Vorticity-divergence semi-Lagrangian global atmospheric model SL-AV20: dynamical core
Tolstykh, Mikhail; Shashkin, Vladimir; Fadeev, Rostislav; Goyman, Gordey
2017-05-01
SL-AV (semi-Lagrangian, based on the absolute vorticity equation) is a global hydrostatic atmospheric model. Its latest version, SL-AV20, provides global operational medium-range weather forecast with 20 km resolution over Russia. The lower-resolution configurations of SL-AV20 are being tested for seasonal prediction and climate modeling. The article presents the model dynamical core. Its main features are a vorticity-divergence formulation at the unstaggered grid, high-order finite-difference approximations, semi-Lagrangian semi-implicit discretization and the reduced latitude-longitude grid with variable resolution in latitude. The accuracy of SL-AV20 numerical solutions using a reduced lat-lon grid and the variable resolution in latitude is tested with two idealized test cases. Accuracy and stability of SL-AV20 in the presence of the orography forcing are tested using the mountain-induced Rossby wave test case. The results of all three tests are in good agreement with other published model solutions. It is shown that the use of the reduced grid does not significantly affect the accuracy up to the 25 % reduction in the number of grid points with respect to the regular grid. Variable resolution in latitude allows us to improve the accuracy of a solution in the region of interest.
Lagrangian structures in time-periodic vortical flows
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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.
Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics
Webb, G. M.; Anco, S. C.
2016-02-01
The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.
Mass deformed world-sheet action of semi local vortices
Energy Technology Data Exchange (ETDEWEB)
Jiang, Yunguo [School of Space Science and Physics, Shandong University at Weihai,264209 Weihai (China); Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment,264209 Weihai (China)
2014-02-10
The mass deformed effective world-sheet theory of semi local vortices was constructed via the field theoretical method. By Euler-Lagrangian equations, the Ansatze for both the gauge field and the adjoint scalar were solved, this ensures that zero modes of vortices are minimal excitations of the system. Up to the 1/g{sup 2} order, all profiles are solved. The mass deformed effective action was obtained by integrating out the transverse plane of the vortex string. The effective theory interpolates between the local vortex and the lump. Respecting certain normalization conditions, the effective theory shows a Seiberg-like duality, which agrees with the result of the Kähler quotient construction.
Blender, R.
2009-04-01
An approach for the reconstruction of atmospheric flow is presented which uses space- and time-dependent fields of density ?, potential vorticity Q and potential temperature Î& cedil;[J. Phys. A, 38, 6419 (2005)]. The method is based on the fundamental equations without approximation. The basic idea is to consider the time-dependent continuity equation as a condition for zero divergence of momentum in four dimensions (time and space, with unit velocity in time). This continuity equation is solved by an ansatz for the four-dimensional momentum using three conserved stream functions, the potential vorticity, potential temperature and a third field, denoted as ?-potential. In zonal flows, the ?-potential identifies the initial longitude of particles, whereas potential vorticity and potential temperature identify mainly meridional and vertical positions. Since the Lagrangian tracers Q, Î&,cedil; and ? determine the Eulerian velocity field, the reconstruction combines the Eulerian and the Lagrangian view of hydrodynamics. In stationary flows, the ?-potential is related to the Bernoulli function. The approach requires that the gradients of the potential vorticity and potential temperature do not vanish when the velocity remains finite. This behavior indicates a possible interrelation with stability conditions. Examples with analytical solutions are presented for a Rossby wave and zonal and rotational shear flows.
Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices.
Huhn, F; van Rees, W M; Gazzola, M; Rossinelli, D; Haller, G; Koumoutsakos, P
2015-08-01
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
Semi-Lagrangian methods in air pollution models
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A. B. Hansen
2011-06-01
Full Text Available Various semi-Lagrangian methods are tested with respect to advection in air pollution modeling. The aim is to find a method fulfilling as many of the desirable properties by Rasch andWilliamson (1990 and Machenhauer et al. (2008 as possible. The focus in this study is on accuracy and local mass conservation.
The methods tested are, first, classical semi-Lagrangian cubic interpolation, see e.g. Durran (1999, second, semi-Lagrangian cubic cascade interpolation, by Nair et al. (2002, third, semi-Lagrangian cubic interpolation with the modified interpolation weights, Locally Mass Conserving Semi-Lagrangian (LMCSL, by Kaas (2008, and last, semi-Lagrangian cubic interpolation with a locally mass conserving monotonic filter by Kaas and Nielsen (2010.
Semi-Lagrangian (SL interpolation is a classical method for atmospheric modeling, cascade interpolation is more efficient computationally, modified interpolation weights assure mass conservation and the locally mass conserving monotonic filter imposes monotonicity.
All schemes are tested with advection alone or with advection and chemistry together under both typical rural and urban conditions using different temporal and spatial resolution. The methods are compared with a current state-of-the-art scheme, Accurate Space Derivatives (ASD, see Frohn et al. (2002, presently used at the National Environmental Research Institute (NERI in Denmark. To enable a consistent comparison only non-divergent flow configurations are tested.
The test cases are based either on the traditional slotted cylinder or the rotating cone, where the schemes' ability to model both steep gradients and slopes are challenged.
The tests showed that the locally mass conserving monotonic filter improved the results significantly for some of the test cases, however, not for all. It was found that the semi-Lagrangian schemes, in almost every case, were not able to outperform the current ASD scheme
Flux form Semi-Lagrangian methods for parabolic problems
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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.
Vortices, semi-local vortices in gauged linear sigma model
International Nuclear Information System (INIS)
Kim, Namkwon
1998-11-01
We consider the static (2+1)D gauged linear sigma model. By analyzing the governing system of partial differential equations, we investigate various aspects of the model. We show the existence of energy finite vortices under a partially broken symmetry on R 2 with the necessary condition suggested by Y. Yang. We also introduce generalized semi-local vortices and show the existence of energy finite semi-local vortices under a certain condition. The vacuum manifold for the semi-local vortices turns out to be graded. Besides, with a special choice of a representation, we show that the O(3) sigma model of which target space is nonlinear is a singular limit of the gauged linear sigma model of which target space is linear. (author)
Lagrangian investigations of vorticity dynamics in compressible turbulence
Parashar, Nishant; Sinha, Sawan Suman; Danish, Mohammad; Srinivasan, Balaji
2017-10-01
In this work, we investigate the influence of compressibility on vorticity-strain rate dynamics. Well-resolved direct numerical simulations of compressible homogeneous isotropic turbulence performed over a cubical domain of 10243 are employed for this study. To clearly identify the influence of compressibility on the time-dependent dynamics (rather than on the one-time flow field), we employ a well-validated Lagrangian particle tracker. The tracker is used to obtain time correlations between the instantaneous vorticity vector and the strain-rate eigenvector system of an appropriately chosen reference time. In this work, compressibility is parameterized in terms of both global (turbulent Mach number) and local parameters (normalized dilatation-rate and flow field topology). Our investigations reveal that the local dilatation rate significantly influences these statistics. In turn, this observed influence of the dilatation rate is predominantly associated with rotation dominated topologies (unstable-focus-compressing, stable-focus-stretching). We find that an enhanced dilatation rate (in both contracting and expanding fluid elements) significantly enhances the tendency of the vorticity vector to align with the largest eigenvector of the strain-rate. Further, in fluid particles where the vorticity vector is maximally misaligned (perpendicular) at the reference time, vorticity does show a substantial tendency to align with the intermediate eigenvector as well. The authors make an attempt to provide physical explanations of these observations (in terms of moment of inertia and angular momentum) by performing detailed calculations following tetrads {approach of Chertkov et al. ["Lagrangian tetrad dynamics and the phenomenology of turbulence," Phys. Fluids 11(8), 2394-2410 (1999)] and Xu et al. ["The pirouette effect in turbulent flows," Nat. Phys. 7(9), 709-712 (2011)]} in a compressible flow field.
Directory of Open Access Journals (Sweden)
P. M. James
2002-06-01
Full Text Available An ozone mini-hole is a synoptic-scale area of strongly reduced column total ozone, which undergoes a growth-decay cycle in association with baroclinic weather systems. The tracks of mini-hole events recorded during the TOMS observation period over the Northern Hemisphere provide a database for building anomaly fields of various meteorological parameters, following each mini-hole center in a Lagrangian sense. The resulting fields provide, for the first time, a complete mean Lagrangian picture of the three-dimensional structure of typical ozone mini-holes in the Northern Hemisphere. Mini-holes are shown to be associated with anomalous warm anticyclonic flow in the upper troposphere and cold cyclonic anomalies in the middle stratosphere. Ascending air columns occur upstream and descent downstream of the mini-hole centers. Band-pass filtering is used to reveal the transient synoptic nature of mini-holes embedded within larger scale circulation anomalies. Significant correlations between ozone and Ertel’s potential vorticity on isentropes (IPV both near the tropopause and in the middle stratosphere are shown and then utilized by reconstructing the Lagrangian analysis to follow local IPV anomalies instead of ozone minima. By using IPV as a proxy for ozone, the geopotential anomaly dipolar structure in the vertical characteristic of mini-holes is shown to result from a superposition of two largely independent dynamical components, stratospheric and tropospheric, typically operating on different time scales. Hence, ozone mini-holes may be viewed primarily as phenomena of coincidence.Key words. Meteorology and atmospheric dynamics (middle atmosphere dynamics; synoptic-scale meteorology
Directory of Open Access Journals (Sweden)
P. M. James
Full Text Available An ozone mini-hole is a synoptic-scale area of strongly reduced column total ozone, which undergoes a growth-decay cycle in association with baroclinic weather systems. The tracks of mini-hole events recorded during the TOMS observation period over the Northern Hemisphere provide a database for building anomaly fields of various meteorological parameters, following each mini-hole center in a Lagrangian sense. The resulting fields provide, for the first time, a complete mean Lagrangian picture of the three-dimensional structure of typical ozone mini-holes in the Northern Hemisphere. Mini-holes are shown to be associated with anomalous warm anticyclonic flow in the upper troposphere and cold cyclonic anomalies in the middle stratosphere. Ascending air columns occur upstream and descent downstream of the mini-hole centers. Band-pass filtering is used to reveal the transient synoptic nature of mini-holes embedded within larger scale circulation anomalies. Significant correlations between ozone and Ertel’s potential vorticity on isentropes (IPV both near the tropopause and in the middle stratosphere are shown and then utilized by reconstructing the Lagrangian analysis to follow local IPV anomalies instead of ozone minima. By using IPV as a proxy for ozone, the geopotential anomaly dipolar structure in the vertical characteristic of mini-holes is shown to result from a superposition of two largely independent dynamical components, stratospheric and tropospheric, typically operating on different time scales. Hence, ozone mini-holes may be viewed primarily as phenomena of coincidence.
Key words. Meteorology and atmospheric dynamics (middle atmosphere dynamics; synoptic-scale meteorology
The semi-Lagrangian method on curvilinear grids
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Hamiaz Adnane
2016-09-01
Full Text Available We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
Felici, Helene Marie
1992-01-01
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.
Semi-implicit semi-Lagrangian modelling of the atmosphere: a Met Office perspective
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Benacchio Tommaso
2016-09-01
Full Text Available The semi-Lagrangian numerical method, in conjunction with semi-implicit time integration, provides numerical weather prediction models with numerical stability for large time steps, accurate modes of interest, and good representation of hydrostatic and geostrophic balance. Drawing on the legacy of dynamical cores at the Met Office, the use of the semi-implicit semi-Lagrangian method in an operational numerical weather prediction context is surveyed, together with details of the solution approach and associated issues and challenges. The numerical properties and performance of the current operational version of the Met Office’s numerical model are then investigated in a simplified setting along with the impact of different modelling choices.
An unconditionally stable fully conservative semi-Lagrangian method
Lentine, Michael
2011-04-01
Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had. © 2011 Elsevier Inc.
Weak stability of Lagrangian solutions to the semigeostrophic equations
International Nuclear Information System (INIS)
Faria, Josiane C O; Lopes Filho, Milton C; Nussenzveig Lopes, Helena J
2009-01-01
In (Cullen and Feldman 2006 SIAM J. Math. Anal. 37 137–95), Cullen and Feldman proved the existence of Lagrangian solutions for the semigeostrophic system in physical variables with initial potential vorticity in L p , p > 1. Here, we show that a subsequence of the Lagrangian solutions corresponding to a strongly convergent sequence of initial potential vorticities in L 1 converges strongly in L q , q < ∞, to a Lagrangian solution, in particular extending the existence result of Cullen and Feldman to the case p = 1. We also present a counterexample for Lagrangian solutions corresponding to a sequence of initial potential vorticities converging in BM. The analytical tools used include techniques from optimal transportation, Ambrosio's results on transport by BV vector fields and Orlicz spaces
Space-Time Transformation in Flux-form Semi-Lagrangian Schemes
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Peter C. Chu Chenwu Fan
2010-01-01
Full Text Available With a finite volume approach, a flux-form semi-Lagrangian (TFSL scheme with space-time transformation was developed to provide stable and accurate algorithm in solving the advection-diffusion equation. Different from the existing flux-form semi-Lagrangian schemes, the temporal integration of the flux from the present to the next time step is transformed into a spatial integration of the flux at the side of a grid cell (space for the present time step using the characteristic-line concept. The TFSL scheme not only keeps the good features of the semi-Lagrangian schemes (no Courant number limitation, but also has higher accuracy (of a second order in both time and space. The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation. Computational stability and high accuracy makes this scheme useful in ocean modeling, computational fluid dynamics, and numerical weather prediction.
A conservative scheme for 2D and 3D adaptive semi-Lagrangian advection
Behrens, Jörn; Mentrup, Lars
2005-01-01
This article describes a 2D and 3D adaptive and mass conservingsemi-Lagrangian advection scheme for atmospheric transport problems. Fromthe integral form of the conservation law we derive a semi-Lagrangian schemebased on conservation of mass along trajectories. The mapping of mass fromthe old (adaptively refined and possibly different) grid to the upstream controlvolume is performed by a mass packet based scheme, essentially consistingof a sub-grid discretization. We validate the new adaptive...
An unconditionally stable fully conservative semi-Lagrangian method
Lentine, Michael; Gré tarsson, Jó n Tó mas; Fedkiw, Ronald
2011-01-01
of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving
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.
Multiphase Interface Tracking with Fast Semi-Lagrangian Contouring.
Li, Xiaosheng; He, Xiaowei; Liu, Xuehui; Zhang, Jian J; Liu, Baoquan; Wu, Enhua
2016-08-01
We propose a semi-Lagrangian method for multiphase interface tracking. In contrast to previous methods, our method maintains an explicit polygonal mesh, which is reconstructed from an unsigned distance function and an indicator function, to track the interface of arbitrary number of phases. The surface mesh is reconstructed at each step using an efficient multiphase polygonization procedure with precomputed stencils while the distance and indicator function are updated with an accurate semi-Lagrangian path tracing from the meshes of the last step. Furthermore, we provide an adaptive data structure, multiphase distance tree, to accelerate the updating of both the distance function and the indicator function. In addition, the adaptive structure also enables us to contour the distance tree accurately with simple bisection techniques. The major advantage of our method is that it can easily handle topological changes without ambiguities and preserve both the sharp features and the volume well. We will evaluate its efficiency, accuracy and robustness in the results part with several examples.
Seakeeping with the semi-Lagrangian particle finite element method
Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio
2017-07-01
The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.
Finite Element Based Lagrangian Vortex Dynamics Model for Wind Turbine Aerodynamics
International Nuclear Information System (INIS)
McWilliam, Michael K; Crawford, Curran
2014-01-01
This paper presents a novel aerodynamic model based on Lagrangian Vortex Dynamics (LVD) formulated using a Finite Element (FE) approach. The advantage of LVD is improved fidelity over Blade Element Momentum Theory (BEMT) while being faster than Numerical Navier-Stokes Models (NNSM) in either primitive or velocity-vorticity formulations. The model improves on conventional LVD in three ways. First, the model is based on an error minimization formulation that can be solved with fast root finding algorithms. In addition to improving accuracy, this eliminates the intrinsic numerical instability of conventional relaxed wake simulations. The method has further advantages in optimization and aero-elastic simulations for two reasons. The root finding algorithm can solve the aerodynamic and structural equations simultaneously, avoiding Gauss-Seidel iteration for compatibility constraints. The second is that the formulation allows for an analytical definition for sensitivity calculations. The second improvement comes from a new discretization scheme based on an FE formulation and numerical quadrature that decouples the spatial, influencing and temporal meshes. The shape for each trailing filament uses basis functions (interpolating splines) that allow for both local polynomial order and element size refinement. A completely independent scheme distributes the influencing (vorticity) elements along the basis functions. This allows for concentrated elements in the near wake for accuracy and progressively less in the far-wake for efficiency. Finally the third improvement is the use of a far-wake model based on semi-infinite vortex cylinders where the radius and strength are related to the wake state. The error-based FE formulation allows the transition to the far wake to occur across a fixed plane
A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system
International Nuclear Information System (INIS)
Besse, Nicolas; Latu, Guillaume; Ghizzo, Alain; Sonnendruecker, Eric; Bertrand, Pierre
2008-01-01
In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strong laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to
GYSELA, a full-f global gyrokinetic Semi-Lagrangian code for ITG turbulence simulations
International Nuclear Information System (INIS)
Grandgirard, V.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Crouseilles, N.; Latu, G.; Sonnendruecker, E.; Besse, N.; Bertrand, P.
2006-01-01
This work addresses non-linear global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence with the GYSELA code. The particularity of GYSELA code is to use a fixed grid with a Semi-Lagrangian (SL) scheme and this for the entire distribution function. The 4D non-linear drift-kinetic version of the code already showns the interest of such a SL method which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been upgrated to run 5D simulations of toroidal ITG turbulence. Linear benchmarks and non-linear first results prove that semi-lagrangian codes can be a credible alternative for gyrokinetic simulations
Gyrofluid potential vorticity equation and turbulent equipartion states
DEFF Research Database (Denmark)
Madsen, Jens; Juul Rasmussen, Jens; Naulin, Volker
2015-01-01
. The equation is relevant for transport barriers in magnetically confined plasmas because particle density, ion temperature and the radial electric field are mutually coupled through the potential vorticity. The potential vorticity equation is derived from an energy conserving, four-field, electrostatic, full......An equation governing potential vorticity in a magnetized plasmas is derived. The equation is analogous to Ertel's theorem. In the long wave-length limit the potential vorticity equals the ratio of the gyro-frequency plus the E × B- and diamagnetic polarization densities to the particle density...
An online-coupled NWP/ACT model with conserved Lagrangian levels
Sørensen, B.; Kaas, E.; Lauritzen, P. H.
