducted his study off the coast of Newfoundland in the aftermath of the Titanic disaster. We briefly review Taylor's classic work and then apply these same principles to a case of sea fog formation and dissipation off the coast of California. The resources used in this study consist of: 1) land-based surface and upper-air observations, 2) NDBC (National Data Buoy Center) observations from moored buoys equipped to measure dew point temperature as well as the standard surface observations at sea (wind, sea surface temperature, pressure, and air temperature), 3) satellite observations of cloud, and 4) a one-dimensional (vertically directed) boundary layer model that tracks with the surface air motion and makes use of sophisticated turbulence-radiation parameterizations. Results of the investigation indicate that delicate interplay and interaction between the radiation and turbulence processes makes accurate forecasts of sea fog onset unlikely in the near future. This pessimistic attitude stems from inadequacy of the existing network of observations and uncertainties in modeling dynamical processes within the boundary layer.
Disentangling the Cosmic Web with Lagrangian Submanifold
Shandarin, Sergei F.; Medvedev, Mikhail V.
2016-10-01
The Cosmic Web is a complicated highly-entangled geometrical object. Remarkably it has formed from practically Gaussian initial conditions, which may be regarded as the simplest departure from exactly uniform universe in purely deterministic mapping. The full complexity of the web is revealed neither in configuration no velocity spaces considered separately. It can be fully appreciated only in six-dimensional (6D) phase space. However, studies of the phase space is complicated by the fact that every projection of it on a three-dimensional (3D) space is multivalued and contained caustics. In addition phase space is not a metric space that complicates studies of geometry. We suggest to use Lagrangian submanifold i.e., x = x(q), where both x and q are 3D vectors instead of the phase space for studies the complexity of cosmic web in cosmological N-body dark matter simulations. Being fully equivalent in dynamical sense to the phase space it has an advantage of being a single valued and also metric space.
Top marine predators track Lagrangian coherent structures.
Tew Kai, Emilie; Rossi, Vincent; Sudre, Joel; Weimerskirch, Henri; Lopez, Cristobal; Hernandez-Garcia, Emilio; Marsac, Francis; Garçon, Veronique
2009-05-19
Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great Frigatebird. Using a newly developed dynamic concept, the finite-size Lyapunov exponent (FSLE), we identified Lagrangian coherent structures (LCSs) present in the surface flow in the channel over a 2-month observation period (August and September 2003). By comparing seabird satellite positions with LCS locations, we demonstrate that frigatebirds track precisely these structures in the Mozambique Channel, providing the first evidence that a top predator is able to track these FSLE ridges to locate food patches. After comparing bird positions during long and short trips and different parts of these trips, we propose several hypotheses to understand how frigatebirds can follow these LCSs. The birds might use visual and/or olfactory cues and/or atmospheric current changes over the structures to move along these biologic corridors. The birds being often associated with tuna schools around foraging areas, a thorough comprehension of their foraging behavior and movement during the breeding season is crucial not only to seabird ecology but also to an appropriate ecosystemic approach to fisheries in the channel.
A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints
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.}
A Dynamic Job Shop Scheduling Method Based on Lagrangian Relaxation
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
Due to the complexity of dynamic job shop scheduling in flexible manufacturing s ystem(FMS), many heuristic rules are still used today. A dynamic scheduling appr oach based on Lagrangian relaxation is proposed to improve the quality and guara ntee the real-time capability of dynamic scheduling. The proposed method makes use of the dynamic predictive optimal theory combined with Lagrangian relaxation to obtain a good solution that can be evaluated quantitatively. The Lagrangian multipliers introduced here are capable of describing machine predictive states and system capacity constraints. This approach can evaluate the suboptimality of the scheduling systems. It can also quickly obtain high quality feasible schedu les, thus enabling Lagrangian relaxation to be better used in the dynamic schedu ling of manufacturing system. The efficiency and effectiveness of this method ar e verified by numerical experiments.
Remarks on the Lagrangian representation of bi-Hamiltonian equations
Pavlov, M. V.; Vitolo, R. F.
2017-03-01
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2 =LτA1. We use this result in order to find the Lagrangian representation when A2 is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components.
Second post-Newtonian Lagrangian dynamics of spinning compact binaries
Energy Technology Data Exchange (ETDEWEB)
Huang, Li; Wu, Xin [Nanchang University, Department of Physics and Institute of Astronomy, Nanchang (China); Ma, DaZhu [Hubei University for Nationalities, School of Science, Enshi (China)
2016-09-15
The leading-order spin-orbit coupling is included in a post-Newtonian Lagrangian formulation of spinning compact binaries, which consists of the Newtonian term, first post-Newtonian (1PN) and 2PN non-spin terms and 2PN spin-spin coupling. This leads to a 3PN spin-spin coupling occurring in the derived Hamiltonian. The spin-spin couplings are mainly responsible for chaos in the Hamiltonians. However, the 3PN spin-spin Hamiltonian is small and has different signs, compared with the 2PN spin-spin Hamiltonian equivalent to the 2PN spin-spin Lagrangian. As a result, the probability of the occurrence of chaos in the Lagrangian formulation without the spin-orbit coupling is larger than that in the Lagrangian formulation with the spin-orbit coupling. Numerical evidences support this claim. (orig.)
Construction of Lagrangians and Hamiltonians from the Equation of Motion
Yan, C. C.
1978-01-01
Demonstrates that infinitely many Lagrangians and Hamiltonians can be constructed from a given equation of motion. Points out the lack of an established criterion for making a proper selection. (Author/GA)
A discrete Lagrangian based direct approach to macroscopic modelling
Sarkar, Saikat; Nowruzpour, Mohsen; Reddy, J. N.; Srinivasa, A. R.
2017-01-01
A direct discrete Lagrangian based approach, designed at a length scale of interest, to characterize the response of a body is proposed. The main idea is to understand the dynamics of a deformable body via a Lagrangian corresponding to a coupled interaction of rigid particles in the reduced dimension. We argue that the usual practice of describing the laws of a deformable body in the continuum limit is redundant, because for most of the practical problems, analytical solutions are not available. Since continuum limit is not taken, the framework automatically relaxes the requirement of differentiability of field variables. The discrete Lagrangian based approach is illustrated by deriving an equivalent of the Euler-Bernoulli beam model. A few test examples are solved, which demonstrate that the derived non-local model predicts lower deflections in comparison to classical Euler-Bernoulli beam solutions. We have also included crack propagation in thin structures for isotropic and anisotropic cases using the Lagrangian based approach.
Don't worry. Lagrangian drift kinetics is OK
Burby, Joshua
2015-11-01
I show that standard Lagrangian (i.e. variational) drift kinetics with uE × B ~vth and Hgc =Ho + ɛH1 +ɛ2H2 has an unphysically-large phase space; where a valid initial condition ought to consist of (F , E , B) specified at t = 0 , Lagrangian drift kinetics requires initial time derivatives of the electromagnetic field to be specified as well. This phenomenon occurs because the guiding center coordinate transformation depends on time derivatives of the electromagnetic field, and this leads to the appearance of a time derivative of E in H2. I also show how to ``renormalize'' the Lagrangian approach to drift kinetics in a way that manifestly preserves the correct structure of the initial value problem. Starting from this modified Lagrangian procedure, I derive the drift kinetic system's Poisson bracket. Work supported by DOE contract # DE-AC02-09CH11466.
Geometry of Lagrangian First-order Classical Field Theories
Echeverría-Enríquez, A; Román-Roy, N; Echeverr\\'ia-Enr\\'iquez, Arturo; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso
1996-01-01
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the {\\sl Euler-Lagrange equations} in two equivalent ways: as the result of a variational problem and developing the {\\sl jet field formalism} (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied.
The complete HEFT Lagrangian after the LHC Run I
Brivio, I; Gonzalez-Garcia, M C; Merlo, L
2016-01-01
The complete effective chiral Lagrangian for a dynamical Higgs is presented and constrained by means of a global analysis including electroweak precision data together with Higgs and triple gauge boson coupling data from the LHC Run~I. The operators' basis up to next-to-leading order in the expansion consists of 148 (188 considering right-handed neutrinos) flavour universal terms and it is presented here making explicit the custodial nature of the operators. This effective Lagrangian provides the most general description of the physical Higgs couplings once the electroweak symmetry is assumed, and it allows for deviations from the $SU(2)_L$ doublet nature of the Standard Model Higgs. The comparison with the effective linear Lagrangian constructed with an exact $SU(2)_L$ doublet Higgs and considering operators with at most canonical dimension six is presented. A promising strategy to disentangle the two descriptions consists in analysing i) anomalous signals present only in the chiral Lagrangian and not expect...
Classical Nonminimal Lagrangians and Kinematic Tests of Special Relativity
Schreck, M
2016-01-01
This article gives a brief summary on recently obtained classical lagrangians for the nonminimal fermion sector of the Standard-Model Extension (SME). Such lagrangians are adequate descriptions of classical particles that are subject to a Lorentz-violating background field based on the SME. Explicitly, lagrangians were obtained for the leading nonminimal contributions of the m, a, c, e, and f coefficients. These results were then used to interpret classical, kinematic tests of Special Relativity in the framework of the nonminimal SME. This led to new constraints on certain nonminimal controlling coefficients. Although the experiments were very sophisticated in the era when they were carried out, their sensitivities for detecting Lorentz violation were still far away from the Planck scale. Obtaining the novel constraints can be considered as a proof-of-principle demonstrating the applicability of the classical lagrangians computed.
Flux form Semi-Lagrangian methods for parabolic problems
Directory of Open Access Journals (Sweden)
Bonaventura Luca
2016-09-01
Full Text Available A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and stability analysis is proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection diffusion and nonlinear parabolic problems.
Integration over families of Lagrangian submanifolds in BV formalism
Mikhailov, Andrei
2016-01-01
Gauge fixing is interpreted in BV formalims as a choice of Lagrangian submanifold in an odd symplectic manifold. A natural construction defines an integration procedure on families of Lagrangian submanifolds. In string perturbation theory, the moduli space integrals of higher genus amplitudes can be interpreted this way. We discuss the role of symmetries in this construction. We also discuss its applications to string worldsheet sigma-model, in particular to the construction of vertex operators.
Addendum to "Coherent Lagrangian vortices: The black holes of turbulence"
Haller, G.; Beron-Vera, F. J.
2014-01-01
In Haller and Beron-Vera (2013) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null-geodesics of the Lorentzian metric associated with a generalized Green-Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here we give an improved discussion on this analogy.