2012-04-01
Numerical weather and climate modelling is under constant development. Semi-implicit semi-Lagrangian (SISL) models have proven to be numerically efficient in both short-range weather forecasts and climate models, due to the ability to use long time steps. Chemical/aerosol feedback mechanism are becoming more and more relevant in NWP as well as climate models, since the biogenic and anthropogenic emissions can have a direct effect on the dynamics and radiative properties of the atmosphere. To include chemical feedback mechanisms in the NWP models, on-line coupling is crucial. In 3D semi-Lagrangian schemes with quasi-Lagrangian vertical coordinates the Lagrangian levels are remapped to Eulerian model levels each time step. This remapping introduces an undesirable tendency to smooth sharp gradients and creates unphysical numerical diffusion in the vertical distribution. A semi-Lagrangian advection method is introduced, it combines an inherently mass conserving 2D semi-Lagrangian scheme, with a SISL scheme employing both hybrid vertical coordinates and a fully Lagrangian vertical coordinate. This minimizes the vertical diffusion and thus potentially improves the simulation of the vertical profiles of moisture, clouds, and chemical constituents. Since the Lagrangian levels suffer from traditional Lagrangian limitations caused by the convergence and divergence of the flow, remappings to the Eulerian model levels are generally still required - but this need only be applied after a number of time steps - unless dynamic remapping methods are used. For this several different remapping methods has been implemented. The combined scheme is mass conserving, consistent, and multi-tracer efficient.
A mass and momentum conserving unsplit semi-Lagrangian framework for simulating multiphase flows
Energy Technology Data Exchange (ETDEWEB)
Owkes, Mark, E-mail: mark.owkes@montana.edu [Mechanical and Industrial Engineering, Montana State University, Bozeman, MT 59717 (United States); Desjardins, Olivier [Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853 (United States)
2017-03-01
In this work, we present a computational methodology for convection and advection that handles discontinuities with second order accuracy and maintains conservation to machine precision. This method can transport a variety of discontinuous quantities and is used in the context of an incompressible gas–liquid flow to transport the phase interface, momentum, and scalars. The proposed method provides a modification to the three-dimensional, unsplit, second-order semi-Lagrangian flux method of Owkes & Desjardins (JCP, 2014). The modification adds a refined grid that provides consistent fluxes of mass and momentum defined on a staggered grid and discrete conservation of mass and momentum, even for flows with large density ratios. Additionally, the refined grid doubles the resolution of the interface without significantly increasing the computational cost over previous non-conservative schemes. This is possible due to a novel partitioning of the semi-Lagrangian fluxes into a small number of simplices. The proposed scheme is tested using canonical verification tests, rising bubbles, and an atomizing liquid jet.
A Computational Realization of a Semi-Lagrangian Method for Solving the Advection Equation
Directory of Open Access Journals (Sweden)
Alexander Efremov
2014-01-01
Full Text Available A parallel implementation of a method of the semi-Lagrangian type for the advection equation on a hybrid architecture computation system is discussed. The difference scheme with variable stencil is constructed on the base of an integral equality between the neighboring time levels. The proposed approach allows one to avoid the Courant-Friedrichs-Lewy restriction on the relation between time step and mesh size. The theoretical results are confirmed by numerical experiments. Performance of a sequential algorithm and several parallel implementations with the OpenMP and CUDA technologies in the C language has been studied.
On the link between martian total ozone and potential vorticity
Holmes, James A.; Lewis, Stephen R.; Patel, Manish R.
2017-01-01
We demonstrate for the first time that total ozone in the martian atmosphere is highly correlated with the dynamical tracer, potential vorticity, under certain conditions. The degree of correlation is investigated using a Mars global circulation model including a photochemical model. Potential vorticity is the quantity of choice to explore the dynamical nature of polar vortices because it contains information on winds and temperature in a single scalar variable. The correlation is found to display a distinct seasonal variation, with a strong positive correlation in both northern and southern winter at poleward latitudes in the northern and southern hemisphere respectively. The identified strong correlation implies variations in polar total ozone during winter are predominantly controlled by dynamical processes in these spatio-temporal regions. The weak correlation in northern and southern summer is due to the dominance of photochemical reactions resulting from extended exposure to sunlight. The total ozone/potential vorticity correlation is slightly weaker in southern winter due to topographical variations and the preference for ozone to accumulate in Hellas basin. In northern winter, total ozone can be used to track the polar vortex edge. The ozone/potential vorticity ratio is calculated for both northern and southern winter on Mars for the first time. Using the strong correlation in total ozone and potential vorticity in northern winter inside the polar vortex, it is shown that potential vorticity can be used as a proxy to deduce the distribution of total ozone where satellites cannot observe for the majority of northern winter. Where total ozone observations are available on the fringes of northern winter at poleward latitudes, the strong relationship of total ozone and potential vorticity implies that total ozone anomalies in the surf zone of the northern polar vortex can potentially be used to determine the origin of potential vorticity filaments.
Potential vorticity field in the Bay of Bengal during southwest monsoon
Digital Repository Service at National Institute of Oceanography (India)
Murty, V.S.N.; Rao, D.P.
theta), potential vorticity distribution is complex due to wind and freshwater forcings. The beta -effect dominates the potential vorticity field on 26.9 sigma theta isopycnal. The field of potential vorticity closely follows that of circulation...
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).
Semi-analytic variable charge solitary waves involving dust phase-space vortices (holes)
Energy Technology Data Exchange (ETDEWEB)
Tribeche, Mouloud; Younsi, Smain; Amour, Rabia; Aoutou, Kamel [Plasma Physics Group, Faculty of Sciences-Physics, Theoretical Physics Laboratory, University of Bab-Ezzouar, USTHB BP 32, El Alia, Algiers 16111 (Algeria)], E-mail: mtribeche@usthb.dz
2009-09-15
A semi-analytic model for highly nonlinear solitary waves involving dust phase-space vortices (holes) is outlined. The variable dust charge is expressed in terms of the Lambert function and we take advantage of this transcendental function to investigate the localized structures that may occur in a dusty plasma with variable charge trapped dust particles. Our results which complement the previously published work on this problem (Schamel et al 2001 Phys. Plasmas 8 671) should be of basic interest for experiments that involve the trapping of dust particles in ultra-low-frequency dust acoustic modes.
Semi-analytic variable charge solitary waves involving dust phase-space vortices (holes)
International Nuclear Information System (INIS)
Tribeche, Mouloud; Younsi, Smain; Amour, Rabia; Aoutou, Kamel
2009-01-01
A semi-analytic model for highly nonlinear solitary waves involving dust phase-space vortices (holes) is outlined. The variable dust charge is expressed in terms of the Lambert function and we take advantage of this transcendental function to investigate the localized structures that may occur in a dusty plasma with variable charge trapped dust particles. Our results which complement the previously published work on this problem (Schamel et al 2001 Phys. Plasmas 8 671) should be of basic interest for experiments that involve the trapping of dust particles in ultra-low-frequency dust acoustic modes.
Felici, Helene M.; Drela, Mark
1993-01-01
A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.
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
Potential Vorticity Evolution in the Co-orbital Region of Embedded Protoplanets
International Nuclear Information System (INIS)
Koller, J.
2004-01-01
This thesis presents two-dimensional hydrodynamic disk simulations with embedded protoplanets, emphasizing the non-linear dynamics in the co-orbital region. In particular, it demonstrates how a protoplanetary disk responds to embedded low mass planets at the inviscid limit. Since the potential vorticity (PV) flow is not conserved, due to the spiral shocks and possibly boundary layer effects emanating from the planet, the PV profile develops inflection points which eventually render the flow unstable. Vortices are produced in association with the potential vorticity minima. Born in the separatrix region, these vortices experience close encounters with the planet, consequently exerting strong torques on the planet. The existence of these vortices, if confirmed, have important implications on planetary migration rates. The formation of vortices is discussed in more detail and a key parameter is found which depends solely on planet mass and sound speed. With this key parameter, one can predict the disk evolution, PV growth rates, and threshold conditions for forming vortices in the co-orbital region. An analytical estimate for the change of PV due to shocks is compared to the actual change in PV in the hydrodynamic simulations. They match well except in the inner region where vortices form. In addition, extensive resolution tests were carried out but uncertainties remain about the physics of this particular region
Helicity and potential vorticity in the surface boundary layer turbulence
Chkhetiani, Otto; Kurgansky, Michael; Koprov, Boris; Koprov, Victor
2016-04-01
An experimental measurement of all three components of the velocity and vorticity vectors, as well as the temperature and its gradient, and potential vorticity, has been developed using four acoustic anemometers. Anemometers were placed at vertices of a tetrahedron, the horizontal base of which was a rectangular triangle with equal legs, and the upper point was exactly above the top of the right angle. The distance from the surface to the tetrahedron its base was 5.5 m, and the lengths of legs and a vertical edge were 5 m. The measurements were carried out of total duration near 100 hours both in stable and unstable stratification conditions (at the Tsimlyansk Scientific Station in a uniform area of virgin steppe 700 x 650 m, August 2012). A covariance-correlation matrix for turbulent variations in all measured values has been calculated. In the daytime horizontal and vertical components of the helicity are of the order of -0.03 and +0.01 m s-2, respectively. The nighttime signs remain unchanged, but the absolute values are several times smaller. It is confirmed also by statistics of a relative helicity. The cospectra and spectral correlation coefficients have been calculated for all helicity components. The time variations in the components of "instantaneous" relative helicity and potential vorticity are considered. Connections of helicity with Monin-Obukhov length and the wind vertical profile structure are discussed. This work was supported by the Russian Science Foundation (Project No 14-27-00134).
Cucco, Andrea; Umgiesser, Georg
2015-09-15
In this work, we investigated if the Eulerian and the Lagrangian approaches for the computation of the Transport Time Scales (TTS) of semi-enclosed water bodies can be used univocally to define the spatial variability of basin flushing features. The Eulerian and Lagrangian TTS were computed for both simplified test cases and a realistic domain: the Venice Lagoon. The results confirmed the two approaches cannot be adopted univocally and that the spatial variability of the water renewal capacity can be investigated only through the computation of both the TTS. A specific analysis, based on the computation of a so-called Trapping Index, was then suggested to integrate the information provided by the two different approaches. The obtained results proved the Trapping Index to be useful to avoid any misleading interpretation due to the evaluation of the basin renewal features just from an Eulerian only or from a Lagrangian only perspective. Copyright © 2015 Elsevier Ltd. All rights reserved.
On the theory of point vortices in two-dimensional Bose liquids
International Nuclear Information System (INIS)
Speliotopoulos, A.D.
1991-01-01
The physics and structure of the Kosterlitz-Thouless phase transition, as it is applied to superfluidity in two dimensions, will be studied by looking at the origins and properties of point vortices in a Bose Liquid. A lagrangian for the two-dimensional vortex gas is derived from a general microscopic lagrangian for 4 He atoms on an arbitrary compact Riemann Surface without boundary. In the contrast density limit the vortex hamiltonian obtained from this lagrangian is found to be the same as the Kosterlitz and Thouless coulombic interaction hamiltonian. The dynamics and symmetries of the vortex gas on compact Riemann Surfaces are analyzed using lagrangian dynamics and Dirac's theory of constraints is used to formulate the hamiltonian dynamics for the system. The superfluid phase transition of the general vortex gas, in which the circulations may be any non-zero integer, is studied. When the net circulation of the system is not zero the absence of a superfluid phase is shown. When the net circulation of the vortices vanishes, presence of off-diagonal long range order is demonstrated and the existence of an order parameter is proposed. The transition temperature for general vortex gas is shown to be the Kosterlitz-Thouless temperature. An upper bound for the average vortex number density is established for the general vortex gas and an exact expression is derived for the Kosterlitz-Thouless ensemble
Lagrangian relaxation based algorithm for trigeneration planning with storages
DEFF Research Database (Denmark)
Rong, Aiying; Lahdelma, Risto; Luh, Peter
2008-01-01
of three energy commodities follows a joint characteristic. This paper presents a Lagrangian relaxation (LR) based algorithm for trigeneration planning with storages based on deflected subgradient optimization method. The trigeneration planning problem is modeled as a linear programming (LP) problem...... an effective method for the long-term planning problem based on the proper strategy to form Lagrangian subproblems and solve the Lagrangian dual (LD) problem based on deflected subgradient optimization method. We also develop a heuristic for restoring feasibility from the LD solution. Numerical results based...
A variable resolution nonhydrostatic global atmospheric semi-implicit semi-Lagrangian model
Pouliot, George Antoine
2000-10-01
The objective of this project is to develop a variable-resolution finite difference adiabatic global nonhydrostatic semi-implicit semi-Lagrangian (SISL) model based on the fully compressible nonhydrostatic atmospheric equations. To achieve this goal, a three-dimensional variable resolution dynamical core was developed and tested. The main characteristics of the dynamical core can be summarized as follows: Spherical coordinates were used in a global domain. A hydrostatic/nonhydrostatic switch was incorporated into the dynamical equations to use the fully compressible atmospheric equations. A generalized horizontal variable resolution grid was developed and incorporated into the model. For a variable resolution grid, in contrast to a uniform resolution grid, the order of accuracy of finite difference approximations is formally lost but remains close to the order of accuracy associated with the uniform resolution grid provided the grid stretching is not too significant. The SISL numerical scheme was implemented for the fully compressible set of equations. In addition, the generalized minimum residual (GMRES) method with restart and preconditioner was used to solve the three-dimensional elliptic equation derived from the discretized system of equations. The three-dimensional momentum equation was integrated in vector-form to incorporate the metric terms in the calculations of the trajectories. Using global re-analysis data for a specific test case, the model was compared to similar SISL models previously developed. Reasonable agreement between the model and the other independently developed models was obtained. The Held-Suarez test for dynamical cores was used for a long integration and the model was successfully integrated for up to 1200 days. Idealized topography was used to test the variable resolution component of the model. Nonhydrostatic effects were simulated at grid spacings of 400 meters with idealized topography and uniform flow. Using a high
An improved Lagrangian relaxation and dual ascent approach to facility location problems
DEFF Research Database (Denmark)
Jörnsten, Kurt; Klose, Andreas
2016-01-01
not be reduced to the same extent as in the case of ordinary semi-Lagrangian relaxation. Hence, an effective method for optimizing the Lagrangian dual function is of utmost importance for obtaining a computational advantage from the simplified Lagrangian dual function. In this paper, we suggest a new dual ascent...... method for optimizing both the semi-Lagrangian dual function as well as its simplified form for the case of a generic discrete facility location problem and apply the method to the uncapacitated facility location problem. Our computational results show that the method generally only requires a very few...
Numerical simulation using vorticity-vector potential formulation
Tokunaga, Hiroshi
1993-01-01
An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the
A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics
Directory of Open Access Journals (Sweden)
E. Kaas
2013-11-01
Full Text Available A new hybrid Eulerian–Lagrangian numerical scheme (HEL for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass-conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place; i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.
Energy Technology Data Exchange (ETDEWEB)
Bartels, J; Peters, D [Rostock Univ. (Germany). Inst. fuer Atmosphaerenphysik
1998-12-31
The poleward advection of upper-tropospheric air is investigated for poleward Rossby wave breaking events. During boreal winter months the isentropic deformations of the tropopause are examined using maps of Ertel`s potential vorticity (EPV) and contour advection (CA) calculations. The role of ambient baro-tropic flow is further examined by idealized numerical models. In the vicinity of the tropopause the characteristic Lagrangian transport of air masses for ECMWF-analysis data are compared with high resolution (T106) ECHAM4 experiments. (author) 3 refs.
Energy Technology Data Exchange (ETDEWEB)
Bartels, J.; Peters, D. [Rostock Univ. (Germany). Inst. fuer Atmosphaerenphysik
1997-12-31
The poleward advection of upper-tropospheric air is investigated for poleward Rossby wave breaking events. During boreal winter months the isentropic deformations of the tropopause are examined using maps of Ertel`s potential vorticity (EPV) and contour advection (CA) calculations. The role of ambient baro-tropic flow is further examined by idealized numerical models. In the vicinity of the tropopause the characteristic Lagrangian transport of air masses for ECMWF-analysis data are compared with high resolution (T106) ECHAM4 experiments. (author) 3 refs.
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.
Conservation properties and potential systems of vorticity-type equations
International Nuclear Information System (INIS)
Cheviakov, Alexei F.
2014-01-01
Partial differential equations of the form divN=0, N t +curl M=0 involving two vector functions in R 3 depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R 4 (t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations, it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented
Two species of vortices in massive gauged non-linear sigma models
International Nuclear Information System (INIS)
Alonso-Izquierdo, A.; Fuertes, W. García; Guilarte, J. Mateos
2015-01-01
Non-linear sigma models with scalar fields taking values on ℂℙ"n complex manifolds are addressed. In the simplest n=1 case, where the target manifold is the S"2 sphere, we describe the scalar fields by means of stereographic maps. In this case when the U(1) symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnetic field, similar and richer self-dual vortices of different species in the south and north charts can be found by slightly modifying the potential. Two different situations are envisaged: either the vacuum orbit lies on a parallel in the sphere, or one pole and the same parallel form the vacuum orbit. Besides the self-dual vortices of two species, there exist BPS domain walls in the second case. Replacing the Maxwell contribution of the gauge field to the action by the second Chern-Simons secondary class, only possible in (2+1)-dimensional Minkowski space-time, new BPS topological defects of two species appear. Namely, both BPS vortices and domain ribbons in the south and the north charts exist because the vacuum orbit consits of the two poles and one parallel. Formulation of the gauged ℂℙ"2 model in a reference chart shows a self-dual structure such that BPS semi-local vortices exist. The transition functions to the second or third charts break the U(1)×SU(2) semi-local symmetry, but there is still room for standard self-dual vortices of the second species. The same structures encompassing N complex scalar fields are easily generalized to gauged ℂℙ"N models.
Two species of vortices in massive gauged non-linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Alonso-Izquierdo, A. [Departamento de Matemática Aplicada, Universidad de Salamanca,Facultad de Ciencias Agrarias y Ambientales, Av. Filiberto Villalobos 119, E-37008 Salamanca (Spain); Fuertes, W. García [Departamento de Física, Universidad de Oviedo, Facultad de Ciencias, Calle Calvo Sotelo s/n, E-33007 Oviedo (Spain); Guilarte, J. Mateos [Departamento de Física Fundamental, Universidad de Salamanca, Facultad de Ciencias, Plaza de la Merced, E-37008 Salamanca (Spain)
2015-02-23
Non-linear sigma models with scalar fields taking values on ℂℙ{sup n} complex manifolds are addressed. In the simplest n=1 case, where the target manifold is the S{sup 2} sphere, we describe the scalar fields by means of stereographic maps. In this case when the U(1) symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnetic field, similar and richer self-dual vortices of different species in the south and north charts can be found by slightly modifying the potential. Two different situations are envisaged: either the vacuum orbit lies on a parallel in the sphere, or one pole and the same parallel form the vacuum orbit. Besides the self-dual vortices of two species, there exist BPS domain walls in the second case. Replacing the Maxwell contribution of the gauge field to the action by the second Chern-Simons secondary class, only possible in (2+1)-dimensional Minkowski space-time, new BPS topological defects of two species appear. Namely, both BPS vortices and domain ribbons in the south and the north charts exist because the vacuum orbit consits of the two poles and one parallel. Formulation of the gauged ℂℙ{sup 2} model in a reference chart shows a self-dual structure such that BPS semi-local vortices exist. The transition functions to the second or third charts break the U(1)×SU(2) semi-local symmetry, but there is still room for standard self-dual vortices of the second species. The same structures encompassing N complex scalar fields are easily generalized to gauged ℂℙ{sup N} models.
International Nuclear Information System (INIS)
Beyl, L.M.
1979-01-01
It is shown that the Einstein, Weyl, supergravity and superconformal theories are special cases of gauge transformations in SU(4vertical-barN). This group is shown to contain SU(2,2) x SU(N) x U(1) for its commuting or Bose part, and to contain 8N supersymmetry generators for its anticommuting or Fermi part. Using the electromagnetic Lagrangian as a model, a super-Lagrangian is constructed for vector potentials. Invariance is automatic in free space, but, in the presence of matter, restrictions on the supersymmetry transformations are necessary. The Weyl action and the Einstein cosmological field equations are obtained in the appropriate limits. Finally, a super-Lagrangian is constructed from nongeometric principles which includes the Dirac Lagrangian and except for a sum over symmetry indices resembles the electron-electromagnetic Lagrangian
QED3 formulation of vortices in boson condensates and metafluid
International Nuclear Information System (INIS)
Soares, Thales Costa; Spalenza, Wesley; Helayel Neto, Jose Abdalla
2002-01-01
Full text: One consider a system of many non-relativistic particles as a fluid, going from the discrete set of space-time coordinates of each particle to a continuous field. With an interparticle potential that satisfies a number of physically reasonable assumptions, one shows how the Lagrangian describing the motion of the fluid displays an exact local gauge invariance governed by a scalar parameter. The conserved quantity associated to this local symmetry is derived and discussed in the light of planar Electrodynamics, with photons identified as sound waves in the fluid and point-like charges corresponding to vortices with azimuthal circulation. On the other hand, exploiting further the field configurations of planar Electrodynamics, one finds a peculiar source for the electrostatic sector with azimuthal electric field and a string-like scalar potential. This work sets out to attempt at establishing a parallel between this vortex-like electric field configurations in fluid dynamics. Vortices in boson condensates and the fluid dynamics of the condensates are reassessed and translated into electromagnetic fields of planar (Chern-Simons massive) QED. On The other hand, the metafluid equations, once suitable reduced from 3 to 2 space dimensions, are also seen to match field configurations of Maxwell (massless photons) planar QED. (author)
Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex
Curbelo, Jezabel; José García-Garrido, Víctor; Mechoso, Carlos Roberto; Mancho, Ana Maria; Wiggins, Stephen; Niang, Coumba
2017-07-01
In this paper we study the three-dimensional (3-D) Lagrangian structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using Lagrangian descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of Lagrangian transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the Lagrangian structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex Lagrangian patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.
Error Propagation dynamics: from PIV-based pressure reconstruction to vorticity field calculation
Pan, Zhao; Whitehead, Jared; Richards, Geordie; Truscott, Tadd; USU Team; BYU Team
2017-11-01
Noninvasive data from velocimetry experiments (e.g., PIV) have been used to calculate vorticity and pressure fields. However, the noise, error, or uncertainties in the PIV measurements would eventually propagate to the calculated pressure or vorticity field through reconstruction schemes. Despite the vast applications of pressure and/or vorticity field calculated from PIV measurements, studies on the error propagation from the velocity field to the reconstructed fields (PIV-pressure and PIV-vorticity are few. In the current study, we break down the inherent connections between PIV-based pressure reconstruction and PIV-based vorticity calculation. The similar error propagation dynamics, which involve competition between physical properties of the flow and numerical errors from reconstruction schemes, are found in both PIV-pressure and PIV-vorticity reconstructions.
Streaming vorticity flux from oscillating walls with finite amplitude
Wu, J. Z.; Wu, X. H.; Wu, J. M.
1993-01-01
How to describe vorticity creation from a moving wall is a long standing problem. This paper discusses relevant issues at the fundamental level. First, it is shown that the concept of 'vorticity flux due to wall acceleration' can be best understood by following fluid particles on the wall rather than observing the flow at fixed spatial points. This is of crucial importance when the time-averaged flux is to be considered. The averaged flux has to be estimated in a wall-fixed frame of reference (in which there is no flux due to wall acceleration at all); or, if an inertial frame of reference is used, the generalized Lagrangian mean (GLM) also gives the same result. Then, for some simple but typical configurations, the time-averaged vorticity flux from a harmonically oscillating wall with finite amplitude is analyzed, without appealing to small perturbation. The main conclusion is that the wall oscillation will produce an additional mean vorticity flux (a fully nonlinear streaming effect), which is partially responsible for the mechanism of vortex flow control by waves. The results provide qualitative explanation for some experimentally and/or computationally observed phenomena.
Effects of outer perturbances on dynamics of wake vortices
International Nuclear Information System (INIS)
Baranov, N.A.; Belotserkovsky, A.S.; Turchak, L.I.
2004-01-01
One of the problems in aircraft flight safety is reduction of the risk related with aircraft encounter with wake vortices generated by other aircraft. An efficient approach to this problem is design of systems providing information on areas of potential danger of wake vortices to pilots in real time. The main components of such a system are a unit for calculations of wake vortices behind aircraft and a unit for calculations of areas of potential danger. A promising way to development of real time algorithms for calculation of wake vortices is the use of vortex methods in CFD based on the hypothesis of quasi-3D flow in the area of wake vorticity. The mathematical model developed by our team calculates positions and intensity of wake vortices past aircraft taking account of such effects as viscous dissipation of vortices, effects of ambient turbulence, wind shear, as well as viscous interaction between wake vortices and the underlying surface. The necessity of including the last factor could be stems from the fact that in the case where wake vortices are in close proximity of the rigid surface, the viscous interaction between the wake vortices and the surface boundary layer results in the boundary layer separation changing the overall intensity and dynamics of the wake vortices. To evaluate the boundaries of the danger areas the authors use an approach based on calculation of additional aerodynamic forces and moments acting on the aircraft encountering wake vortices by means of evaluation of the aircraft additional velocities and angular rates corresponding to distribution of disturbed velocities on the aircraft surface. These criteria could be based on local characteristics of the vorticity areas or on characteristics related to the perturbation effects on the aircraft. The latter characteristics include the actual aerodynamic roll moment, the maximum angular rate or the maximum roll of the aircraft under perturbations in the wake vortices. To estimate the accuracy
Samaké, Abdoulaye; Rampal, Pierre; Bouillon, Sylvain; Ólason, Einar
2017-12-01
We present a parallel implementation framework for a new dynamic/thermodynamic sea-ice model, called neXtSIM, based on the Elasto-Brittle rheology and using an adaptive mesh. The spatial discretisation of the model is done using the finite-element method. The temporal discretisation is semi-implicit and the advection is achieved using either a pure Lagrangian scheme or an Arbitrary Lagrangian Eulerian scheme (ALE). The parallel implementation presented here focuses on the distributed-memory approach using the message-passing library MPI. The efficiency and the scalability of the parallel algorithms are illustrated by the numerical experiments performed using up to 500 processor cores of a cluster computing system. The performance obtained by the proposed parallel implementation of the neXtSIM code is shown being sufficient to perform simulations for state-of-the-art sea ice forecasting and geophysical process studies over geographical domain of several millions squared kilometers like the Arctic region.
A study on assimilating potential vorticity data
Li, Yong; Ménard, Richard; Riishøjgaard, Lars Peter; Cohn, Stephen E.; Rood, Richard B.
1998-08-01
The correlation that exists between the potential vorticity (PV) field and the distribution of chemical tracers such as ozone suggests the possibility of using tracer observations as proxy PV data in atmospheric data assimilation systems. Especially in the stratosphere, there are plentiful tracer observations but a general lack of reliable wind observations, and the correlation is most pronounced. The issue investigated in this study is how model dynamics would respond to the assimilation of PV data. First, numerical experiments of identical-twin type were conducted with a simple univariate nuding algorithm and a global shallow water model based on PV and divergence (PV-D model). All model fields are successfully reconstructed through the insertion of complete PV data alone if an appropriate value for the nudging coefficient is used. A simple linear analysis suggests that slow modes are recovered rapidly, at a rate nearly independent of spatial scale. In a more realistic experiment, appropriately scaled total ozone data from the NIMBUS-7 TOMS instrument were assimilated as proxy PV data into the PV-D model over a 10-day period. The resulting model PV field matches the observed total ozone field relatively well on large spatial scales, and the PV, geopotential and divergence fields are dynamically consistent. These results indicate the potential usefulness that tracer observations, as proxy PV data, may offer in a data assimilation system.
Classification of hemispheric monthly mean stratospheric potential vorticity fields
Directory of Open Access Journals (Sweden)
R. Huth
Full Text Available Monthly mean NCEP reanalysis potential vorticity fields at the 650 K isentropic level over the Northern and Southern Hemispheres between 1979 and 1997 were studied using multivariate analysis tools. Principal component analysis in the T-mode was applied to demonstrate the validity of such statistical techniques for the study of stratospheric dynamics and climatology. The method, complementarily applied to both the raw and anomaly fields, was useful in determining and classifying the characteristics of winter and summer PV fields on both hemispheres, in particular, the well-known differences in the behaviour and persistence of the polar vortices. It was possible to identify such features as sudden warming events in the Northern Hemisphere and final warming dates in both hemispheres. The stratospheric impact of other atmospheric processes, such as volcanic eruptions, also identified though the results, must be viewed at this stage as tentative. An interesting change in behaviour around 1990 was detected over both hemispheres.
Key words. Meteorology and atmospheric dynamics (middle atmosphere dynamics; general circulation; climatology
Directory of Open Access Journals (Sweden)
P. Senthilkumaran
2012-01-01
Full Text Available Interference of optical beams with optical vortices is often encountered in singular optics. Since interferometry makes the phase observable by intensity measurement, it brings out a host of applications and helps to understand the optical vortex. In this article we present an optical vortex interferometer that can be used in optical testing and has the potential to increase the accuracy of measurements. In an optical vortex interferometer (OVI, a lattice of vortices is formed, and the movement of the cores of these vortices is tracked when one of the interfering beams is deformed. Instead of multiple vortices in an OVI, an isolated single vortex also finds applications in optical testing. Finally, singularity in scalar and vector fields is presented, and the relation between them is illustrated by the superposition of these beams.
Stable Non-Abelian Semi-Superfluid Vortices in Dense QCD
Chatterjee, Chandrasekhar; Nitta, Muneto
Color superconductivity is expected to be formed in high density quark matter where color symmetry is spontaneously broken in the presence of di-quark condensate. Stable non-Abelian vortices or color magnetic flux tubes exist in the color-flavor locked phase at asymptotically high density. CP2 Nambu-Goldstone (NG) bosons and Majorana fermions belonging to the triplet representation are localized around a non-Abelian vortex. We discuss the zero mode analysis and the low-energy effective world sheet theory of a non-Abelian vortex. We determine the interactions of these bosonic and fermionic modes by using the nonlinear realization method. We also discuss the Aharanov-Bohm (AB) phases of charged particles, such as, electrons, muons, and color-flavor locked mesons made of tetra-quarks encircling around a non-Abelian vortex in the presence of electro-magnetic fields. This is a review based on our recent works [1-3].
Implications of Lagrangian transport for coupled chemistry-climate simulations
Stenke, A.; Dameris, M.; Grewe, V.; Garny, H.
2008-10-01
For the first time a purely Lagrangian transport algorithm is applied in a fully coupled chemistry-climate model (CCM). We use the Lagrangian scheme ATTILA for the transport of water vapour, cloud water and chemical trace species in the ECHAM4.L39(DLR)/CHEM (E39C) CCM. The advantage of the Lagrangian approach is that it is numerically non-diffusive and therefore maintains steeper and more realistic gradients than the operational semi-Lagrangian transport scheme. In case of radiatively active species changes in the simulated distributions feed back to model dynamics which in turn affect the modelled transport. The implications of the Lagrangian transport scheme for stratospheric model dynamics and tracer distributions in the upgraded model version E39C-ATTILA (E39C-A) are evaluated by comparison with observations and results of the E39C model with the operational semi-Lagrangian advection scheme. We find that several deficiencies in stratospheric dynamics in E39C seem to originate from a pronounced modelled wet bias and an associated cold bias in the extra-tropical lowermost stratosphere. The reduction of the simulated moisture and temperature bias in E39C-A leads to a significant advancement of stratospheric dynamics in terms of the mean state as well as annual and interannual variability. As a consequence of the favourable numerical characteristics of the Lagrangian transport scheme and the improved model dynamics, E39C-A generally shows more realistic stratospheric tracer distributions: Compared to E39C high stratospheric chlorine (Cly) concentrations extend further downward and agree now well with analyses derived from observations. Therefore E39C-A realistically covers the altitude of maximum ozone depletion in the stratosphere. The location of the ozonopause, i.e. the transition from low tropospheric to high stratospheric ozone values, is also clearly improved in E39C-A. Furthermore, the simulated temporal evolution of stratospheric Cly in the past is
Spindles and active vortices in a model of confined filament-motor mixtures.
Head, David A; Briels, Wj; Gompper, Gerhard
2011-11-16
Robust self-organization of subcellular structures is a key principle governing the dynamics and evolution of cellular life. In fission yeast cells undergoing division, the mitotic spindle spontaneously emerges from the interaction of microtubules, motor proteins and the confining cell walls, and asters and vortices have been observed to self-assemble in quasi-two dimensional microtubule-kinesin assays. There is no clear microscopic picture of the role of the active motors driving this pattern formation, and the relevance of continuum modeling to filament-scale structures remains uncertain. Here we present results of numerical simulations of a discrete filament-motor protein model confined to a pressurised cylindrical box. Stable spindles, nematic configurations, asters and high-density semi-asters spontaneously emerge, the latter pair having also been observed in cytosol confined within emulsion droplets. State diagrams are presented delineating each stationary state as the pressure, motor speed and motor density are varied. We further highlight a parameter regime where vortices form exhibiting collective rotation of all filaments, but have a finite life-time before contracting to a semi-aster. Quantifying the distribution of life-times suggests this contraction is a Poisson process. Equivalent systems with fixed volume exhibit persistent vortices with stochastic switching in the direction of rotation, with switching times obeying similar statistics to contraction times in pressurised systems. Furthermore, we show that increasing the detachment rate of motors from filament plus-ends can both destroy vortices and turn some asters into vortices. We have shown that discrete filament-motor protein models provide new insights into the stationary and dynamical behavior of active gels and subcellular structures, because many phenomena occur on the length-scale of single filaments. Based on our findings, we argue the need for a deeper understanding of the microscopic
Discrete-time Calogero-Moser system and Lagrangian 1-form structure
International Nuclear Information System (INIS)
Yoo-Kong, Sikarin; Lobb, Sarah; Nijhoff, Frank
2011-01-01
We study the Lagrange formalism of the (rational) Calogero-Moser (CM) system, both in discrete time and continuous time, as a first example of a Lagrangian 1-form structure in the sense of the recent paper (Lobb and Nijhoff 2009 J. Phys. A: Math. Theor.42 454013). The discrete-time model of the CM system was established some time ago arising as a pole reduction of a semi-discrete version of the Kadomtsev-Petviashvili (KP) equation, and was shown to lead to an exactly integrable correspondence (multivalued map). In this paper, we present the full KP solution based on the commutativity of the discrete-time flows in the two discrete KP variables. The compatibility of the corresponding Lax matrices is shown to lead directly to the relevant closure relation on the level of the Lagrangians. Performing successive continuum limits on both the level of the KP equation and the level of the CM system, we establish the proper Lagrangian 1-form structure for the continuum case of the CM model. We use the example of the three-particle case to elucidate the implementation of the novel least-action principle, which was presented in Lobb and Nijhoff (2009), for the simpler case of Lagrangian 1-forms. (paper)
Schroeder, Craig; Zheng, Wen; Fedkiw, Ronald
2012-01-01
-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension force, which when treated explicitly leads to a tight time step restriction. By applying surface tension
Lagrangian fluid description with simple applications in compressible plasma and gas dynamics
International Nuclear Information System (INIS)
Schamel, Hans
2004-01-01
The Lagrangian fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid elements, not only presents an alternative to the more common Eulerian description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as Lagrangian codes and experimental techniques are developed utilizing the Lagrangian point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum--as seen in laboratory experiments--is interpreted by means of the Lagrangian fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the Lagrangian flow velocity is given by its initial value and hence the Lagrangian velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one
Lagrangian fluid description with simple applications in compressible plasma and gas dynamics
Schamel, Hans
2004-03-01
The Lagrangian fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid elements, not only presents an alternative to the more common Eulerian description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as Lagrangian codes and experimental techniques are developed utilizing the Lagrangian point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum-as seen in laboratory experiments-is interpreted by means of the Lagrangian fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the Lagrangian flow velocity is given by its initial value and hence the Lagrangian velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one-dimension (1D
Stratosphere-troposphere exchange in an extratropical cyclone, calculated with a Lagrangian method
Directory of Open Access Journals (Sweden)
M. Sigmond
Full Text Available A Lagrangian technique is developed and applied to calculate stratosphere-troposphere exchange in an extratropical cyclone. This exchange is computed from the potential vorticity or PV along trajectories, calculated from ECMWF circulation data. Special emphasis is put on the statistical significance of the results. The computed field of the cross-tropopause flux is dominated by elongated patterns of statistically significant large downward and small upward fluxes. The downward fluxes mainly occur in the lower part of the considered tropopause folds. The upward fluxes are found near the entrance of the folds, in the tropopause ridges. The ratio between the area averaged downward and upward cross-tropopause fluxes increases with increasing strength of the cyclone. Since the largest fluxes are shown to occur in the regions with the largest wind shear, where PV-mixing is thought to cause large cross-tropopause fluxes, the results are expected to be reliable, at least in a qualitative sense. The position of a tropopause fold along the northwest coast of Africa is confirmed by total ozone observations. The results indicate that the applied Lagrangian technique is an appropriate tool for diagnosing stratosphere-troposphere exchange.
Key words: Meteorology and atmospheric dynamics (general circulation; mesoscale meteorology; middle atmosphere dynamics
Stratosphere-troposphere exchange in an extratropical cyclone, calculated with a Lagrangian method
Directory of Open Access Journals (Sweden)
M. Sigmond
2000-05-01
Full Text Available A Lagrangian technique is developed and applied to calculate stratosphere-troposphere exchange in an extratropical cyclone. This exchange is computed from the potential vorticity or PV along trajectories, calculated from ECMWF circulation data. Special emphasis is put on the statistical significance of the results. The computed field of the cross-tropopause flux is dominated by elongated patterns of statistically significant large downward and small upward fluxes. The downward fluxes mainly occur in the lower part of the considered tropopause folds. The upward fluxes are found near the entrance of the folds, in the tropopause ridges. The ratio between the area averaged downward and upward cross-tropopause fluxes increases with increasing strength of the cyclone. Since the largest fluxes are shown to occur in the regions with the largest wind shear, where PV-mixing is thought to cause large cross-tropopause fluxes, the results are expected to be reliable, at least in a qualitative sense. The position of a tropopause fold along the northwest coast of Africa is confirmed by total ozone observations. The results indicate that the applied Lagrangian technique is an appropriate tool for diagnosing stratosphere-troposphere exchange.Key words: Meteorology and atmospheric dynamics (general circulation; mesoscale meteorology; middle atmosphere dynamics
A Lagrangian dynamic subgrid-scale model turbulence
Meneveau, C.; Lund, T. S.; Cabot, W.