Merging matter and geometry in the same Lagrangian
Directory of Open Access Journals (Sweden)
Hendrik Ludwig
2015-12-01
Full Text Available We show that a Lagrangian density proportional to −gLm2/R reduces to a pressuron theory of gravity that is indistinguishable from General Relativity in the dust limit. The combination of matter and geometry in the same Lagrangian density intrinsically satisfies Mach's Principle — since matter cannot exist without curvature and vice versa — while it may have the correct phenomenology in order to describe actual gravity.
Lagrangian formulation of continuum with internal long-range interactions
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Based on a new definition of nonlocal variable,this paper establishes the Lagrangian formulation for continuum with internal long-range interactions.Distinguished from the existing theories,the nonlocal term in the Lagrangian formulation automatically satisfies the zero mean condition determined by the action and reaction law.By this formulation,elastic wave in a rod with the internal long-range interactions is investigated.The dispersion of the elastic wave is predicted.
BRST Lagrangian construction for spin-2 field in Einstein space
Energy Technology Data Exchange (ETDEWEB)
Buchbinder, I.L., E-mail: joseph@tspu.edu.r [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation); Krykhtin, V.A., E-mail: krykhtin@tspu.edu.r [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation); Laboratory of Mathematical Physics, Tomsk Polytechnic University, Tomsk 634034 (Russian Federation); Lavrov, P.M., E-mail: lavrov@tspu.edu.r [Department of Mathematical Analysis, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation)
2010-03-01
We explore a new possibility of BRST construction in higher spin field theory to obtain a consistent Lagrangian for massive spin-2 field in Einstein space. Such approach automatically leads to gauge invariant Lagrangian with suitable auxiliary and Stueckelberg fields. It is proved that in this case a propagation of spin-2 field is hyperbolic and causal. Also we extend notion of partial masslessness for spin-2 field in the background under consideration.
Forecasting Future Sea Ice Conditions: A Lagrangian Approach
2014-09-30
that survives the summer melt season in each of the Arctic peripheral seas. The Lagrangian Model is forced with weekly mean satellite-derived sea- ice ...GCM to drive the Lagrangian code and map the regions for the multi-year ice surviving the summer melt in each of the Arctic peripheral seas in todays...1995, Emery et al. 1997, Meier et al. 2000, Tschudi et al. 2010) 3- Assess whether the source region of sea ice melting in peripheral seas in the
Interactive Lagrangian density between massive photons and gravitons
Institute of Scientific and Technical Information of China (English)
DENG Yan-bin
2006-01-01
The interactive Lagrangian density of massive photons and gravitons is proposed after an investigation into the interaction between photons with or without mass under the influence of gravity either as classical field, gravitational wave, or gravitons from a perspective of quantum field. This interactive Lagrangian density can provide a step-stone for further research of gravitational wave and the possible rest mass of photon.
Parsakhoo, Zahra; Shao, Yaping
2017-04-01
Near-surface turbulent mixing has considerable effect on surface fluxes, cloud formation and convection in the atmospheric boundary layer (ABL). Its quantifications is however a modeling and computational challenge since the small eddies are not fully resolved in Eulerian models directly. We have developed a Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer based on the Ito Stochastic Differential Equation (SDE) for air parcels (particles). Due to the complexity of the mixing in the ABL, we find that linear Ito SDE cannot represent convections properly. Three strategies have been tested to solve the problem: 1) to make the deterministic term in the Ito equation non-linear; 2) to change the random term in the Ito equation fractional, and 3) to modify the Ito equation by including Levy flights. We focus on the third strategy and interpret mixing as interaction between at least two stochastic processes with different Lagrangian time scales. The model is in progress to include the collisions among the particles with different characteristic and to apply the 3D model for real cases. One application of the model is emphasized: some land surface patterns are generated and then coupled with the Large Eddy Simulation (LES).
Generalized Lagrangian dynamics of physical and non-physical systems
Sandler, U.
2014-12-01
In this paper, we show how to study the evolution of a complex system, given imprecise knowledge about the state of the system and the dynamics laws. It will be shown that dynamics of these systems is equivalent to Lagrangian (or Hamiltonian) mechanics in a n+1-dimensional space, where n is a system's dimensionality. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's equations gain a non-zero right side proportional to the derivative of the Lagrangian with respect to the action. Examples of such systems are unstable systems, systems with dissipation and systems which can remember their history. Moreover, in certain situations, the Lagrangian could be a set-valued function. The corresponding equations of motion then become differential inclusions instead of differential equations. We will also show that the principal of least action is a consequence of the causality principle and the local topology of the state space and not an independent axiom of classical mechanics. We emphasize that our adaptation of Lagrangian mechanics does not use or depend on specific properties of the physical system being modeled. Therefore, this Lagrangian approach may be equally applied to non-physical systems. An example of such an application is presented as well.
Quantum fidelity for arbitrary Gaussian states
Banchi, Leonardo; Pirandola, Stefano
2015-01-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
On Arbitrary Phases in Quantum Amplitude Amplification
Hoyer, P
2000-01-01
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\\tan(\\phi/2)=\\tan(\\phi/2)(1-2a)$, where $\\phi$ and $\\phi$ are the phases used and where $a$ is the success probability of the given algorithm. Thus the choice of phases depends nontrivially and nonlinearly on the success probability. Utilizing this condition, we give methods for constructing quantum algorithms that succeed with certainty and for implementing arbitrary rotations. We also conclude that phase errors of order up to $\\frac{1}{\\sqrt{a}}$ can be tolerated in amplitude amplification.
Snake beam: a paraxial arbitrary focal line
Rosen, Joseph; Yariv, Amnon
1995-01-01
The creation of paraxial arbitrary focal lines by a Fourier computer-generated hologram is demonstrated. The desired focal line is represented by a series of connected straight line segments, each of which is implemented by a radial harmonic function located on a different radial portion of the entire hologram. Each subhologram is multiplied by appropriate linear and quadratic phase functions and is shifted by some distance from the center. The two phase factors determine the location of each...
Acoustic Casimir Pressure for Arbitrary Media
Barcenas, J; Esquivel-Sirvent, R
2004-01-01
In this paper we derive a general expression for the acoustic Casimir pressure between two parallel slabs made of arbitrary materials and whose acoustic reflection coefficients are not equal. The formalism is based on the calculation of the local density of modes using a Green's function approach. The results for the Casimir acoustic pressure are generalized to a sphere/plate configuration using the proximity theorem
Loading Arbitrary Knowledge Bases in Matrix Browser
2009-01-01
This paper describes the work done on Matrix Browser, which is a recently developed graphical user interface to explore and navigate complex networked information spaces. This approach presents a new way of navigating information nets in windows explorer like widget. The problem on hand was how to export arbitrary knowledge bases in Matrix Browser. This was achieved by identifying the relationships present in knowledge bases and then by forming the hierarchies from this data and these hierarc...
Polarization for arbitrary discrete memoryless channels
Sasoglu, Eren; Telatar, Emre; Arikan, Erdal
2009-01-01
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for the binary case leads to polarization. This method can be extended to channels of composite input alphabet sizes by decomposing such channels into a set of channels with prime input alphabet sizes. It is also shown that all discrete memoryless channels can...
A compressible real gas eulerian model for LES of fuel sprays
Knudsen, Edward; Doran, Eric
2015-11-01
A compressible solver for eulerian multiphase spray simulations is presented. This large eddy simulation solver employs a Peng-Robinson (PR) equation of state to describe mixtures of two species such as liquid dodecane and gaseous nitrogen. Modeling challenges associated with the use of PR are discussed, as are the resource requirements associated with using a compressible formulation to describe liquids when full fuel injector applications are considered. The solver is analyzed using canonical cases and the Spray A experiment from the Engine Combustion Network.
A Two-Continua Approach to Eulerian Simulation of Water Spray
DEFF Research Database (Denmark)
Nielsen, Michael Bang; Østerby, Ole
2013-01-01
Physics based simulation of the dynamics of water spray - water droplets dispersed in air - is a means to increase the visual plausibility of computer graphics modeled phenomena such as waterfalls, water jets and stormy seas. Spray phenomena are frequently encountered by the visual effects industry...... into the operator splitting methodology as well as (semi-)implicit discretizations of droplet diffusion and the drag force with improved stability properties. As shown by several examples, our approach allows us to more faithfully capture the dynamics of spray than previous Eulerian methods....
Covariant formulation of the governing equations of continuum mechanics in an Eulerian description
Schöberl, Markus; Schlacher, Kurt
2007-05-01
We present the balance relations for a continuum in the Eulerian formulation in a pure covariant fashion. Based on the analysis of nonrelativistic particle mechanics, we adapt the covariant description to the case of a continuum. The use of the covariant Nijenhuis differential as well as the splitting of the vertical configuration bundle are the key objects that allow a coordinate-free representation. We state the balance equations such that they are valid, also when time variant transformations are applied, which leads to a nontrivial space-time connection and a metric which explicitly depends on the time.
Polarization Mode Dispersion Probability Distribution for Arbitrary Mode Coupling
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The probability distribution of the differential group delay for arbitrary mode coupling is simulated with Monte-Carlo method. Fitting the simulation results, we obtain probability distribution function for arbitrary mode coupling.
Numerical uncertainty at mesoscale in a Lagrangian model in complex terrain
Directory of Open Access Journals (Sweden)
J. Brioude
2012-04-01
Full Text Available Recently, it has been shown that mass conservation in Lagrangian models is improved by using time-average winds out of Eulerian models. In this study, we evaluate the mass conservation and trajectory uncertainties in complex terrain at mesoscale using the FLEXPART Lagrangian particle dispersion model coupled with the WRF mesoscale model. The specific form of vertical wind used is found to have a large effect. Time average wind with time average sigma dot (σ·, instantaneous wind with geometric cartesian vertical wind (w and instantaneous wind with σ· are used to simulate mixing ratios of a passive tracer in forward and backward runs using different time interval outputs and horizontal resolutions in California. Mass conservation in the FLEXPART model was not an issue when using time-average wind or instantaneous wind with σ·. However, mass was poorly conserved using instantaneous wind with w, with a typical variation of 25% within 24 h.