1994-01-01
A new formulation of the dynamic subgrid-scale model is tested in which the error associated with the Germano identity is minimized over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to flows in complex geometries that do not possess homogeneous directions. The characteristic Lagrangian time scale over which the averaging is performed is chosen such that the model is purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested successfully in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are superior to those of the plane-averaged dynamic model. The relationship between the averaged terms in the model and vortical structures (worms) that appear in the LES is investigated. Computational overhead is kept small (about 10 percent above the CPU requirements of the volume or plane-averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.
Next Generation Extended Lagrangian Quantum-based Molecular Dynamics
Negre, Christian
2017-06-01
A new framework for extended Lagrangian first-principles molecular dynamics simulations is presented, which overcomes shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while maintaining important advantages of the unified extended Lagrangian formulation of density functional theory pioneered by Car and Parrinello three decades ago. The new framework allows, for the first time, energy conserving, linear-scaling Born-Oppenheimer molecular dynamics simulations, which is necessary to study larger and more realistic systems over longer simulation times than previously possible. Expensive, self-consinstent-field optimizations are avoided and normal integration time steps of regular, direct Born-Oppenheimer molecular dynamics can be used. Linear scaling electronic structure theory is presented using a graph-based approach that is ideal for parallel calculations on hybrid computer platforms. For the first time, quantum based Born-Oppenheimer molecular dynamics simulation is becoming a practically feasible approach in simulations of +100,000 atoms-representing a competitive alternative to classical polarizable force field methods. In collaboration with: Anders Niklasson, Los Alamos National Laboratory.
Yearsley, J. R.
2017-12-01
The semi-Lagrangian numerical scheme employed by RBM, a model for simulating time-dependent, one-dimensional water quality constituents in advection-dominated rivers, is highly scalable both in time and space. Although the model has been used at length scales of 150 meters and time scales of three hours, the majority of applications have been at length scales of 1/16th degree latitude/longitude (about 5 km) or greater and time scales of one day. Applications of the method at these scales has proven successful for characterizing the impacts of climate change on water temperatures in global rivers and on the vulnerability of thermoelectric power plants to changes in cooling water temperatures in large river systems. However, local effects can be very important in terms of ecosystem impacts, particularly in the case of developing mixing zones for wastewater discharges with pollutant loadings limited by regulations imposed by the Federal Water Pollution Control Act (FWPCA). Mixing zone analyses have usually been decoupled from large-scale watershed influences by developing scenarios that represent critical scenarios for external processes associated with streamflow and weather conditions . By taking advantage of the particle-tracking characteristics of the numerical scheme, RBM can provide results at any point in time within the model domain. We develop a proof of concept for locations in the river network where local impacts such as mixing zones may be important. Simulated results from the semi-Lagrangian numerical scheme are treated as input to a finite difference model of the two-dimensional diffusion equation for water quality constituents such as water temperature or toxic substances. Simulations will provide time-dependent, two-dimensional constituent concentration in the near-field in response to long-term basin-wide processes. These results could provide decision support to water quality managers for evaluating mixing zone characteristics.
Energy Technology Data Exchange (ETDEWEB)
Wu, Jie-Zhi [Peking Univ., Beijing (China). College of Engineering; Ma, Hui-Yang [Univ. of Chinese Academy of Sciences, Beijing (China). Dept. of Physics; Zhou, Ming-De [Arizona Univ., Tucson, AZ (United States). Dept. of Aerospace and Mechanical Engineering
2015-11-01
This book is a comprehensive and intensive book for graduate students in fluid dynamics as well as scientists, engineers and applied mathematicians. Offering a systematic introduction to the physical theory of vortical flows at graduate level, it considers the theory of vortical flows as a branch of fluid dynamics focusing on shearing process in fluid motion, measured by vorticity. It studies vortical flows according to their natural evolution stages,from being generated to dissipated. As preparation, the first three chapters of the book provide background knowledge for entering vortical flows. The rest of the book deals with vortices and vortical flows, following their natural evolution stages. Of various vortices the primary form is layer-like vortices or shear layers, and secondary but stronger form is axial vortices mainly formed by the rolling up of shear layers. Problems are given at the end of each chapter and Appendix, some for helping understanding the basic theories, and some involving specific applications; but the emphasis of both is always on physical thinking.
International Nuclear Information System (INIS)
Wu, Jie-Zhi; Ma, Hui-Yang; Zhou, Ming-De
2015-01-01
This book is a comprehensive and intensive book for graduate students in fluid dynamics as well as scientists, engineers and applied mathematicians. Offering a systematic introduction to the physical theory of vortical flows at graduate level, it considers the theory of vortical flows as a branch of fluid dynamics focusing on shearing process in fluid motion, measured by vorticity. It studies vortical flows according to their natural evolution stages,from being generated to dissipated. As preparation, the first three chapters of the book provide background knowledge for entering vortical flows. The rest of the book deals with vortices and vortical flows, following their natural evolution stages. Of various vortices the primary form is layer-like vortices or shear layers, and secondary but stronger form is axial vortices mainly formed by the rolling up of shear layers. Problems are given at the end of each chapter and Appendix, some for helping understanding the basic theories, and some involving specific applications; but the emphasis of both is always on physical thinking.
Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: numerical testing
Rõõm, Rein; Männik, Aarne; Luhamaa, Andres; Zirk, Marko
2007-01-01
The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and non-hydrostatic effect presentation capability. Comparison demonstrates good (in strong primary wave generation) to satisfactory (in weak ...
Vortices and vortex lattices in quantum ferrofluids
International Nuclear Information System (INIS)
Martin, A M; Marchant, N G; Parker, N G; O’Dell, D H J
2017-01-01
The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose–Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross–Pitaevskii equation, ranging from analytic treatments based on the Thomas–Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii–Kosterlitz–Thouless transition. (topical review)
Vortices and vortex lattices in quantum ferrofluids
Martin, A. M.; Marchant, N. G.; O'Dell, D. H. J.; Parker, N. G.
2017-03-01
The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.
Multi-dimensional upwinding-based implicit LES for the vorticity transport equations
Foti, Daniel; Duraisamy, Karthik
2017-11-01
Complex turbulent flows such as rotorcraft and wind turbine wakes are characterized by the presence of strong coherent structures that can be compactly described by vorticity variables. The vorticity-velocity formulation of the incompressible Navier-Stokes equations is employed to increase numerical efficiency. Compared to the traditional velocity-pressure formulation, high order numerical methods and sub-grid scale models for the vorticity transport equation (VTE) have not been fully investigated. Consistent treatment of the convection and stretching terms also needs to be addressed. Our belief is that, by carefully designing sharp gradient-capturing numerical schemes, coherent structures can be more efficiently captured using the vorticity-velocity formulation. In this work, a multidimensional upwind approach for the VTE is developed using the generalized Riemann problem-based scheme devised by Parish et al. (Computers & Fluids, 2016). The algorithm obtains high resolution by augmenting the upwind fluxes with transverse and normal direction corrections. The approach is investigated with several canonical vortex-dominated flows including isolated and interacting vortices and turbulent flows. The capability of the technique to represent sub-grid scale effects is also assessed. Navy contract titled ``Turbulence Modelling Across Disparate Length Scales for Naval Computational Fluid Dynamics Applications,'' through Continuum Dynamics, Inc.
Spindles and active vortices in a model of confined filament-motor mixtures
Directory of Open Access Journals (Sweden)
Head David A
2011-11-01
Full Text Available Abstract Background Robust self-organization of subcellular structures is a key principle governing the dynamics and evolution of cellular life. In fission yeast cells undergoing division, the mitotic spindle spontaneously emerges from the interaction of microtubules, motor proteins and the confining cell walls, and asters and vortices have been observed to self-assemble in quasi-two dimensional microtubule-kinesin assays. There is no clear microscopic picture of the role of the active motors driving this pattern formation, and the relevance of continuum modeling to filament-scale structures remains uncertain. Results Here we present results of numerical simulations of a discrete filament-motor protein model confined to a pressurised cylindrical box. Stable spindles, nematic configurations, asters and high-density semi-asters spontaneously emerge, the latter pair having also been observed in cytosol confined within emulsion droplets. State diagrams are presented delineating each stationary state as the pressure, motor speed and motor density are varied. We further highlight a parameter regime where vortices form exhibiting collective rotation of all filaments, but have a finite life-time before contracting to a semi-aster. Quantifying the distribution of life-times suggests this contraction is a Poisson process. Equivalent systems with fixed volume exhibit persistent vortices with stochastic switching in the direction of rotation, with switching times obeying similar statistics to contraction times in pressurised systems. Furthermore, we show that increasing the detachment rate of motors from filament plus-ends can both destroy vortices and turn some asters into vortices. Conclusions We have shown that discrete filament-motor protein models provide new insights into the stationary and dynamical behavior of active gels and subcellular structures, because many phenomena occur on the length-scale of single filaments. Based on our findings, we argue
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.
Unsteady force estimation using a Lagrangian drift-volume approach
McPhaden, Cameron J.; Rival, David E.
2018-04-01
A novel Lagrangian force estimation technique for unsteady fluid flows has been developed, using the concept of a Darwinian drift volume to measure unsteady forces on accelerating bodies. The construct of added mass in viscous flows, calculated from a series of drift volumes, is used to calculate the reaction force on an accelerating circular flat plate, containing highly-separated, vortical flow. The net displacement of fluid contained within the drift volumes is, through Darwin's drift-volume added-mass proposition, equal to the added mass of the plate and provides the reaction force of the fluid on the body. The resultant unsteady force estimates from the proposed technique are shown to align with the measured drag force associated with a rapid acceleration. The critical aspects of understanding unsteady flows, relating to peak and time-resolved forces, often lie within the acceleration phase of the motions, which are well-captured by the drift-volume approach. Therefore, this Lagrangian added-mass estimation technique opens the door to fluid-dynamic analyses in areas that, until now, were inaccessible by conventional means.
Fu, Yuan; Zhang, Da-peng; Xie, Xi-lin
2018-04-01
In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed.
Lagrangian statistics in weakly forced two-dimensional turbulence.
Rivera, Michael K; Ecke, Robert E
2016-01-01
Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.
National Research Council Canada - National Science Library
Green, Sheldon I
1995-01-01
... . . . . . . . . . . . . . . . Vorticity Kinematics and Dynamics - Physical Principles The Vorticity Equation with Examples . . . . Summary . . . . . . . . . . . . . . . . . Vorticity in Orthogonal...
Correlations between Abelian monopoles and center vortices
Energy Technology Data Exchange (ETDEWEB)
Hosseini Nejad, Seyed Mohsen, E-mail: smhosseininejad@ut.ac.ir; Deldar, Sedigheh, E-mail: sdeldar@ut.ac.ir
2017-04-15
We study the correlations between center vortices and Abelian monopoles for SU(3) gauge group. Combining fractional fluxes of monopoles, center vortex fluxes are constructed in the thick center vortex model. Calculating the potentials induced by fractional fluxes constructing the center vortex flux in a thick center vortex-like model and comparing with the potential induced by center vortices, we observe an attraction between fractional fluxes of monopoles constructing the center vortex flux. We conclude that the center vortex flux is stable, as expected. In addition, we show that adding a contribution of the monopole-antimonopole pairs in the potentials induced by center vortices ruins the Casimir scaling at intermediate regime.
Potential vorticity dynamics for global scale circulations
International Nuclear Information System (INIS)
Lu, C.; Schubert, W.
1994-01-01
One of the most notable advances in extratropical dynamics this decade has been the understanding of large-scale atmospheric and oceanic processes by using potential vorticity dynamics, the so called open-quotes IPV thinking.close quotes This analysis method has also been successfully extended to some tropical atmospheric circulation systems such as hurricanes and the Hadley circulation. The fundamental idea behind such a dynamic system rests with the fact that PV is a tracer-like quantity since it is conserved (in the absence of friction and diabatic heating) following a fluid particle and carries both significant dynamic and thermodynamic information regarding fluid motion. Thus, the prediction and inversion of PV form the most succinct dynamic view of atmospheric and oceanic motions. Furthermore, PV dynamics provides access to many insightful dynamic analyses such as: Propagation of Rossby waves, barotropic and baroclinic instabilities for shear flows, and wave-mean flow interactions. All these features make IPV analysis a very attractive tool for studying geophysical fluid systems
Mang, Andreas; Biros, George
2017-01-01
We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.
High order curvilinear finite elements for elastic–plastic Lagrangian dynamics
International Nuclear Information System (INIS)
Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
2014-01-01
This paper presents a high-order finite element method for calculating elastic–plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame [1,2]. In order to handle transition to plastic flow, we formulate the stress–strain relation in rate (or incremental) form and augment our semi-discrete equations for Lagrangian hydrodynamics with an additional evolution equation for the deviatoric stress which is valid for arbitrary order spatial discretizations of the kinematic and thermodynamic variables. The semi-discrete equation for the deviatoric stress rate is developed for 2D planar, 2D axisymmetric and full 3D geometries. For each case, the strain rate is approximated via a collocation method at zone quadrature points while the deviatoric stress is approximated using an L 2 projection onto the thermodynamic basis. We apply high order, energy conserving, explicit time stepping methods to the semi-discrete equations to develop the fully discrete method. We conclude with numerical results from an extensive series of verification tests that demonstrate several practical advantages of using high-order finite elements for elastic–plastic flow
Diagnostic study on the relation between ozone and vorticity potential
Energy Technology Data Exchange (ETDEWEB)
Abdel Basset, H. [Department of Astronomy and Meteorology, Faculty of Science, Al Azhar University, Nasr City, Cairo (Egypt); Gahein, A. [Egyptian Meteorological Authority, Cairo (Egypt)
2003-04-01
A diagnostic analysis of a Mediterranean system and the associated tropopause folding for the period 27 February to 10 March, 1987 is presented. Geopotential height, potential vorticity (PV) and relative humidity distributions were diagnosed. The analysis indicates clear correlation between the development of the cut-off low and the tropopause folding. A series of vertical cross-sections at the ends of the jet streaks demonstrated that a fold could be captured using potential vorticity and relative humidity. Q-vectors were employed to investigate vertical motion in the vicinity of the fold and showed the exact positions of descent corresponding to the fold along the entire length of the jet streak. The analysis also shows that the strong correlation between total ozone and column integrated vorticity potential holds well for all levels. As both quantities are integrals through the atmosphere, this result is consistent with, but does not prove, a high independent linear dependence between ozone and PV. More case studies are needed to assure the high linear dependence between ozone and PV. The maximum transport of ozone from the stratosphere to the troposphere is coinciding with the maximum developing system, and also with the maximum values of PV. [Spanish] Se presenta un analisis diagnostico de un Sistema mediterraneo y del pliegue de la tropopausa asociado durante el periodo del 27 de febrero al 10 de marzo de 1987. Se diagnosticaron la altitud neopotencial, el potencial de vorticidad y la distribucion de la humedad relativa. El analisis indica una correlacion clara entre el desarrollo de la baja segregada y el pliegue de la tropopausa. Una serie de cortes verticales en los extremos de las trazas del chorro demostraron que el pliegue puede ser capturado utilizando el potencial de vorticidad y la humedad relativa. Para investigar la movilidad vertical en la vecindad del pliegue se utilizaron vectores Q, y se demostraron las posiciones exactas de descenso
Scott, James R.
1991-01-01
A numerical method is developed for solving periodic, three-dimensional, vortical flows around lifting airfoils in subsonic flow. The first-order method that is presented fully accounts for the distortion effects of the nonuniform mean flow on the convected upstream vortical disturbances. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Using an elliptic coordinate transformation, the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the Mach number and reduced frequency. The numerical scheme is validated through extensive comparisons with known solutions to unsteady vortical flow problems. In general, it is seen that the agreement between the numerical and analytical results is very good for reduced frequencies ranging from 0 to 4, and for Mach numbers ranging from .1 to .8. Numerical results are also presented for a wide variety of flow configurations for the purpose of determining the effects of airfoil thickness, angle of attack, camber, and Mach number on the unsteady lift and moment of airfoils subjected to periodic vortical gusts. It is seen that each of these parameters can have a significant effect on the unsteady airfoil response to the incident disturbances, and that the effect depends strongly upon the reduced frequency and the dimensionality of the gust. For a one-dimensional (transverse) or two-dimensional (transverse and longitudinal) gust, the results indicate that airfoil thickness increases the unsteady lift and moment at the low reduced frequencies but decreases it at the high reduced frequencies. The results show that an increase in airfoil Mach number leads to a significant increase in the unsteady lift and moment for the low reduced frequencies, but a
Alternative kinetic energy metrics for Lagrangian systems
Sarlet, W.; Prince, G.
2010-11-01
We examine Lagrangian systems on \\ {R}^n with standard kinetic energy terms for the possibility of additional, alternative Lagrangians with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such Lagrangians. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous Lagrangians for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom.
Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme
Rõõm, Rein; Männik, Aarne; Luhamaa, Andres
2007-01-01
Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller–Pearce–White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which res...
Dynamical properties of vortical structures on the beta-plane
DEFF Research Database (Denmark)
Sutyrin, G.G.; Hesthaven, J.S.; Lynov, Jens-Peter
1994-01-01
The long-time evolution of monopolar and dipolar vortices influenced by the large-scale gradient of the ambient potential vorticity (the beta-effect) is studied by direct numerical solutions of the equivalent barotropic quasi-geostrophic equation. Translation and reorganization of vortical...... structures are shown to depend strongly on their intensity. Transport of trapped fluid by vortical structures is illustrated by calculating particle trajectories and by considering closed isolines of potential vorticity and the streamfunction in a co-moving reference frame. The initial behaviour of strong...... monopoles is found to be well described by a recent approximate theory for the evolution of azimuthal mode one, even for times longer than the linear Rossby wave period. In the long-time limit, strong monopoles transport particles mainly westward, although the meridional displacement is several times larger...
Piecewise Potential Vorticity Inversion for Intense Extratropical Cyclones
Seiler, C.; Zwiers, F. W.
2017-12-01
Global climate models (GCMs) tend to simulate too few intense extratropical cyclones (ETCs) in the Northern Hemisphere (NH) under historic climate conditions. This bias may arise from the interactions of multiple drivers, including surface temperature gradients, latent heating in the lower troposphere, and the upper-level jet stream. Previous attempts to quantify the importance of these drivers include idealized model experiments or statistical approaches. The first method however cannot easily be implemented for a multi-GCM ensemble, and the second approach does not disentangle the interactions among drivers, nor does it prove causality. An alternative method that overcomes these limitations is piecewise potential vorticity inversion (PPVI). PPVI derives the wind and geopotential height fields by inverting potential vorticity (PV) for discrete atmospheric levels. Despite being a powerful diagnostic tool, PPVI has primarily been used to study the dynamics of individual events only. This study presents the first PPVI climatology for the 5% most intense NH ETCs that occurred from 1980 to 2016. Conducting PPVI to 3273 ETC tracks identified in ERA-Interim reanalysis, we quantified the contributions from 3 atmospheric layers to ETC intensity. The respective layers are the surface (1000 hPa), a lower atmospheric level (700-850 hPa) and an upper atmospheric level (100-500 hPa) that are associated with the contributions from surface temperature gradients, latent heating, and the jet stream, respectively. Results show that contributions are dominated by the lower level (40%), followed by the upper level (20%) and the surface (17%), while the remaining 23% are associated with the background flow. Contributions from the surface and the lower level are stronger in the western ocean basins owed to the presence of the warm ocean currents, while contributions from the upper level are stronger in the eastern basins. Vertical cross sections of ETC-centered composites show an
Vorticity and Λ polarization in baryon rich matter
Baznat, Mircea; Gudima, Konstantin; Prokhorov, George; Sorin, Alexander; Teryaev, Oleg; Zakharov, Valentin
2018-02-01
The polarization of Λ hyperons due to axial chiral vortical effect is discussed. The effect is proportional to (strange) chemical potential and is pronounced at lower energies in baryon-rich matter. The polarization of ¯ has the same sihn and larger magnitude. The emergence of vortical structures is observed in kinetic QGSM models. The hydrodynamical helicity separation receives the contribution of longitudinal velocity and vorticity implying the quadrupole structure of the latter. The transition from the quark vortical effects to baryons in confined phase may be achieved by exploring the axial charge. At the hadronic level the polarization corresponds to the cores of quantized vortices in pionic superfluid. The chiral vortical effects may be also studied in the frmework of Wigner function establishing the relation to the thermodynamical approach to polarization.