Uncertainties in surface residence time (a backtrajectory product commonly used in source receptor studies or inverse modeling calculated for each backtrajectory run were also analyzed. The smallest uncertainties were systematically found when using time-average wind. Uncertainties using instantaneous wind with σ· were slightly larger, as long as the time interval of output was sufficiently small. The largest uncertainties were found when using instantaneous wind with w. Those uncertainties were found to be linearly correlated with the local average gradient of orography. Differences in uncertainty were much smaller when trajectories were calculated over flat terrain. For a typical run at mesoscale in complex terrain, 4 km horizontal resolution
Numerical uncertainty at mesoscale in a Lagrangian model in complex terrain
Directory of Open Access Journals (Sweden)
J. Brioude
2012-09-01
Full Text Available Recently, it has been shown that mass conservation in Lagrangian models is improved by using time-average winds out of Eulerian models. In this study, we evaluate the mass conservation and trajectory uncertainties in complex terrain at mesoscale using the FLEXPART Lagrangian particle dispersion model coupled with the WRF mesoscale model. The specific form of vertical wind used is found to have a large effect. Time average wind with time average sigma dot (σ·, instantaneous wind with geometric cartesian vertical wind (w and instantaneous wind with σ· are used to simulate mixing ratios of a passive tracer in forward and backward runs using different time interval outputs and horizontal resolutions in California. Mass conservation in the FLEXPART model was not an issue when using time-average wind or instantaneous wind with σ·. However, mass was poorly conserved using instantaneous wind with w, with a typical variation of 25% within 24 h.
Uncertainties in surface residence time (a backtrajectory product commonly used in source receptor studies or inverse modeling calculated for each backtrajectory run were also analyzed. The smallest uncertainties were systematically found when using time-average wind. Uncertainties using instantaneous wind with σ· were slightly larger, as long as the time interval of output was sufficiently small. The largest uncertainties were found when using instantaneous wind with w. Those uncertainties were found to be linearly correlated with the local average gradient of orography. Differences in uncertainty were much smaller when trajectories were calculated over flat terrain. For a typical run at mesoscale in complex terrain, 4 km horizontal resolution
Lagrangian modelling of ocean surface waves and synthetic aperture radar wave measurements
Energy Technology Data Exchange (ETDEWEB)
Fouques, Sebastien
2005-07-01
, along with a RAR modulation transfer function (MTF) with a larger amplitude. Eventually, an optimization of the RAR MTF is carried out by making use of the co-located database and the dependency of the optimized parameters on the wind velocity is studied. In the last three articles. Lagrangian models for ocean surface waves are investigated, and the main results are the following. In Article III, ocean surface properties such as the slope and the curvature are studied for linear irregular waves, and the difference between the Eulerian and the Lagrangian wave spectra is illustrated. In addition, some features of the second-order Lagrangian solution for irregular long-crested waves are presented. Then, in Article IV, the Lagrangian equations of motion, as given in Lamb (1932), are extended to include the irrotational flow assumption and simplified by eliminating the pressure. The first-order solution for two-dimensional irregular waves given by Pierson (1961) is modified through a change of variables that makes the mass conservation equation be fulfilled exactly, instead of being correct to the first order only. The resulting waves show higher sharp crests than in Pierson's solution, in which some water locally and temporary disappears in the vicinity of the surface. Furthermore, a three-dimensional second-order irrotational solution is derived. Monte Carlo simulations of irregular long-crested waves reveal that the fronts of some waves may steepen, while the fluid located on their back side and near the surface is hurled forward, in a way similar to an early stage breaking wave. Then, it is demonstrated that at the second order, short-crested waves develop curved crests owing to a non-uniform current field. Finally, the ability of the Lagrangian formalism to describe capillary waves is investigated in Article V. Assuming that surface tension is the only restoring force, the profile of the first-order monochromatic solution is the same as for gravity waves, with
Lagrangian modelling of ocean surface waves and synthetic aperture radar wave measurements
Energy Technology Data Exchange (ETDEWEB)
Fouques, Sebastien
2005-07-01
, along with a RAR modulation transfer function (MTF) with a larger amplitude. Eventually, an optimization of the RAR MTF is carried out by making use of the co-located database and the dependency of the optimized parameters on the wind velocity is studied. In the last three articles. Lagrangian models for ocean surface waves are investigated, and the main results are the following. In Article III, ocean surface properties such as the slope and the curvature are studied for linear irregular waves, and the difference between the Eulerian and the Lagrangian wave spectra is illustrated. In addition, some features of the second-order Lagrangian solution for irregular long-crested waves are presented. Then, in Article IV, the Lagrangian equations of motion, as given in Lamb (1932), are extended to include the irrotational flow assumption and simplified by eliminating the pressure. The first-order solution for two-dimensional irregular waves given by Pierson (1961) is modified through a change of variables that makes the mass conservation equation be fulfilled exactly, instead of being correct to the first order only. The resulting waves show higher sharp crests than in Pierson's solution, in which some water locally and temporary disappears in the vicinity of the surface. Furthermore, a three-dimensional second-order irrotational solution is derived. Monte Carlo simulations of irregular long-crested waves reveal that the fronts of some waves may steepen, while the fluid located on their back side and near the surface is hurled forward, in a way similar to an early stage breaking wave. Then, it is demonstrated that at the second order, short-crested waves develop curved crests owing to a non-uniform current field. Finally, the ability of the Lagrangian formalism to describe capillary waves is investigated in Article V. Assuming that surface tension is the only restoring force, the profile of the first-order monochromatic solution is the same as for gravity waves, with
Full-Eulerian fluid-structure coupling simulation of hyperelastic channel flow
Nagano, Naohiro; Sugiyama, Kazuyasu; Takeuchi, Shintaro; Satoshi, II; Takagi, Shu; Matsumoto, Yoichiro
2010-11-01
A full-Eulerian simulation for coupling a Newtonian fluid and hyperelastic material is conducted. The system involves an interaction problem between the fluid and hyperelastic walls and is driven by pressure difference, mimicking a blood flow in a blood vessel. A single set of the governing equations for the fluid and solid is employed, and a volume-of-fluid idea is employed to describe a multi-component geometry. The solid stress is defined in Eulerian frame by using a left Cauchy-Green deformation tensor, and the temporal change in the solid deformation is described by updating the tensor. The method employs a uniform fixed grid system for both fluid and solid and it does not require any mesh generation or reconstruction, aiming at facilitating the practical bio-mechanical fluid-structure analysis based on a medical image. The validity of the simulation results is established through comparison with a theoretical prediction. As an application of the present method, pulsating flows are simulated to demonstrate a nonlinear behavior of the flow rate on the pulsating amplitude, and an effect of employing an anisotropic hyperelastic material is discussed.
Consalvi, Jean-Louis
2017-01-01
The time-averaged Radiative Transfer Equation (RTE) introduces two unclosed terms, known as `absorption Turbulence Radiation Interaction (TRI)' and `emission TRI'. Emission TRI is related to the non-linear coupling between fluctuations of the absorption coefficient and fluctuations of the Planck function and can be described without introduction any approximation by using a transported PDF method. In this study, a hybrid flamelet/ Stochastic Eulerian Field Model is used to solve the transport equation of the one-point one-time PDF. In this formulation, the steady laminar flamelet model (SLF) is coupled to a joint Probability Density Function (PDF) of mixture fraction, enthalpy defect, scalar dissipation rate, and soot quantities and the PDF transport equation is solved by using a Stochastic Eulerian Field (SEF) method. Soot production is modeled by a semi-empirical model and the spectral dependence of the radiatively participating species, namely combustion products and soot, are computed by using a Narrow Band Correlated-k (NBCK) model. The model is applied to simulate an ethylene/methane turbulent jet flame burning in an oxygen-enriched environment. Model results are compared with the experiments and the effects of taken into account Emission TRI on flame structure, soot production and radiative loss are discussed.
ASHEE: a compressible, equilibrium-Eulerian model for volcanic ash plumes
Cerminara, Matteo; Berselli, Luigi Carlo
2015-01-01
A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations for a mixture of gases and solid particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model, valid for low concentration regimes and small particles Stokes $St<0.2$. When $St < 0.001$ the model reduces to the dusty-gas one. The new model is significantly faster than the Eulerian model while retaining the capability to describe gas-particle non-equilibrium. Direct numerical simulation accurately reproduce the dynamics of isotropic turbulence in subsonic regime. For gas-particle mixtures, it describes the main features of density fluctuations and the preferential concentration of particles by turbulence, verifying the model reliability and suitability for the simulation of high-Reynolds number and high-temperature ...
Circuits with arbitrary gates for random operators
Jukna, S
2010-01-01
We consider boolean circuits computing n-operators f:{0,1}^n --> {0,1}^n. As gates we allow arbitrary boolean functions; neither fanin nor fanout of gates is restricted. An operator is linear if it computes n linear forms, that is, computes a matrix-vector product y=Ax over GF(2). We prove the existence of n-operators requiring about n^2 wires in any circuit, and linear n-operators requiring about n^2/\\log n wires in depth-2 circuits, if either all output gates or all gates on the middle layer are linear.
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.
Description of the spin structure function g_1 at arbitrary $x$ and arbitrary Q^2
Ermolaev, B I; Troyan, S I
2007-01-01
The explicit expressions describing the structure function g_1 at arbitrary x and Q^2 are obtained. In the first place, they combine the well-known DGLAP expressions for g_1 with the total resummation of leading logarithms of x, which makes possible to cover the kinematic region of arbitrary x and large Q^2. In order to cover the small-Q^2 region the shift Q^2 -> Q^2 + mu^2 in the large-Q^2 expressions for g_1 is suggested and values of mu are estimated. The expressions obtained do not require singular factors x^{-a} in the fits for initial parton densities.
On Eulerian equilibria in K-order approximation of the gyrostat in the three-body problem
Directory of Open Access Journals (Sweden)
J. A. Vera
2006-01-01
the main result of this work, the number of Eulerian equilibria in an approximate dynamics of order k for k≥1 is independent of the order of truncation of the potential if the gyrostat S0 is close to the sphere. The instability of Eulerian equilibria is proven for any approximate dynamics if the gyrostat is close to the sphere. In this way, we generalize the classical results on equilibria of the three-body problem and many of those obtained by other authors using more classic techniques for the case of rigid bodies.
Energy Technology Data Exchange (ETDEWEB)
Truchot, B.
2005-12-15
The objective of this work is to develop an Eulerian two phase model to improve the prediction of fuel injection in internal combustion engines, particularly the dense liquid zone close to the nozzle. Lagrangian models, usually used in engine simulations, are based on the assumption of dispersed two phase flows with low liquid volume fraction, which is not fulfilled in the case of direct injection engine technology. Different Eulerian approaches are available in the literature. Physical phenomena that occur near the nozzle and characteristics of each model lead to the choice of a two fluids two pressures model. Several open terms appear in the equations of the model: exchange between the two phases and turbulent correlations. Closures of exchange terms are based on the spherical droplets hypothesis while a RANS approach is adopted to close turbulent correlations. This model has been integrated in the IFP CFD code, IFP-C3D. Several numerical tests and analytical validations (for single and two phase flows) have been then carried out in order to check the correct implementation of equations and the predictivity of the model and closures. Modifications in the turbulent model of the gas have required validations in both the gas phase (flow behind a sudden enlargement) and the liquid phase (pure liquid injection). A two phase mixing layer has been then used to validate the whole model. Finally, injection tests have been achieved under realistic conditions (similar to those encountered in automotive engines) in order to check the feasibility of engine computations using the developed Eulerian approach. These tests have also allowed to check the compatibility of this approach with the specificities of engine simulations (especially mesh movement). (author)
Institute of Scientific and Technical Information of China (English)
SantiagoLain; RicardoAliod
2000-01-01
A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent flows.Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows.It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced.An extension of the standard k-c turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.