Thomas, Leif N.
2008-08-01
A mechanism for the generation of intrathermocline eddies (ITEs) at wind-forced fronts is examined using a high resolution numerical simulation. Favorable conditions for ITE formation result at fronts forced by "down-front" winds, i.e. winds blowing in the direction of the frontal jet. Down-front winds exert frictional forces that reduce the potential vorticity (PV) within the surface boundary in the frontal outcrop, providing a source for the low-PV water that is the materia prima of ITEs. Meandering of the front drives vertical motions that subduct the low-PV water into the pycnocline, pooling it into the coherent anticyclonic vortex of a submesoscale ITE. As the fluid is subducted along the outcropping frontal isopycnal, the low-PV water, which at the surface is associated with strongly baroclinic flow, re-expresses itself as water with nearly zero absolute vorticity. This generation of strong anticyclonic vorticity results from the tilting of the horizontal vorticity of the frontal jet, not from vortex squashing. During the formation of the ITE, high-PV water from the pycnocline is upwelled alongside the subducting low-PV surface water. The positive correlation between the ITE's velocity and PV fields results in an upward, along-isopycnal eddy PV flux that scales with the surface frictional PV flux driven by the wind. The relationship between the eddy and wind-induced frictional PV flux is nonlocal in time, as the eddy PV flux persists long after the wind forcing is shut off. The ITE's PV flux affects the large-scale flow by driving an eddy-induced transport or bolus velocity down the outcropping isopycnal layer with a magnitude that scales with the Ekman velocity.
VORTICAL MODEL OF THE WING COVERED WITH CONTINUOUSLY DISTRIBUTED CIRCULATION OF THE VORTICAL LAYER
Directory of Open Access Journals (Sweden)
B. L. Artamonov
2014-01-01
Full Text Available The linear vortical model ot the final scope of a wing is exsamined. It representis the flat rectangular spatial veil covered with continuously distributed vortical layer. Elements of digitization of a veil are the quadrangular panels laying on its surface. Method, algorithms and the program of calculation of three making vectors of inductive speed from any guided rectangular platform covered with a vortical layer are created. Its intensity linearly changes on the surface of a platform. The decision is received in elementary functions. The numerical way solves the task of a definition of the law of circulation of the attached whirlwinds in scope of a wing and calculation of its aerodynamic characteristics, being based on the accepted vortical model and a hypothesis of flat sections.
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.
Rockwood, Matthew P.
The flow around a circular cylinder, a canonical bluff body, has been extensively studied in the literature to determine the mechanisms that cause the formation of vortices in the cylinder wake. Understanding of these mechanisms has led to myriad attempts to control the vortices either to mitigate the oscillating forces they cause, or to augment them in order to enhance mixing in the near-wake. While these flow control techniques have been effective at low Reynolds numbers, they generally lose effectiveness or require excessive power at Reynolds numbers commonly experienced in practical applications. For this reason, new methods for identifying the locations of vortices and their shedding time could increase the effectiveness of the control techniques. In the current work, two-dimensional, two-component velocity data was collected in the wake of a circular cylinder using a planar digital particle image velocimetry (DPIV) measurement system at Reynolds numbers of 9,000 and 19,000. This experimental data, as well as two-dimensional simulation data at a Reynolds number of 150, and three-dimensional simulation data at a Reynolds number of 400, is used to calculate the finite-time Lyapunov exponent (FTLE) field. The locations of Lagrangian saddles, identified as non-parallel intersections of positive and negative time FTLE ridges, are shown to indicate the timing of von Karman vortex shedding in the wake of a circular cylinder. The Lagrangian saddle found upstream of a forming and subsequently shedding vortex is shown to clearly accelerate away from the cylinder surface as the vortex begins to shed. This provides a novel, objective method to determine the timing of vortex shedding. The saddles are impossible to track in real-time, however, since future flow field data is needed for the computation of the FTLE fields. In order to detect the Lagrangian saddle acceleration without direct access to the FTLE, the saddle dynamics are connected to measurable surface quantities
International Nuclear Information System (INIS)
Reichardt, Charles
2008-01-01
When a sufficiently strong magnetic field is applied to a superconductor, some of the field can pierce it through the generation of magnetic vortices, each of which contains a quantized amount of magnetic flux. Although the superconducting state of the material outside each vortex is maintained (and destroyed within each vortex), the interaction of vortices with a current passing through the material can cause them to move, dissipating energy and thereby generating a source of electrical resistance. The ability to manipulate an individual superconducting vortex represents a powerful tool for studying the dynamics of vortices and the superconductors that support them. It could also lead to the development of a new class of fluxon-based electronics.
Wong, Kelvin K. L.; Kelso, Richard M.; Worthley, Stephen G.; Sanders, Prashanthan; Mazumdar, Jagannath; Abbott, Derek
2008-12-01
Modelling of non-stationary cardiac structures is complicated by the complexity of their intrinsic and extrinsic motion. The first known study of haemodynamics due to the beating of heart was made by Leonardo Da Vinci, giving the idea of fluid-solid interaction by describing how vortices develop during cardiac structural interaction with the blood. Heart morphology affects in changes of cardio dynamics during the systolic and diastolic phrases. In a chamber of the heart, vortices are discovered to exist as the result of the unique morphological changes of the cardiac chamber wall by using flow-imaging techniques such as phase contrast magnetic resonance imaging. The first part of this paper attempts to quantify vortex characteristics by means of calculating vorticity numerically and devising two dimensional vortical flow maps. The technique relies on determining the properties of vorticity using a statistical quantification of the flow maps and comparison of these quantities based on different scenarios. As the characteristics of our vorticity maps vary depending on the phase of a cardiac cycle, there is a need for robust quantification method to analyse vorticity. In the second part of the paper, the approach is then utilised for examining vortices within the human right atrium. Our study has shown that a proper quantification of vorticity for the flow field can indicate the strength and number of vortices within a heart chamber.
Exact Lagrangian caps and non-uniruled Lagrangian submanifolds
Dimitroglou Rizell, Georgios
2015-04-01
We make the elementary observation that the Lagrangian submanifolds of C n , n≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov-Eliashberg algebra is acyclic.
Management of Vortices Trailing Flapped Wings via Separation Control
Greenblatt, David
2005-01-01
A pilot study was conducted on a flapped semi-span model to investigate the concept and viability of near-wake vortex management via separation control. Passive control was achieved by means of a simple fairing and active control was achieved via zero mass-flux blowing slots. Vortex sheet strength, estimated by integrating surface pressure ports, was used to predict vortex characteristics by means of inviscid rollup relations. Furthermore, vortices trailing the flaps were mapped using a seven-hole probe. Separation control was found to have a marked effect on vortex location, strength, tangential velocity, axial velocity and size over a wide range of angles of attack and control conditions. In general, the vortex trends were well predicted by the inviscid rollup relations. Manipulation of the separated flow near the flap edges exerted significant control over both outboard and inboard edge vortices while producing negligible lift excursions. Dynamic separation and attachment control was found to be an effective means for dynamically perturbing the vortex from arbitrarily long wavelengths down to wavelengths less than a typical wingspan. In summary, separation control has the potential for application to time-independent or time-dependent wake alleviation schemes, where the latter can be deployed to minimize adverse effects on ride-quality and dynamic structural loading.
On stability of vortices in three-dimensional self-attractive Bose-Einstein condensates
International Nuclear Information System (INIS)
Malomed, Boris A.; Lederer, Falk; Mazilu, Dumitru; Mihalache, Dumitru
2007-01-01
Results of accurate analysis of stability are reported for localized vortices in the Bose-Einstein condensate (BEC) with the negative scattering length, trapped in an anisotropic potential with the aspect ratio Ω. The cases of Ω-bar 1 and Ω-bar 1 correspond to the 'pancake' (nearly-2D) and 'cigar-shaped' (nearly-1D) configurations, respectively (in the latter limit, the vortices become 'tubular' solitons). The analysis is based on the 3D Gross-Pitaevskii equation. The family of solutions with vorticity S=1 is accurately predicted by the variational approximation. The relative size of the stability area for the vortices with S=1 (which was studied, in a part, before) increases with the decrease of Ω in terms of the number of atoms, but decreases in terms of the chemical potential. All states with S>=2 are unstable, while the stability of the ordinary solitons (S=0) obeys the Vakhitov-Kolokolov criterion. The stability predictions are verified by direct simulations of the full 3D equation
International Nuclear Information System (INIS)
Hojman, S.
1982-01-01
We present a review of the inverse problem of the Calculus of Variations, emphasizing the ambiguities which appear due to the existence of equivalent Lagrangians for a given classical system. In particular, we analyze the properties of equivalent Lagrangians in the multidimensional case, we study the conditions for the existence of a variational principle for (second as well as first order) equations of motion and their solutions, we consider the inverse problem of the Calculus of Variations for singular systems, we state the ambiguities which emerge in the relationship between symmetries and conserved quantities in the case of equivalent Lagrangians, we discuss the problems which appear in trying to quantize classical systems which have different equivalent Lagrangians, we describe the situation which arises in the study of equivalent Lagrangians in field theory and finally, we present some unsolved problems and discussion topics related to the content of this article. (author)
International Nuclear Information System (INIS)
Amitava Choudhuri; Subrata Ghosh; Talukdar, B.
2011-01-01
We identify two alternative Lagrangian representations for the damped harmonic oscillator characterised by a frictional coefficient γ. The first one is explicitly time independent while the second one involves time parameter explicitly. With separate attention to both Lagrangians we make use of the Noether theorem to compute the variational symmetries and conservation laws in order to study how association between them changes as one goes from one representation to the other. In the case of time independent representation squeezing symmetry leads to conservation of angular momentum for γ = 0, while for the time-dependent Lagrangian the same conserved quantity results from rotational invariance. The Lie algebra (g) of the symmetry vectors that leaves the action corresponding to the time-independent Lagrangian invariant is semi-simple. On the other hand, g is only a simple Lie algebra for the action characterised by the time-dependent Lagrangian. (authors)
有理Runge-Kutta法を用いたSemi-Lagrangian海洋モデルの開発
上原, 克人; Uehara, Katsuto
1997-01-01
A new Semi-Lagrangian scheme using Rational Runge-Kutta method (RKSL scheme)is developed for reduced-gravity ocean model. It is superior to Semi-Implicit/Semi-Lagrangian (SISL) scheme in handling lateral boundaries, whereas it can take longer time-step than usual external Eulerian schemes. To evaluate this new scheme, experiments simulating the mid-depth circulation of the Mediterranean outflow region in the eastern North Atlantic were made by using the RKSL scheme, the SISL scheme, and cente...
Polarization in heavy-ion collisions: magnetic field and vorticity
Baznat, M.; Gudima, K.; Prokhorov, G.; Sorin, A.; Teryaev, O.; Zakharov, V.
2017-12-01
The polarization of hyperons due to axial chiral vortical effect is discussed. The effect is proportional to (strange) chemical potential and is pronounced at lower energies, contrary to that of magnetic field. The polarization of antihyperons has the same sign and larger magnitude. The emergence of vortical structures is observed in kinetic QGSM models. The hydrodynamical helicity separation receives the contribution of longitudinal velocity and vorticity implying the quadrupole structure of the latter. The transition from the quark vortical effects to baryons in confined phase may be achieved by exploring the axial charge. At the hadronic level the polarization corresponds to the cores of quantized vortices in pionic superfluid. The chiral vortical effects may be also studied in the frmework of Wigner function establishing the relation to the thermodynamical approach to polarization.
Coherent Lagrangian swirls among submesoscale motions.
Beron-Vera, F J; Hadjighasem, A; Xia, Q; Olascoaga, M J; Haller, G
2018-03-05
The emergence of coherent Lagrangian swirls (CLSs) among submesoscale motions in the ocean is illustrated. This is done by applying recent nonlinear dynamics tools for Lagrangian coherence detection on a surface flow realization produced by a data-assimilative submesoscale-permitting ocean general circulation model simulation of the Gulf of Mexico. Both mesoscale and submesoscale CLSs are extracted. These extractions prove the relevance of coherent Lagrangian eddies detected in satellite-altimetry-based geostrophic flow data for the arguably more realistic ageostrophic multiscale flow.
Making sound vortices by metasurfaces
Energy Technology Data Exchange (ETDEWEB)
Ye, Liping; Qiu, Chunyin, E-mail: cyqiu@whu.edu.cn; Lu, Jiuyang; Tang, Kun; Ke, Manzhu; Peng, Shasha [Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072 (China); Jia, Han [State Key Laboratory of Acoustics and Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190 (China); Liu, Zhengyou [Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072 (China); Institute for Advanced Studies, Wuhan University, Wuhan 430072 (China)
2016-08-15
Based on the Huygens-Fresnel principle, a metasurface structure is designed to generate a sound vortex beam in airborne environment. The metasurface is constructed by a thin planar plate perforated with a circular array of deep subwavelength resonators with desired phase and amplitude responses. The metasurface approach in making sound vortices is validated well by full-wave simulations and experimental measurements. Potential applications of such artificial spiral beams can be anticipated, as exemplified experimentally by the torque effect exerting on an absorbing disk.
Lagrangian descriptors in dissipative systems.
Junginger, Andrej; Hernandez, Rigoberto
2016-11-09
The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory-that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of Lagrangian descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the Lagrangian descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the Lagrangian descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.
A new circulation type classification based upon Lagrangian air trajectories
Directory of Open Access Journals (Sweden)
Alexandre M. Ramos
2014-10-01
Full Text Available A new classification method of the large-scale circulation characteristic for a specific target area (NW Iberian Peninsula is presented, based on the analysis of 90-h backward trajectories arriving in this area calculated with the 3-D Lagrangian particle dispersion model FLEXPART. A cluster analysis is applied to separate the backward trajectories in up to five representative air streams for each day. Specific measures are then used to characterise the distinct air streams (e.g., curvature of the trajectories, cyclonic or anticyclonic flow, moisture evolution, origin and length of the trajectories. The robustness of the presented method is demonstrated in comparison with the Eulerian Lamb weather type classification.A case study of the 2003 heatwave is discussed in terms of the new Lagrangian circulation and the Lamb weather type classifications. It is shown that the new classification method adds valuable information about the pertinent meteorological conditions, which are missing in an Eulerian approach. The new method is climatologically evaluated for the five-year time period from December 1999 to November 2004. The ability of the method to capture the inter-seasonal circulation variability in the target region is shown. Furthermore, the multi-dimensional character of the classification is shortly discussed, in particular with respect to inter-seasonal differences. Finally, the relationship between the new Lagrangian classification and the precipitation in the target area is studied.
Remarks on gauge variables and singular Lagrangians
International Nuclear Information System (INIS)
Chela-Flores, J.; Janica-de-la-Torre, R.; Kalnay, A.J.; Rodriguez-Gomez, J.; Rodriguez-Nunez, J.; Tascon, R.
1977-01-01
The relevance is discussed of gauge theory, based on a singular Lagrangian density, to the foundations of field theory. The idea that gauge transformations could change the physics of systems where the Lagrangian is singular is examined. (author)
Some Lagrangians for systems without a Lagrangian
International Nuclear Information System (INIS)
Nucci, M C; Leach, P G L
2011-01-01
We demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle.
Solitary magnetohydrodynamic vortices
International Nuclear Information System (INIS)
Silaev, I.I.; Skvortsov, A.T.
1990-01-01
This paper reports on the analytical description of fluid flow by means of localized vortices which is traditional for hydrodynamics, oceanology, plasma physics. Recently it has been widely applied to different structure turbulence models. Considerable results involved have been presented where it was shown that in magnetohydrodynamics alongside with the well-known kinds of localized vortices (e.g. Hill's vortex), which are characterized by quite a weak decrease of disturbed velocity or magnetic field (as a power of the inverse distance from vortex center), the vortices with screening (or solitary vortices) may exist. All disturbed parameters either exponentially vanish or become identically zero in outer region in the latter case. (In a number of papers numerical simulations of such the vortices are presented). Solutions in a form of solitary vortices are of particular interest due to their uniformity and solitonlike behavior. On the basis of these properties one can believe for such structures to occur in real turbulent flows
Theory of concentrated vortices an introduction
Alekseenko, S V; Okulov, V L
2007-01-01
Vortex motion is one of the basic states of a flowing continuum. Intere- ingly, in many cases vorticity is space-localized, generating concentrated vortices. Vortex filaments having extremely diverse dynamics are the most characteristic examples of such vortices. Notable examples, in particular, include such phenomena as self-inducted motion, various instabilities, wave generation, and vortex breakdown. These effects are typically ma- fested as a spiral (or helical) configuration of a vortex axis. Many publications in the field of hydrodynamics are focused on vortex motion and vortex effects. Only a few books are devoted entirely to v- tices, and even fewer to concentrated vortices. This work aims to highlight the key problems of vortex formation and behavior. The experimental - servations of the authors, the impressive visualizations of concentrated vortices (including helical and spiral) and pictures of vortex breakdown primarily motivated the authors to begin this work. Later, the approach based on the hel...
Vorticity imbalance and stability in relation to convection
Read, W. L.; Scoggins, J. R.
1977-01-01
A complete synoptic-scale vorticity budget was related to convection storm development in the eastern two-thirds of the United States. The 3-h sounding interval permitted a study of time changes of the vorticity budget in areas of convective storms. Results of analyses revealed significant changes in values of terms in the vorticity equation at different stages of squall line development. Average budgets for all areas of convection indicate systematic imbalance in the terms in the vorticity equation. This imbalance resulted primarily from sub-grid scale processes. Potential instability in the lower troposphere was analyzed in relation to the development of convective activity. Instability was related to areas of convection; however, instability alone was inadequate for forecast purposes. Combinations of stability and terms in the vorticity equation in the form of indices succeeded in depicting areas of convection better than any one item separately.
Agradient velocity, vortical motion and gravity waves in a rotating shallow-water model
Sutyrin Georgi, G.