*-Regular Leavitt Path Algebras of Arbitrary Graphs
Institute of Scientific and Technical Information of China (English)
Gonzalo ARANDA PINO; Kulumani RANGASWAMY; Lia VA(S)
2012-01-01
If K is a field with involution and E an arbitrary graph,the involution from K naturally induces an involution of the Leavitt path algebra LK(E).We show that the involution on LK(E) is proper if the involution on K is positive-definite,even in the case when the graph E is not necessarily finite or row-finite.It has been shown that the Leavitt path algebra LK(E) is regular if and only if E is acyclic.We give necessary and sufficient conditions for LK(E) to be *-regular (i.e.,regular with proper involution).This characterization of *-regularity of a Leavitt path algebra is given in terms of an algebraic property of K,not just a graph-theoretic property of E.This differs from the.known characterizations of various other algebraic properties of a Leavitt path algebra in terms of graphtheoretic properties of E alone.As a corollary,we show that Handelman's conjecture (stating that every *-regular ring is unit-regular) holds for Leavitt path algebras.Moreover,its generalized version for rings with local units also continues to hold for Leavitt path algebras over arbitrary graphs.
Correlation Imaging with Arbitrary Sampling Trajectories
Li, Yu
2014-01-01
The presented work aims to develop a generalized linear approach to image reconstruction with arbitrary sampling trajectories for high-speed MRI. This approach is based on a previously developed image reconstruction framework, "correlation imaging" (1). In the presented work, correlation imaging with arbitrary sampling trajectories is implemented in a multi-dimensional hybrid space that is formed from the physical sampling space and a virtually defined space. By introducing an undersampling trajectory with both uniformity and randomness in the hybrid space, correlation imaging may take advantage of multiple image reconstruction mechanisms including coil sensitivity encoding, data sparsity and information sharing. This hybrid-space implementation is demonstrated in multi-slice 2D imaging, multi-scan imaging, and radial dynamic imaging. Since more information is used in image reconstruction, it is found that hybrid-space correlation imaging outperforms several conventional techniques. The presented approach will benefit clinical MRI by enabling correlation imaging to be used to accelerate multi-scan clinical protocols that need different sampling trajectories in different scans. PMID:24629517
A Lagrangian fluctuation-dissipation relation for scalar turbulence
Drivas, Theodore D
2016-01-01
An exact relation is derived between the dissipation of scalar fluctuations and the variance of the scalar inputs (due to initial scalar values, scalar sources, and boundary fluxes) as those are sampled by stochastic Lagrangian trajectories. Previous work on the Kraichnan (1968) model of turbulent scalar advection has shown that anomalous scalar dissipation, non-vanishing in the limit of vanishing viscosity and diffusivity, is in that model due to Lagrangian spontaneous stochasticity, or non-determinism of the Lagrangian particle trajectories in the limit. We here extend this result to scalars advected by any incompressible velocity field. For fluid flows in domains without walls (e.g. periodic boxes) and for insulating/impermeable walls with zero scalar fluxes, we prove that anomalous scalar dissipation and spontaneous stochasticity are completely equivalent. For flows with imposed scalar values or non-vanishing scalar fluxes at the walls, spontaneous stochasticity still implies anomalous scalar dissipation ...
A new approach to Lagrangian investigations of isotropic turbulence
Barjona, Manuel; B. da Silva, Carlos; Idmec Team
2016-11-01
A new numerical approach is used in conjunction with direct numerical simulations (DNS) of statistically stationary (forced) isotropic turbulence to investigate the high Reynolds number scaling properties of turbulence characteristics in a Lagrangian frame. The new method provides an alternative route to the determination of the classical Lagrangian turbulence quantities, such as the second order Lagrangian velocity structure function and two point particle separation, at a much higher Reynolds number than as obtained in previous numerical simulations, and displays excellent agreement with the classical theoretical predictions and existing numerical simulations and experimental data. The authors acknowledge the Laboratory for Advanced Computing at University of Coimbra for providing HPC, computing, consulting resources that have contributed to the research results reported within this paper. URL http://www.lca.uc.pt.
Collaborative production planning between supply chain partners by Lagrangian relaxation
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A collaborative planning framework based on the Lagrangian Relaxation was developed to coordinate and optimize the production planning of independent partners in multiple tier supply chains. Linking constraints and dependent demand constraints were added to the monolithic Multi-Level, multi-item Capacitated Lot Sizing Problem (MLCLSP). MLCLSP was Lagrangian relaxed and decomposed into facility-separable subproblems.Surrogate gradient algorithm was used to update Lagrangian multipliers, which coordinate decentralized decisions of the facilities. Production planning of independent partners could be appropriately coordinated and optimized by this framework without intruding their decision authorities and private information. Experimental results show that the proposed coordination mechanism and procedure come close to optimal results as obtained by central coordination.