2004-07-01
A new approach to modelling slow vortical motion and fast inertia-gravity waves is suggested within the rotating shallow-water primitive equations with arbitrary topography. The velocity is exactly expressed as a sum of the gradient wind, described by the Bernoulli function,B, and the remaining agradient part, proportional to the velocity tendency. Then the equation for inverse potential vorticity,Q, as well as momentum equations for agradient velocity include the same source of intrinsic flow evolution expressed as a single term J (B, Q), where J is the Jacobian operator (for any steady state J (B, Q) = 0). Two components of agradient velocity are responsible for the fast inertia-gravity wave propagation similar to the traditionally used divergence and ageostrophic vorticity. This approach allows for the construction of balance relations for vortical dynamics and potential vorticity inversion schemes even for moderate Rossby and Froude numbers assuming the characteristic value of |J(B, Q)| = to be small. The components of agradient velocity are used as the fast variables slaved to potential vorticity that allows for diagnostic estimates of the velocity tendency, the direct potential vorticity inversion with the accuracy of 2 and the corresponding potential vorticity-conserving agradient velocity balance model (AVBM). The ultimate limitations of constructing the balance are revealed in the form of the ellipticity condition for balanced tendency of the Bernoulli function which incorporates both known criteria of the formal stability: the gradient wind modified by the characteristic vortical Rossby wave phase speed should be subcritical. The accuracy of the AVBM is illustrated by considering the linear normal modes and coastal Kelvin waves in the f-plane channel with topography.
Lagrangian postprocessing of computational hemodynamics.
Shadden, Shawn C; Arzani, Amirhossein
2015-01-01
Recent advances in imaging, modeling, and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries, and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows.
Next generation extended Lagrangian first principles molecular dynamics.
Niklasson, Anders M N
2017-08-07
Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.
International Nuclear Information System (INIS)
Weinberg, S.
1979-01-01
The author presents an argument that phenomenological Lagrangians can be used not only to reproduce the soft pion results of current algebra, but also to justify these results, without any use of operator algebra, and shows how phenomenological Lagrangians can be used to calculate corrections to the leading soft pion results to any desired order in external momenta. The renormalization group is used to elucidate the structure of these corrections. Corrections due to the finite mass of the pion are treated and speculations are made about another possible application of phenomenological Lagrangians. (Auth.)
Decay or collapse: Aircraft wake vortices in grid turbulence
Ren, M.; Elsenaar, A.; van Heijst, G.J.F.; Kuczaj, Arkadiusz K.; Geurts, Bernardus J.
2006-01-01
Trailing vortices are naturally shed by airplanes and they typically evolve into a counter-rotating vortex pair. Downstream of the aircraft, these vortices can persist for a very long time and extend for several kilometers. This poses a potential hazard to following aircraft, particularly during
Point vortex description of drift wave vortices: Dynamics and transport
International Nuclear Information System (INIS)
Kono, M.; Horton, W.
1991-05-01
Point-vortex description for drift wave vortices is formulated based on the Hasegawa-Mima equation to study elementary processes for the interactions of vortices as well as statistical properties like vortex diffusion. Dynamical properties of drift wave vortices known by numerical experiments are recovered. Furthermore a vortex diffusion model discussed by Horton based on numerical simulations is shown to be analytically obtained. A variety of phenomena arising from the short-range nature of the interaction force of point vortices are suggested. 12 refs., 10 figs
L-GRAAL: Lagrangian graphlet-based network aligner.
Malod-Dognin, Noël; Pržulj, Nataša
2015-07-01
Discovering and understanding patterns in networks of protein-protein interactions (PPIs) is a central problem in systems biology. Alignments between these networks aid functional understanding as they uncover important information, such as evolutionary conserved pathways, protein complexes and functional orthologs. A few methods have been proposed for global PPI network alignments, but because of NP-completeness of underlying sub-graph isomorphism problem, producing topologically and biologically accurate alignments remains a challenge. We introduce a novel global network alignment tool, Lagrangian GRAphlet-based ALigner (L-GRAAL), which directly optimizes both the protein and the interaction functional conservations, using a novel alignment search heuristic based on integer programming and Lagrangian relaxation. We compare L-GRAAL with the state-of-the-art network aligners on the largest available PPI networks from BioGRID and observe that L-GRAAL uncovers the largest common sub-graphs between the networks, as measured by edge-correctness and symmetric sub-structures scores, which allow transferring more functional information across networks. We assess the biological quality of the protein mappings using the semantic similarity of their Gene Ontology annotations and observe that L-GRAAL best uncovers functionally conserved proteins. Furthermore, we introduce for the first time a measure of the semantic similarity of the mapped interactions and show that L-GRAAL also uncovers best functionally conserved interactions. In addition, we illustrate on the PPI networks of baker's yeast and human the ability of L-GRAAL to predict new PPIs. Finally, L-GRAAL's results are the first to show that topological information is more important than sequence information for uncovering functionally conserved interactions. L-GRAAL is coded in C++. Software is available at: http://bio-nets.doc.ic.ac.uk/L-GRAAL/. n.malod-dognin@imperial.ac.uk Supplementary data are available at
Linearized potential vorticity mode and its role in transition to baroclinic instability
International Nuclear Information System (INIS)
Pieri, Alexandre; Salhi, Aziz; Cambon, Claude; Godeferd, Fabien
2011-01-01
Stratified shear flows have been studied using Rapid Distortion Theory (RDT) and DNS. If this flow is in addition subjected to vertical rotation, a slaved horizontal stratification is forced and baroclinic instability can occur. In this context, the RDT analysis shows an extention of the unstable domain up to a Richardson number Ri of 1. This work is completed here with new results on transition to baroclinic instability. Especially, the role of k x ≈ 0 modes (small streamwise wavenumbers) and the importance of coupling with the potential vorticity mode u (Ω pot ) is shown to be determinant for dramatic transient growth at intermediate times.
Compressible dynamic stall vorticity flux control using a dynamic ...
Indian Academy of Sciences (India)
systems, such as a wind turbine, are prevented from ever entering dynamic stall, essentially disregarding potential ... future generations of such systems, an overwhelming need has developed to avail this benefit safely. ... approach must diffuse the vorticity prior to its coalescence, but keep the vorticity over the airfoil up to ...
A vorticity based approach to handle the fluid-structure interaction problems
Energy Technology Data Exchange (ETDEWEB)
Farahbakhsh, Iman; Ghassemi, Hassan [Department of Ocean Engineering, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Sabetghadam, Fereidoun, E-mail: i.farahbakhsh@aut.ac.ir [Mechanical and Aerospace Engineering Department, Science and Research Branch, Islamic Azad University (IAU), Tehran (Iran, Islamic Republic of)
2016-02-15
A vorticity based approach for the numerical solution of the fluid-structure interaction problems is introduced in which the fluid and structure(s) can be viewed as a continuum. Retrieving the vorticity field and recalculating a solenoidal velocity field, specially at the fluid-structure interface, are the kernel of the proposed algorithm. In the suggested method, a variety of constitutive equations as a function of left Cauchy–Green deformation tensor can be applied for modeling the structure domain. A nonlinear Mooney–Rivlin and Saint Venant–Kirchhoff model are expressed in terms of the left Cauchy–Green deformation tensor and the presented method is able to model the behavior of a visco-hyperelastic structure in the incompressible flow. Some numerical experiments, with considering the neo-Hookean model for structure domain, are executed and the results are validated via the available results from literature. (paper)
Spontaneous CP breaking in QCD and the axion potential: an effective Lagrangian approach
Di Vecchia, Paolo; Rossi, Giancarlo; Veneziano, Gabriele; Yankielowicz, Shimon
2017-12-01
Using the well-known low-energy effective Lagrangian of QCD — valid for small (non-vanishing) quark masses and a large number of colors — we study in detail the regions of parameter space where CP is spontaneously broken/unbroken for a vacuum angle θ = π. In the CP broken region there are first order phase transitions as one crosses θ = π, while on the (hyper)surface separating the two regions, there are second order phase transitions signalled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the CP spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised if the QCD parameters fall in the above mentioned CP broken region, in spite of the fact that the axion solves the strong- CP problem. These last results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.
Airfoil Drag Reduction using Controlled Trapped Vorticity Concentrations
Desalvo, Michael; Glezer, Ari
2017-11-01
The aerodynamic performance of a lifting surface at low angles of attack (when the base flow is fully attached) is improved through fluidic modification of its ``apparent'' shape by superposition of near-surface trapped vorticity concentrations. In the present wind tunnel investigations, a controlled trapped vorticity concentration is formed on the pressure surface of an airfoil (NACA 4415) using a hybrid actuator comprising a passive obstruction of scale O(0.01c) and an integral synthetic jet actuator. The jet actuation frequency [Stact O(10)] is selected to be at least an order of magnitude higher than the characteristic unstable frequency of the airfoil wake, thereby decoupling the actuation from the global instabilities of the base flow. Regulation of vorticity accumulation in the vicinity of the actuator by the jet effects changes in the local pressure, leading in turn to changes in the airfoil's drag and lift. Trapped vorticity can lead to a significant reduction in drag and reduced lift (owing to the sense of the vorticity), e.g. at α =4° and Re = 6.7 .105 the drag and lift reductions are 14% and 2%, respectively. PIV measurements show the spatial variation in the distribution of vorticity concentrations and yield estimates of the corresponding changes in circulation.
Theory and simulations of electron vortices generated by magnetic pushing
Energy Technology Data Exchange (ETDEWEB)
Richardson, A. S.; Angus, J. R.; Swanekamp, S. B.; Schumer, J. W. [Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375 (United States); Ottinger, P. F. [An Independent Consultant through ENGILITY, Chantilly, Virginia 20151 (United States)
2013-08-15
Vortex formation and propagation are observed in kinetic particle-in-cell (PIC) simulations of magnetic pushing in the plasma opening switch. These vortices are studied here within the electron-magnetohydrodynamic (EMHD) approximation using detailed analytical modeling. PIC simulations of these vortices have also been performed. Strong v×B forces in the vortices give rise to significant charge separation, which necessitates the use of the EMHD approximation in which ions are fixed and the electrons are treated as a fluid. A semi-analytic model of the vortex structure is derived, and then used as an initial condition for PIC simulations. Density-gradient-dependent vortex propagation is then examined using a series of PIC simulations. It is found that the vortex propagation speed is proportional to the Hall speed v{sub Hall}≡cB{sub 0}/4πn{sub e}eL{sub n}. When ions are allowed to move, PIC simulations show that the electric field in the vortex can accelerate plasma ions, which leads to dissipation of the vortex. This electric field contributes to the separation of ion species that has been observed to occur in pulsed-power experiments with a plasma-opening switch.
Nonautonomous Vortices in (2+1)-Dimensional Graded-Index Waveguide
International Nuclear Information System (INIS)
Lai Xian-Jing; Zhang Jie-Fang; Cai Xiao-Ou
2015-01-01
With the help of self-similarity transformation, we construct and study the nonautonomous vortices with different topological charges inside a planar graded-index nonlinear waveguide, analytically, and numerically. Although these vortices are approximate, they can reflect the real properties of self-similar optical beam during a short-term propagation. Existence of these autonomous vortices require delicate balances between the system parameters such as diffraction, nonlinearity, gain, and external potential. We are concerned with some special but interesting situations, and discussing the changes of the height, width, energy, and central position of the vortices as the increase of propagation distance. Moreover, we are also interested in the azimuthal modulational instability of the system, and comparing our prediction for the modulational instability growth rates to numerical results. (paper)
A contemporary look at Hermann Hankel's 1861 pioneering work on Lagrangian fluid dynamics
Frisch, Uriel; Grimberg, Gérard; Villone, Barbara
2017-12-01
The present paper is a companion to the paper by Villone and Rampf (2017), titled "Hermann Hankel's On the general theory of motion of fluids, an essay including an English translation of the complete Preisschrift from 1861" together with connected documents [Eur. Phys. J. H 42, 557-609 (2017)]. Here we give a critical assessment of Hankel's work, which covers many important aspects of fluid dynamics considered from a Lagrangian-coordinates point of view: variational formulation in the spirit of Hamilton for elastic (barotropic) fluids, transport (we would now say Lie transport) of vorticity, the Lagrangian significance of Clebsch variables, etc. Hankel's work is also put in the perspective of previous and future work. Hence, the action spans about two centuries: from Lagrange's 1760-1761 Turin paper on variational approaches to mechanics and fluid mechanics problems to Arnold's 1966 founding paper on the geometrical/variational formulation of incompressible flow. The 22-year-old Hankel - who was to die 12 years later — emerges as a highly innovative master of mathematical fluid dynamics, fully deserving Riemann's assessment that his Preisschrift contains "all manner of good things."
Vortices in a rotating dark matter condensate
International Nuclear Information System (INIS)
Yu, Rotha P; Morgan, Michael J
2002-01-01
We examine vortices in a self-gravitating dark matter Bose-Einstein condensate (BEC), consisting of ultra-low mass scalar bosons that arise during a late-time cosmological phase transition. Rotation of the dark matter BEC imprints a background phase gradient on the condensate, which establishes a harmonic trap potential for vortices. A numerical simulation of vortex dynamics shows that the vortex number density, n v ∝ r -1 , resulting in a flat velocity profile for the dark matter condensate. (letter to the editor)
Francois, N; Xia, H; Punzmann, H; Shats, M
2013-05-10
We report the generation of large coherent vortices via inverse energy cascade in Faraday wave driven turbulence. The motion of floaters in the Faraday waves is three dimensional, but its horizontal velocity fluctuations show unexpected similarity with two-dimensional turbulence. The inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity, and it is confirmed by computing the third moment of the horizontal velocity fluctuations. This is observed in deep water in a broad range of wavelengths and vertical accelerations. The results broaden the scope of recent findings on Faraday waves in thin layers [A. von Kameke et al., Phys. Rev. Lett. 107, 074502 (2011)].
Chaotic Lagrangian models for turbulent relative dispersion.
Lacorata, Guglielmo; Vulpiani, Angelo
2017-04-01
A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.
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.
Dynamics of fractional vortices in long Josephson junctions
International Nuclear Information System (INIS)
Gaber, Tobias
2007-01-01
In this thesis static and dynamic properties of fractional vortices in long Josephson junctions are investigated. Fractional vortices are circulating supercurrents similar to the well-known Josephson fluxons. Yet, they show the distinguishing property of carrying only a fraction of the magnetic flux quantum. Fractional vortices are interesting non-linear objects. They spontaneously appear and are pinned at the phase discontinuity points of so called 0-κ junctions but can be bend or flipped by external forces like bias currents or magnetic fields. 0-κ junctions and fractional vortices are generalizations of the well-known 0-π junctions and semifluxons, where not only phase jumps of pi but arbitrary values denoted by kappa are considered. By using so-called artificial 0-κ junctions that are based on standard Nb-AlO x -Nb technology the classical dynamics of fractional vortices has been investigated experimentally for the very first time. Here, half-integer zero field steps could be observed. These voltage steps on the junction's current-voltage characteristics correspond to the periodic flipping/hopping of fractional vortices. In addition, the oscillatory eigenmodes of fractional vortices were investigated. In contrast to fluxons fractional vortices have an oscillatory eigenmode with a frequency within the plasma gap. Using resonance spectroscopy the dependence of the eigenmode frequency on the flux carried by the vortex and an applied bias current was determined. (orig.)
Lagrangian Differentiation, Integration and Eigenvalues Problems
International Nuclear Information System (INIS)
Durand, L.
1983-01-01
Calogero recently proposed a new and very powerful method for the solution of Sturm-Liouville eigenvalue problems based on Lagrangian differentiation. In this paper, some results of a numerical investigation of Calogero's method for physical interesting problems are presented. It is then shown that one can 'invert' his differentiation technique to obtain a flexible, factorially convergent Lagrangian integration scheme which should be useful in a variety of problems, e.g. solution of integral equations
Multidimensional Test Assembly Based on Lagrangian Relaxation Techniques. Research Report 98-08.
Veldkamp, Bernard P.
In this paper, a mathematical programming approach is presented for the assembly of ability tests measuring multiple traits. The values of the variance functions of the estimators of the traits are minimized, while test specifications are met. The approach is based on Lagrangian relaxation techniques and provides good results for the two…
Shear and shearless Lagrangian structures in compound channels
Enrile, F.; Besio, G.; Stocchino, A.
2018-03-01
Transport processes in a physical model of a natural stream with a composite cross-section (compound channel) are investigated by means of a Lagrangian analysis based on nonlinear dynamical system theory. Two-dimensional free surface Eulerian experimental velocity fields of a uniform flow in a compound channel form the basis for the identification of the so-called Lagrangian Coherent Structures. Lagrangian structures are recognized as the key features that govern particle trajectories. We seek for two particular class of Lagrangian structures: Shear and shearless structures. The former are generated whenever the shear dominates the flow whereas the latter behave as jet-cores. These two type of structures are detected as ridges and trenches of the Finite-Time Lyapunov Exponents fields, respectively. Besides, shearlines computed applying the geodesic theory of transport barriers mark Shear Lagrangian Coherent Structures. So far, the detection of these structures in real experimental flows has not been deeply investigated. Indeed, the present results obtained in a wide range of the controlling parameters clearly show a different behaviour depending on the shallowness of the flow. Shear and Shearless Lagrangian Structures detected from laboratory experiments clearly appear as the flow develops in shallow conditions. The presence of these Lagrangian Structures tends to fade in deep flow conditions.
International Nuclear Information System (INIS)
Kaminski, J.Z.
1981-01-01
A renormalization group equation for the effective Lagrangian of QED is obtained. Starting from this equation, perturbation theory for the renormalization group equation (PTRGE) is developed. The results are in full agreement with the standard perturbation theory. Conjecturing that the asymptotic effective coupling constant is finite, the effective Lagrangian for a strong magnetic field is obtained, which is proportional to the Maxwellian Lagrangian. For the asymptotically free theories the situation is diametrically opposed to QED. In these cases the effective Lagrangian of the Yang-Mills system tends to infinity for very strong external Yang-Mills fields. (Auth.)
A vorticity transport model to restore spatial gaps in velocity data
Ameli, Siavash; Shadden, Shawn
2017-11-01
Often measurements of velocity data do not have full spatial coverage in the probed domain or near boundaries. These gaps can be due to missing measurements or masked regions of corrupted data. These gaps confound interpretation, and are problematic when the data is used to compute Lagrangian or trajectory-based analyses. Various techniques have been proposed to overcome coverage limitations in velocity data such as unweighted least square fitting, empirical orthogonal function analysis, variational interpolation as well as boundary modal analysis. In this talk, we present a vorticity transport PDE to reconstruct regions of missing velocity vectors. The transport model involves both nonlinear anisotropic diffusion and advection. This approach is shown to preserve the main features of the flow even in cases of large gaps, and the reconstructed regions are continuous up to second order. We illustrate results for high-frequency radar (HFR) measurements of the ocean surface currents as this is a common application of limited coverage. We demonstrate that the error of the method is on the same order of the error of the original velocity data. In addition, we have developed a web-based gateway for data restoration, and we will demonstrate a practical application using available data. This work is supported by the NSF Grant No. 1520825.
Yang, Y.; Sciacchitano, A.; Veldhuis, L.L.M.; Eitelberg, G.
2016-01-01
During the ground operation of aircraft, there is potentially a system of vortices generated from the ground toward the propulsor, commonly denoted as ground vortices. Although extensive research has been conducted on ground vortices induced by turbofans which were simplified by suction tubes, these
Jacobi equations as Lagrange equations of the deformed Lagrangian
International Nuclear Information System (INIS)
Casciaro, B.
1995-03-01
We study higher-order variational derivatives of a generic Lagrangian L 0 = L 0 (t,q,q). We introduce two new Lagrangians, L 1 and L 2 , associated to the first and second-order deformations of the original Lagrangian L 0 . In terms of these Lagrangians, we are able to establish simple relations between the variational derivatives of different orders of a Lagrangian. As a consequence of these relations the Euler-Lagrange and the Jacobi equations are obtained from a single variational principle based on L 1 . We can furthermore introduce an associated Hamiltonian H 1 = H 1 (t,q,q radical,η,η radical) with η equivalent to δq. If L 0 is independent of time then H 1 is a conserved quantity. (author). 15 refs
Hydrodynamical model based on a bag-like Lagrangian
International Nuclear Information System (INIS)
Chiu, C.B.; Lam, C.S.; Wang, K.H.
1976-06-01
Equations of motion of hydrodynamical model are derived from a bag-like Lagrangian by using the technique of information theory. Comments on the break-up of the system and on the properties of decay products are included
Abe homotopy classification of topological excitations under the topological influence of vortices
International Nuclear Information System (INIS)
Kobayashi, Shingo; Kobayashi, Michikazu; Kawaguchi, Yuki; Nitta, Muneto; Ueda, Masahito
2012-01-01
Topological excitations are usually classified by the nth homotopy group π n . However, for topological excitations that coexist with vortices, there are cases in which an element of π n cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of π n corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of π 1 on π n . In this paper, we show that topological excitations coexisting with vortices are classified by the Abe homotopy group κ n . The nth Abe homotopy group κ n is defined as a semi-direct product of π 1 and π n . In this framework, the action of π 1 on π n is understood as originating from noncommutativity between π 1 and π n . We show that a physical charge of a topological excitation can be described in terms of the conjugacy class of the Abe homotopy group. Moreover, the Abe homotopy group naturally describes vortex-pair creation and annihilation processes, which also influence topological excitations. We calculate the influence of vortices on topological excitations for the case in which the order parameter manifold is S n /K, where S n is an n-dimensional sphere and K is a discrete subgroup of SO(n+1). We show that the influence of vortices on a topological excitation exists only if n is even and K includes a nontrivial element of O(n)/SO(n).
A (Dis)continuous finite element model for generalized 2D vorticity dynamics
Bernsen, E.; Bokhove, Onno; van der Vegt, Jacobus J.W.
2005-01-01
A mixed continuous and discontinuous Galerkin finite element discretization is constructed for a generalized vorticity streamfunction formulation in two spatial dimensions. This formulation consists of a hyperbolic (potential) vorticity equation and a linear elliptic equation for a (transport)
Lagrangian motion, coherent structures, and lines of persistent material strain.
Samelson, R M
2013-01-01
Lagrangian motion in geophysical fluids may be strongly influenced by coherent structures that support distinct regimes in a given flow. The problems of identifying and demarcating Lagrangian regime boundaries associated with dynamical coherent structures in a given velocity field can be studied using approaches originally developed in the context of the abstract geometric theory of ordinary differential equations. An essential insight is that when coherent structures exist in a flow, Lagrangian regime boundaries may often be indicated as material curves on which the Lagrangian-mean principal-axis strain is large. This insight is the foundation of many numerical techniques for identifying such features in complex observed or numerically simulated ocean flows. The basic theoretical ideas are illustrated with a simple, kinematic traveling-wave model. The corresponding numerical algorithms for identifying candidate Lagrangian regime boundaries and lines of principal Lagrangian strain (also called Lagrangian coherent structures) are divided into parcel and bundle schemes; the latter include the finite-time and finite-size Lyapunov exponent/Lagrangian strain (FTLE/FTLS and FSLE/FSLS) metrics. Some aspects and results of oceanographic studies based on these approaches are reviewed, and the results are discussed in the context of oceanographic observations of dynamical coherent structures.
Moving vortex matter with coexisting vortices and anti-vortices
International Nuclear Information System (INIS)
Carneiro, Gilson
2009-01-01
Moving vortex matter, driven by transport currents independent of time, in which vortices and anti-vortices coexist is investigated theoretically in thin superconducting films with nanostructured defects. A simple London model is proposed for the vortex dynamics in films with periodic arrays of nanomagnets or cylindrical holes (antidots). Common to these films is that vortex anti-vortex pairs may be created in the vicinity of the defects by relatively small transport currents, because it adds to the current generated by the defects - the nanomagnets screening current, or the antidots backflow current - and may exceed locally the critical value for vortex anti-vortex pair creation. The model assumes that vortex matter dynamics is governed by Langevin equations, modified to account for creation and annihilation of vortex anti-vortex pairs. For pair creation, it is assumed that whenever the total current at some location exceeds a critical value, equal to that needed to separate a vortex from an anti-vortex by a vortex core diameter, a pair is created instantaneously around this location. Pair annihilation occurs by vortex anti-vortex collisions. The model is applied to films at zero external magnetic field and low temperatures. It is found that several moving vortex matter steady-states with equal numbers of vortices and anti-vortices are possible.
The Interaction of Two Surface Vortices Near a Topographic Slope in a Stratified Ocean
Directory of Open Access Journals (Sweden)
Charly de Marez
2017-10-01
Full Text Available We study the influence of bottom topography on the interaction of two identical vortices in a two-layer, quasi-geostrophic model. The two vortices have piecewise-uniform potential vorticity and are lying in the upper layer of the model. The topography is a smooth bottom slope. For two cyclones, topography modifies the merger critical distance and the merger efficiency: the topographic wave and vortices can advect the two cyclones along the shelf when they are initially far from it or towards the shelf when they are initially closer to it. They can also advect the two cyclones towards each other and thus favour merger. The cyclones deform, and the potential vorticity field undergoes filamentation. Regimes of partial vortex merger or of vortex splitting are then observed. The interaction of the vorticity poles in the two layers are analysed to explain the evolution of the two upper layer cyclones. For taller topography, two new regimes appear: vortex drift and splitting; and filamentation and asymmetric merger. They are due to the hetonic coupling of lower layer vorticity with the upper layer vortices (a heton is a baroclinic vortex dipole, carrying heat and momentum and propagating horizontally in the fluid, or to the strong shear that the former exerts on the latter. The interaction of two anticyclones shows regimes of co-rotation or merger, but specifically, it leads to the drift of the two vortices away from the slope, via a hetonic coupling with oppositely-signed vorticity in the lower layer. This vorticity originates in the breaking of the topographic wave. The analysis of passive tracer evolution confirms the inshore or offshore drift of the fluid, the formation of tracer fronts along filaments and its stirring in regions of vortex merger. The trajectories of particles indicate how the fluid initially in the vortices is finally partitioned.
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.
The Mather problem for lower semicontinuous Lagrangians
Gomes, Diogo A.; Terrone, Gabriele
2013-01-01
In this paper we develop the Aubry-Mather theory for Lagrangians in which the potential energy can be discontinuous. Namely we assume that the Lagrangian is lower semicontinuous in the state variable, piecewise smooth with a (smooth) discontinuity surface, as well as coercive and convex in the velocity. We establish existence of Mather measures, various approximation results, partial regularity of viscosity solutions away from the singularity, invariance by the Euler-Lagrange flow away from the singular set, and further jump conditions that correspond to conservation of energy and tangential momentum across the discontinuity. © 2013 Springer Basel.
Primordial vorticity and gradient expansion
Giovannini, Massimo
2012-01-01
The evolution equations of the vorticities of the electrons, ions and photons in a pre-decoupling plasma are derived, in a fully inhomogeneous geometry, by combining the general relativistic gradient expansion and the drift approximation within the Adler-Misner-Deser decomposition. The vorticity transfer between the different species is discussed in this novel framework and a set of general conservation laws, connecting the vorticities of the three-component plasma with the magnetic field intensity, is derived. After demonstrating that a source of large-scale vorticity resides in the spatial gradients of the geometry and of the electromagnetic sources, the total vorticity is estimated to lowest order in the spatial gradients and by enforcing the validity of the momentum constraint. By acknowledging the current bounds on the tensor to scalar ratio in the (minimal) tensor extension of the $\\Lambda$CDM paradigm the maximal comoving magnetic field induced by the total vorticity turns out to be, at most, of the or...
International Nuclear Information System (INIS)
Plyukhin, A.V.
2013-01-01
A model of an autonomous isothermal Brownian motor with an internal propulsion mechanism is considered. The motor is a Brownian particle which is semi-transparent for molecules of surrounding ideal gas. Molecular passage through the particle is controlled by a potential similar to that in the transition rate theory, i.e. characterized by two stationary states with a finite energy difference separated by a potential barrier. The internal potential drop maintains the diode-like asymmetry of molecular fluxes through the particle, which results in the particle's stationary drift.
IMPOSING A LAGRANGIAN PARTICLE FRAMEWORK ON AN EULERIAN HYDRODYNAMICS INFRASTRUCTURE IN FLASH
International Nuclear Information System (INIS)
Dubey, A.; Daley, C.; Weide, K.; Graziani, C.; ZuHone, J.; Ricker, P. M.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid-structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash
Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
Kalita, Jiten C.; Biswas, Sougata; Panda, Swapnendu
2018-04-01
Till date, the sequence of vortices present in the solid corners of steady internal viscous incompressible flows was thought to be infinite. However, the already existing and most recent geometric theories on incompressible viscous flows that express vortical structures in terms of critical points in bounded domains indicate a strong opposition to this notion of infiniteness. In this study, we endeavor to bridge the gap between the two opposing stream of thoughts by diagnosing the assumptions of the existing theorems on such vortices. We provide our own set of proofs for establishing the finiteness of the sequence of corner vortices by making use of the continuum hypothesis and Kolmogorov scale, which guarantee a nonzero scale for the smallest vortex structure possible in incompressible viscous flows. We point out that the notion of infiniteness resulting from discrete self-similarity of the vortex structures is not physically feasible. Making use of some elementary concepts of mathematical analysis and our own construction of diametric disks, we conclude that the sequence of corner vortices is finite.
A Satellite-Based Lagrangian View on Phytoplankton Dynamics
Lehahn, Yoav; d'Ovidio, Francesco; Koren, Ilan
2018-01-01
The well-lit upper layer of the open ocean is a dynamical environment that hosts approximately half of global primary production. In the remote parts of this environment, distant from the coast and from the seabed, there is no obvious spatially fixed reference frame for describing the dynamics of the microscopic drifting organisms responsible for this immense production of organic matter—the phytoplankton. Thus, a natural perspective for studying phytoplankton dynamics is to follow the trajectories of water parcels in which the organisms are embedded. With the advent of satellite oceanography, this Lagrangian perspective has provided valuable information on different aspects of phytoplankton dynamics, including bloom initiation and termination, spatial distribution patterns, biodiversity, export of carbon to the deep ocean, and, more recently, bottom-up mechanisms that affect the distribution and behavior of higher-trophic-level organisms. Upcoming submesoscale-resolving satellite observations and swarms of autonomous platforms open the way to the integration of vertical dynamics into the Lagrangian view of phytoplankton dynamics.
A Satellite-Based Lagrangian View on Phytoplankton Dynamics.
Lehahn, Yoav; d'Ovidio, Francesco; Koren, Ilan
2018-01-03
The well-lit upper layer of the open ocean is a dynamical environment that hosts approximately half of global primary production. In the remote parts of this environment, distant from the coast and from the seabed, there is no obvious spatially fixed reference frame for describing the dynamics of the microscopic drifting organisms responsible for this immense production of organic matter-the phytoplankton. Thus, a natural perspective for studying phytoplankton dynamics is to follow the trajectories of water parcels in which the organisms are embedded. With the advent of satellite oceanography, this Lagrangian perspective has provided valuable information on different aspects of phytoplankton dynamics, including bloom initiation and termination, spatial distribution patterns, biodiversity, export of carbon to the deep ocean, and, more recently, bottom-up mechanisms that affect the distribution and behavior of higher-trophic-level organisms. Upcoming submesoscale-resolving satellite observations and swarms of autonomous platforms open the way to the integration of vertical dynamics into the Lagrangian view of phytoplankton dynamics.
The Born-Infeld vortices induced from a generalized Higgs mechanism.
Han, Xiaosen
2016-04-01
We construct self-dual Born-Infeld vortices induced from a generalized Higgs mechanism. Two specific models of the theory are of focused interest where the Higgs potential is either of a | ϕ | 4 - or | ϕ | 6 -type. For the | ϕ | 4 -model, we obtain a sharp existence and uniqueness theorem for doubly periodic and planar vortices. For doubly periodic solutions, a necessary and sufficient condition for the existence is explicitly derived in terms of the vortex number, the Born-Infeld parameter, and the size of the periodic lattice domain. For the | ϕ | 6 -model, we show that both topological and non-topological vortices are present. This new phenomenon distinguishes the model from the classical Born-Infeld-Higgs theory studied earlier in the literature. A series of results regarding doubly periodic, topological, and non-topological vortices in the | ϕ | 6 -model are also established.
The PDF method for Lagrangian two-phase flow simulations
International Nuclear Information System (INIS)
Minier, J.P.; Pozorski, J.
1996-04-01
A recent turbulence model put forward by Pope (1991) in the context of PDF modelling has been used. In this approach, the one-point joint velocity-dissipation pdf equation is solved by simulating the instantaneous behaviour of a large number of Lagrangian fluid particles. Closure of the evolution equations of these Lagrangian particles is based on stochastic models and more specifically on diffusion processes. Such models are of direct use for two-phase flow modelling where the so-called fluid seen by discrete inclusions has to be modelled. Full Lagrangian simulations have been performed for shear-flows. It is emphasized that this approach gives far more information than traditional turbulence closures (such as the K-ε model) and therefore can be very useful for situations involving complex physics. It is also believed that the present model represents the first step towards a complete Lagrangian-Lagrangian model for dispersed two-phase flow problems. (authors). 21 refs., 6 figs
Complex nonlinear Lagrangian for the Hasegawa-Mima equation
International Nuclear Information System (INIS)
Dewar, R.L.; Abdullatif, R.F.; Sangeetha, G.G.
2005-01-01
The Hasegawa-Mima equation is the simplest nonlinear single-field model equation that captures the essence of drift wave dynamics. Like the Schroedinger equation it is first order in time. However its coefficients are real, so if the potential φ is initially real it remains real. However, by embedding φ in the space of complex functions a simple Lagrangian is found from which the Hasegawa-Mima equation may be derived from Hamilton's Principle. This Lagrangian is used to derive an action conservation equation which agrees with that of Biskamp and Horton. (author)
Wu, Jie-Zhi; Zhou, M-D
2006-01-01
The importance of vorticity and vortex dynamics has now been well rec- nized at both fundamental and applied levels of ?uid dynamics, as already anticipatedbyTruesdellhalfcenturyagowhenhewrotethe?rstmonograph onthesubject, The Kinematics of Vorticity(1954);andasalsoevidencedby the appearance of several books on this ?eld in 1990s. The present book is characterizedbythefollowingfeatures: 1. A basic physical guide throughout the book. The material is directed by a basic observation on the splitting and coupling of two fundamental processes in ?uid motion, i.e., shearing (unique to ?uid) and compre- ing/expanding.Thevorticityplaysakeyroleintheformer,andavortex isnothingbuta?uidbodywithhighconcentrationofvorticitycompared to its surrounding ?uid. Thus, the vorticity and vortex dynamics is - cordinglyde?nedasthetheoryofshearingprocessanditscouplingwith compressing/expandingprocess. 2. A description of the vortex evolution following its entire life.Thisbegins from the generation of vorticity to the formation of thi...
Topology Optimization of Passive Micromixers Based on Lagrangian Mapping Method
Directory of Open Access Journals (Sweden)
Yuchen Guo
2018-03-01
Full Text Available This paper presents an optimization-based design method of passive micromixers for immiscible fluids, which means that the Peclet number infinitely large. Based on topology optimization method, an optimization model is constructed to find the optimal layout of the passive micromixers. Being different from the topology optimization methods with Eulerian description of the convection-diffusion dynamics, this proposed method considers the extreme case, where the mixing is dominated completely by the convection with negligible diffusion. In this method, the mixing dynamics is modeled by the mapping method, a Lagrangian description that can deal with the case with convection-dominance. Several numerical examples have been presented to demonstrate the validity of the proposed method.
Lagrangian statistics across the turbulent-nonturbulent interface in a turbulent plane jet.
Taveira, Rodrigo R; Diogo, José S; Lopes, Diogo C; da Silva, Carlos B
2013-10-01
Lagrangian statistics from millions of particles are used to study the turbulent entrainment mechanism in a direct numerical simulation of a turbulent plane jet at Re(λ) ≈ 110. The particles (tracers) are initially seeded at the irrotational region of the jet near the turbulent shear layer and are followed as they are drawn into the turbulent region across the turbulent-nonturbulent interface (TNTI), allowing the study of the enstrophy buildup and thereby characterizing the turbulent entrainment mechanism in the jet. The use of Lagrangian statistics following fluid particles gives a more correct description of the entrainment mechanism than in previous works since the statistics in relation to the TNTI position involve data from the trajectories of the entraining fluid particles. The Lagrangian statistics for the particles show the existence of a velocity jump and a characteristic vorticity jump (with a thickness which is one order of magnitude greater than the Kolmogorov microscale), in agreement with previous results using Eulerian statistics. The particles initially acquire enstrophy by viscous diffusion and later by enstrophy production, which becomes "active" only deep inside the turbulent region. Both enstrophy diffusion and production near the TNTI differ substantially from inside the turbulent region. Only about 1% of all particles find their way into pockets of irrotational flow engulfed into the turbulent shear layer region, indicating that "engulfment" is not significant for the present flow, indirectly suggesting that the entrainment is largely due to "nibbling" small-scale mechanisms acting along the entire TNTI surface. Probability density functions of particle positions suggests that the particles spend more time crossing the region near the TNTI than traveling inside the turbulent region, consistent with the particles moving tangent to the interface around the time they cross it.
Hadronic interactions from effective chiral Lagrangians of quarks and gluons
International Nuclear Information System (INIS)
Krein, G.
1996-06-01
We discuss the combined used of the techniques of effective chiral field theory and the field theoretic method known as Fock-Tani representation to derive effective hadron interactions. The Fock-Tani method is based on a change of representation by means of a unitary transformation such that the composite hadrons are redescribed by elementary-particle field operators. Application of the unitary transformation on the microscopic quark-quark interaction derived from a chiral effective Lagrangian leads to chiral effective interactions describing all possible processes involving hadrons and their constituents. The formalism is illustrated by deriving the one-pion-exchange potential between the nucleons using the quark-gluon effective chiral Lagrangian of Manohar and Georgi. We also present the results of a study of the saturation properties of the nuclear matter using this formalism. (author). 9 refs., 2 figs
de Vries, A. J.