Local Lagrangian Formalism and Discretization of the Heisenberg Magnet Model
Karpeev, D
2004-01-01
In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global Lagrangian density, a local variational formulation allows one to derive local conservation laws using a version of N\\"other's theorem from the formal variational calculus of Gelfand-Dikii. Using the local Lagrangian form we extend the method of Marsden, Patrick and Schkoller to derive local multisymplectic discretizations directly from the variational principle. We employ a version of the finite element method to discretize the space of sections of the trivial magnetic spin bundle $N = M\\times S^2$ over an appropriate space-time $M$. Since sections do not form a vector space, the usual FEM bases can be used only locally with coordinate transformations intervening on element boundaries, and conservation properties are guaranteed only within an element. We discuss possible w...
Minimal Local Lagrangians for Higher-Spin Geometry
Francia, D
2005-01-01
The Fronsdal Lagrangians for free totally symmetric rank-s tensors rest on suitable trace constraints for their gauge parameters and gauge fields. Only when these constraints are removed, however, the resulting equations reflect the expected free higher-spin geometry. We show that geometric equations, in both their local and non-local forms, can be simply recovered from local Lagrangians with only two additional fields, a rank-(s-3) compensator and a rank-(s-4) Lagrange multiplier. In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n-2) compensator and a rank-(n-3) Lagrange multiplier.
Lagrangian statistics and flow topology in forced 2-D turbulence
Energy Technology Data Exchange (ETDEWEB)
Kadoch, B. [Universite d' Aix-Marseille; Del-Castillo-Negrete, Diego B [ORNL; Bos, W.J.T. [CNRS, Ecole Centrale de Lyon, Universite Claude Bernard Lyon; Schneider, Kai [Universite d' Aix-Marseille
2011-01-01
A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order - 2.
New Lagrangian diagnostics for characterizing fluid flow mixing
Mundel, Ruty; Gildor, Hezi; Rom-Kedar, Vered
2014-01-01
A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two- (and potentially three-) dimensional unsteady flows in both bounded and open domains. Its computation is much easier than all other Lagrangian diagnostics known to us and provides new insights regarding the mixing properties on both short and long time scales and on both spatial plots and distribution diagrams. We demonstrate its applicability to two dimensional flows using two toy models and a data set of surface currents from the Mediterranean Sea.
Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations
Deriglazov, Alexei A
2015-01-01
We obtain Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body with given values of spin and momentum starting from Lagrangian action without auxiliary variables. MPTD-equations correspond to minimal interaction of our spinning particle with gravity. We shortly discuss some novel properties deduced from the Lagrangian form of MPTD-equations: emergence of an effective metric instead of the original one, non-commutativity of coordinates of representative point of the body, spin corrections to Newton potential due to the effective metric as well as spin corrections to the expression for integrals of motion of a given isometry.
Using Upper Tolerances in Lagrangian Relaxation for the DCMSTP
DEFF Research Database (Denmark)
Turkensteen, Marcel
-constraints, the Minimum Spanning Tree Problem (MSTP), is polynomially solvable. We solve the DCMSTP using Lagrangian relaxation. This is the approach in which constraint violations are penalized in the objective function. In an iterative process, the penalty values of violated constraints are increased...... used to approximate the optimal solution value. We present a Lagrangian approach that, as in Volgenant (1989), penalizes violations of the degree-constraints of each vertex. The penalty of a vertex is added to the costs of all edges adjacent to the vertex. Our approach uses upper tolerances...
An extended Lagrangian support vector machine for classifications
Institute of Scientific and Technical Information of China (English)
YANG Xiaowei; SHU Lei; HAO Zhifeng; LIANG Yanchun; LIU Guirong; HAN Xu
2004-01-01
Lagrangian support vector machine (LSVM) cannot solve large problems for nonlinear kernel classifiers. In order to extend the LSVM to solve very large problems, an extended Lagrangian support vector machine (ELSVM) for classifications based on LSVM and SVMlight is presented in this paper. Our idea for the ELSVM is to divide a large quadratic programming problem into a series of subproblems with small size and to solve them via LSVM. Since the LSVM can solve small and medium problems for nonlinear kernel classifiers, the proposed ELSVM can be used to handle large problems very efficiently. Numerical experiments on different types of problems are performed to demonstrate the high efficiency of the ELSVM.
A truly noninterpolating semi-Lagrangian Lax-Wendroff method
Olim, M.
1994-06-01
A truly noninterpolating semi-Lagrangian method has been developed. It is based upon a modification of a standard Lax-Wendroff scheme and is unconditionally stable on a regular rectangular grid. The method is explicit and second-order accurate in both time and space. It is suggested that the computational cost and memory allocation required by this method are the least possible for a semi-Lagrangian algorithm of this order of accuracy. The numerical experiments presented indicate that the algorithm is very accurate indeed.
The anomalous chiral Lagrangian of order $p^6$
Bijnens, J; Talavera, P
2002-01-01
We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$. The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavors, 23 terms for three and five for two flavors. In the two flavor case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well.
Experimental investigation of Lagrangian structure functions in turbulence
DEFF Research Database (Denmark)
Berg, Jacob; Ott, Søren; Mann, Jakob
2009-01-01
Lagrangian properties obtained from a particle tracking velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian structure functions and to measure intermittency at small...... temporal scales. The finiteness of the measurement volume can bias the results significantly. We present a robust way to overcome this obstacle. Despite no fully developed inertial range, we observe strong intermittency at the scale of dissipation. The multifractal model is only partially able to reproduce...