2017-12-26
Extreme precipitation events in the otherwise arid Middle East can cause flooding with dramatic socioeconomic impacts. Most of these events are associated with tropical-extratropical interactions, whereby a stratospheric potential vorticity (PV) intrusion reaches deep into the subtropics and forces an incursion of high poleward vertically integrated water vapor transport (IVT) into the Middle East. This study presents an object-based identification method for extreme precipitation events based on the combination of these two larger-scale meteorological features. The general motivation for this approach is that precipitation is often poorly simulated in relatively coarse weather and climate models, whereas the synoptic-scale circulation is much better represented. The algorithm is applied to ERA-Interim reanalysis data (1979-2015) and detects 90% (83%) of the 99th (97.5th) percentile of extreme precipitation days in the region of interest. Our results show that stratospheric PV intrusions and IVT structures are intimately connected to extreme precipitation intensity and seasonality. The farther south a stratospheric PV intrusion reaches, the larger the IVT magnitude, and the longer the duration of their combined occurrence, the more extreme the precipitation. Our algorithm detects a large fraction of the climatological rainfall amounts (40-70%), heavy precipitation days (50-80%), and the top 10 extreme precipitation days (60-90%) at many sites in southern Israel and the northern and western parts of Saudi Arabia. This identification method provides a new tool for future work to disentangle teleconnections, assess medium-range predictability and improve understanding of climatic changes of extreme precipitation in the Middle East and elsewhere.
de Vries, A. J.; Ouwersloot, H. G.; Feldstein, S. B.; Riemer, M.; El Kenawy, A. M.; McCabe, M. F.; Lelieveld, J.
2018-01-01
Extreme precipitation events in the otherwise arid Middle East can cause flooding with dramatic socioeconomic impacts. Most of these events are associated with tropical-extratropical interactions, whereby a stratospheric potential vorticity (PV) intrusion reaches deep into the subtropics and forces an incursion of high poleward vertically integrated water vapor transport (IVT) into the Middle East. This study presents an object-based identification method for extreme precipitation events based on the combination of these two larger-scale meteorological features. The general motivation for this approach is that precipitation is often poorly simulated in relatively coarse weather and climate models, whereas the synoptic-scale circulation is much better represented. The algorithm is applied to ERA-Interim reanalysis data (1979-2015) and detects 90% (83%) of the 99th (97.5th) percentile of extreme precipitation days in the region of interest. Our results show that stratospheric PV intrusions and IVT structures are intimately connected to extreme precipitation intensity and seasonality. The farther south a stratospheric PV intrusion reaches, the larger the IVT magnitude, and the longer the duration of their combined occurrence, the more extreme the precipitation. Our algorithm detects a large fraction of the climatological rainfall amounts (40-70%), heavy precipitation days (50-80%), and the top 10 extreme precipitation days (60-90%) at many sites in southern Israel and the northern and western parts of Saudi Arabia. This identification method provides a new tool for future work to disentangle teleconnections, assess medium-range predictability, and improve understanding of climatic changes of extreme precipitation in the Middle East and elsewhere.
Form of the manifestly covariant Lagrangian
Johns, Oliver Davis
1985-10-01
The preferred form for the manifestly covariant Lagrangian function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' Lagrangian and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant Lagrangian theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' Lagrangian, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives Lagrangian theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' Lagrangian is a completely adequate basis for covariant Lagrangian theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the Lagrangian and other four-vector equations.
Comparing the dynamics of skyrmions and superconducting vortices
International Nuclear Information System (INIS)
Olson Reichhardt, C.J.; Lin, S.Z.; Ray, D.; Reichhardt, C.
2014-01-01
Highlights: • We describe similarities and differences between skyrmion and vortex dynamics. • The Magnus force can dramatically alter skyrmion transport. • The pinning becomes very weak when the Magnus force is strong. - Abstract: Vortices in type-II superconductors have attracted enormous attention as ideal systems in which to study nonequilibrium collective phenomena, since the self-ordering of the vortices competes with quenched disorder and thermal effects. Dynamic effects found in vortex systems include depinning, nonequilibrium phase transitions, creep, structural order–disorder transitions, and melting. Understanding vortex dynamics is also important for applications of superconductors which require the vortices either to remain pinned or to move in a controlled fashion. Recently, topological defects called skyrmions have been realized experimentally in chiral magnets. Here we highlight similarities and differences between skyrmion dynamics and vortex dynamics. Many of the previous ideas and experimental setups that have been applied to superconducting vortices can also be used to study skyrmions. We also discuss some of the differences between the two systems, such as the potentially large contribution of the Magnus force in the skyrmion system that can dramatically alter the dynamics and transport properties
Low-energy phenomenological chiral Lagrangians
International Nuclear Information System (INIS)
Cavopol, A.V.
1987-01-01
We develop a phenomenological Lagrangian that satisfies the requirements of the so called alternative schemes designed to model low energy meson phenomenology. Linear and nonlinear σ type Lagrangians and symmetry breaking schemes are used to describe pions that exhibit masses proportional to the square of the symmetry breaking term's coefficient, ε. (m π 2 ∼ 0(ε 2 )). The invariance of the theory under coordinate dependent transformations is achieved by introducing gauge fields for both linear and nonlinear Lagrangians. Finally, analogies between the minimal symmetry breaking terms in Quantum Electrodynamics and in our phenomenological lagrangians are used to generate a discussion of the quark-pion mass dependence indicated by the model
Quadratic Lagrangians and Legendre transformation
International Nuclear Information System (INIS)
Magnano, G.
1988-01-01
In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor
Lagrangian submanifolds and dynamics on Lie algebroids
International Nuclear Information System (INIS)
Leon, Manuel de; Marrero, Juan C; MartInez, Eduardo
2005-01-01
In some previous papers, a geometric description of Lagrangian mechanics on Lie algebroids has been developed. In this topical review, we give a Hamiltonian description of mechanics on Lie algebroids. In addition, we introduce the notion of a Lagrangian submanifold of a symplectic Lie algebroid and we prove that the Lagrangian (Hamiltonian) dynamics on Lie algebroids may be described in terms of Lagrangian submanifolds of symplectic Lie algebroids. The Lagrangian (Hamiltonian) formalism on Lie algebroids permits us to deal with Lagrangian (Hamiltonian) functions not defined necessarily on tangent (cotangent) bundles. Thus, we may apply our results to the projection of Lagrangian (Hamiltonian) functions which are invariant under the action of a symmetry Lie group. As a consequence, we obtain that Lagrange-Poincare (Hamilton-Poincare) equations are the Euler-Lagrange (Hamilton) equations associated with the corresponding Atiyah algebroid. Moreover, we prove that Lagrange-Poincare (Hamilton-Poincare) equations are the local equations defining certain Lagrangian submanifolds of symplectic Atiyah algebroids. (topical review)
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
Weyl's Lagrangian in teleparallel form
International Nuclear Information System (INIS)
Burnett, James; Vassiliev, Dmitri
2009-01-01
The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable - the coframe (an orthonormal tetrad of covector fields). We show that when written in terms of this dynamical variable, the Weyl Lagrangian becomes remarkably simple: it is the wedge product of axial torsion of the teleparallel connection with a teleparallel lightlike element of the coframe. We also examine the issues of U(1)-invariance and conformal invariance. Examination of the latter motivates us to introduce a positive scalar field (equivalent to a density) as an additional dynamical variable; this makes conformal invariance self-evident.
Effective lagrangian for strong interactions
International Nuclear Information System (INIS)
Jain, P.
1988-01-01
We attempt to construct a realistic phenomenological Lagrangian in order to describe strong interactions. This is in general a very complicated problem and we shall explore its various aspects. We first include the vector mesons by writing down the most general chiral invariant terms proportional to the Levi-Civita symbol ε μναβ . These terms involve three unknown coefficients, which are calculated by using the experimental results of strong interaction processes. We then calculate the static nucleon properties by finding the solitonic excitations of this model. The results turn out to be, as is also the case for most other vector-pseudoscalar Lagrangians, better than the Skyrme model but are still somewhat different from the experiments. Another aspect that we shall study is the incorporation of scale anomaly of QCD into the Skyrme model. We thus introduce a scalar glueball in our Lagrangian. Here we find an interesting result that the effective glue field dynamically forms a bag for the soliton. Depending on the values of the parameters, we get either a deep bag or a shallow bag. However by including the scalar meson, we find that to get realistic scalar sector we must have the shallow bag. Finally we show some intriguing connections between the chiral quark model, in which the nucleon is described as a solitonic excitation, and the ordinary potential binding quark model
Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics.
Martínez, Enrique; Cawkwell, Marc J; Voter, Arthur F; Niklasson, Anders M N
2015-04-21
Extended Lagrangian Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended Lagrangian Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached at each time step. The thermostated extended Lagrangian framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.
Dynamics of nonstationary dipole vortices
DEFF Research Database (Denmark)
Hesthaven, J.S.; Lynov, Jens-Peter; Nycander, J.
1993-01-01
The dynamics of tilted dipole vortices in the equivalent barotropic vorticity (or Hasegawa-Mima) equation is studied. A recent theory is compared with numerical simulations and found to describe the short time behavior of dipole vortices well. In the long time limit the dipoles are found to eithe...... disintegrate or relax toward a steady eastward propagating dipole vortex. This relaxation is a consequence of nonviscous enstrophy loss by the dipole vortex....
Semi-supervised adaptation in ssvep-based brain-computer interface using tri-training
DEFF Research Database (Denmark)
Bender, Thomas; Kjaer, Troels W.; Thomsen, Carsten E.
2013-01-01
This paper presents a novel and computationally simple tri-training based semi-supervised steady-state visual evoked potential (SSVEP)-based brain-computer interface (BCI). It is implemented with autocorrelation-based features and a Naïve-Bayes classifier (NBC). The system uses nine characters...
Nonquasineutral electron vortices in nonuniform plasmas
Energy Technology Data Exchange (ETDEWEB)
Angus, J. R.; Richardson, A. S.; Swanekamp, S. B.; Schumer, J. W. [Plasma Physics Division, Naval Research Laboratory, Washington, District of Columbia 20375 (United States); Ottinger, P. F. [Engility Corporation, Chantilly, Virginia 20151 (United States)
2014-11-15
Electron vortices are observed in the numerical simulation of current carrying plasmas on fast time scales where the ion motion can be ignored. In plasmas with nonuniform density n, vortices drift in the B × ∇n direction with a speed that is on the order of the Hall speed. This provides a mechanism for magnetic field penetration into a plasma. Here, we consider strong vortices with rotation speeds V{sub ϕ} close to the speed of light c where the vortex size δ is on the order of the magnetic Debye length λ{sub B}=|B|/4πen and the vortex is thus nonquasineutral. Drifting vortices are typically studied using the electron magnetohydrodynamic model (EMHD), which ignores the displacement current and assumes quasineutrality. However, these assumptions are not strictly valid for drifting vortices when δ ≈ λ{sub B}. In this paper, 2D electron vortices in nonuniform plasmas are studied for the first time using a fully electromagnetic, collisionless fluid code. Relatively large amplitude oscillations with periods that correspond to high frequency extraordinary modes are observed in the average drift speed. The drift speed W is calculated by averaging the electron velocity field over the vorticity. Interestingly, the time-averaged W from these simulations matches very well with W from the much simpler EMHD simulations even for strong vortices with order unity charge density separation.
Diabatic modification of potential vorticity in extratropical cyclones
Chagnon, J.
2012-12-01
Representation of diabatic processes and their impact on extratropical cyclones is a likely source of skill degradation in operational numerical weather prediction systems. This investigation examines the source, structure, and magnitude of diabatic potential vorticity (PV) anomalies generated by small-scale and parameterized processes in both mesoscale and global model simulations of extratropical cyclones in the North Atlantic. Simulations of several cold season extratropical storms have been performed using the Met Office Unified Model. Several cases simulated were drawn from the DIAbatic influences on Mesoscale structures in ExTratropical cyclones (DIAMET) observational campaign during which the National Environmental Research Council (NERC) Facility for Airborne Atmospheric Measurement (FAAM) BAE-146 aircraft was deployed. The influence of specific modelled processes was quantified using a set of tracers, each of which represents a history of the PV contributed by a specific segment of the model (e.g., boundary-layer scheme, cloud microphysics, convection scheme , radiation, etc.). This presentation will highlight several differences and similarities in high and low resolution simulations. For example, in high resolution simulations, tropopause folds are sharpened by a tripolar PV anomaly arising from the convection, boundary-layer, and microphysics schemes; this structure is not present in coarser global model simulations. However, a dipole of PV straddling the tropopause is diagnosed in both coarse- and fine-resolution simulations. The PV dipole, which is strongly influenced by long-wave radiative cooling, increases the gradient of PV near the tropopause and therefore modifies the characteristics Rossby wave propagation and moist baroclinic wave growth.
Lagrangian multiforms and multidimensional consistency
Energy Technology Data Exchange (ETDEWEB)
Lobb, Sarah; Nijhoff, Frank [Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT (United Kingdom)
2009-10-30
We show that well-chosen Lagrangians for a class of two-dimensional integrable lattice equations obey a closure relation when embedded in a higher dimensional lattice. On the basis of this property we formulate a Lagrangian description for such systems in terms of Lagrangian multiforms. We discuss the connection of this formalism with the notion of multidimensional consistency, and the role of the lattice from the point of view of the relevant variational principle.
Coherent Vortices in Strongly Coupled Liquids
International Nuclear Information System (INIS)
Ashwin, J.; Ganesh, R.
2011-01-01
Strongly coupled liquids are ubiquitous in both nature and laboratory plasma experiments. They are unique in the sense that their average potential energy per particle dominates over the average kinetic energy. Using ''first principles'' molecular dynamics (MD) simulations, we report for the first time the emergence of isolated coherent tripolar vortices from the evolution of axisymmetric flows in a prototype two-dimensional (2D) strongly coupled liquid, namely, the Yukawa liquid. Linear growth rates directly obtained from MD simulations are compared with a generalized hydrodynamic model. Our MD simulations reveal that the tripolar vortices persist over several turn over times and hence may be observed in strongly coupled liquids such as complex plasma, liquid metals and astrophysical systems such as white dwarfs and giant planetary interiors, thereby making the phenomenon universal.
Coherent Vortices in Strongly Coupled Liquids
Ashwin, J.; Ganesh, R.
2011-04-01
Strongly coupled liquids are ubiquitous in both nature and laboratory plasma experiments. They are unique in the sense that their average potential energy per particle dominates over the average kinetic energy. Using “first principles” molecular dynamics (MD) simulations, we report for the first time the emergence of isolated coherent tripolar vortices from the evolution of axisymmetric flows in a prototype two-dimensional (2D) strongly coupled liquid, namely, the Yukawa liquid. Linear growth rates directly obtained from MD simulations are compared with a generalized hydrodynamic model. Our MD simulations reveal that the tripolar vortices persist over several turn over times and hence may be observed in strongly coupled liquids such as complex plasma, liquid metals and astrophysical systems such as white dwarfs and giant planetary interiors, thereby making the phenomenon universal.
Use of acoustic vortices in acoustic levitation
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Santillan, Arturo Orozco; Juhl, Peter Møller
2009-01-01
Acoustic fields are known to exert forces on the surfaces of objects. These forces are noticeable if the sound pressure is sufficiently high. Two phenomena where acoustic forces are relevant are: i) acoustic levitation, where strong standing waves can hold small objects at certain positions......, counterbalancing their weight, and ii) acoustic vortices, spinning sound fields that can impinge angular momentum and cause rotation of objects. In this contribution, both force-creating sound fields are studied by means of numerical simulations. The Boundary Element Method is employed to this end. The simulation...... of acoustical vortices uses an efficient numerical implementation based on the superposition of two orthogonal sound fields with a delay of 90° between them. It is shown that acoustic levitation and the use of acoustic vortices can be combined to manipulate objects in an efficient and controlled manner without...
Modeling pollutant transport using a meshless-lagrangian particle model
International Nuclear Information System (INIS)
Carrington, D.B.; Pepper, D.W.
2002-01-01
A combined meshless-Lagrangian particle transport model is used to predict pollutant transport over irregular terrain. The numerical model for initializing the velocity field is based on a meshless approach utilizing multiquadrics established by Kansa. The Lagrangian particle transport technique uses a random walk procedure to depict the advection and dispersion of pollutants over any type of surface, including street and city canyons
Potential vorticity dynamics in the Canadian Climate Centre GCM
International Nuclear Information System (INIS)
Koshyk, J.N.; McFarlane, N.
1994-01-01
The global distribution of Ertel potential vorticity (PV), simulated by the Canadian Climate Centre general circulation model (CCC GCM) is examined. An expression for PV in terms of an arbitrary vertical coordinate is formulated. This expression is used to calculate temporally averaged PV from the model temperature and wind fields. It is shown that a good approximation to the temporally averaged PV can be obtained from temporally averaged temperature and wind fields. An equation governing the time evolution of PV in the model vertical coordinate system is also derived. This equation is written in flux form and the associated flux is examined in a lower stratographic region of enhanced gravity-wave drag, above the Tibetan plateau. In this region, the southward transport of PV effected by gravity-wave drag is balanced to a large degree by the advection of PV northward. Finally, results from a recent experimental version of the CCC GCM, with an uppermost level at 1 mb, are used to examine PV dynamics associated with a spontaneous model stratospheric sudden warming. The warming is preceded by 2 successive large amplitude wavenumber 1 disturbances in the lower stratosphere. The second of these leads to splitting of the mid-stratospheric vortex into a double vortex pattern, as is clearly evident on maps of the 850K PV field during the warming period
"Lagrangian" for a Non-Lagrangian Field Theory with N=2 Supersymmetry.
Gadde, Abhijit; Razamat, Shlomo S; Willett, Brian
2015-10-23
We suggest that at least some of the strongly coupled N=2 quantum field theories in 4D can have a nonconformal N=1 Lagrangian description flowing to them at low energies. In particular, we construct such a description for the N=2 rank one superconformal field theory with E(6) flavor symmetry, for which a Lagrangian description was previously unavailable. We utilize this description to compute several supersymmetric partition functions.
Deveaud-Plédran, Benoit
2012-02-01
Polariton quantum fluids may be created both spontaneously through a standard phase transition towards a Bose Einstein condensate, or may be resonantly driven with a well-defined speed. Thanks to the photonic component of polaritons, the properties of the quantum fluid may be accessed rather directly with in particular the possibility of detained interferometric studies. Here, I will detail the dynamics of vortices, obtained with a picosecond time resolution, in different configurations, with in particular their phase dynamics. I will show in particular the dynamics the dynamics of spontaneous creation of a vortex, the dissociation of a full vortex into two half vortices as well as the dynamics of the dissociation of a dark soliton line into a street of pairs of vortices. Work done at EPFL by a dream team of Postdocs PhD students and collaborators: K. Lagoudakis, G. Nardin, T. Paraiso, G. Grosso, F. Manni, Y L'eger, M. Portella Oberli, F. Morier-Genoud and the help of our friend theorists V, Savona, M. Vouters and T. Liew.
Lagrangian cobordism and tropical curves
Sheridan, Nick; Smith, Ivan
2018-01-01
We study a cylindrical Lagrangian cobordism group for Lagrangian torus fibres in symplectic manifolds which are the total spaces of smooth Lagrangian torus fibrations. We use ideas from family Floer theory and tropical geometry to obtain both obstructions to and constructions of cobordisms; in particular, we give examples of symplectic tori in which the cobordism group has no non-trivial cobordism relations between pairwise distinct fibres, and ones in which the degree zero fibre cobordism gr...
A new technique based on the transformation of variables for nonlinear drift and Rossby vortices
International Nuclear Information System (INIS)
Orito, Kohtaro
1996-07-01
The quasi-two-dimensional nonlinear equations for drift and Rossby vortices have some stationary multipole solutions, and especially the dipole vortex solution is called modon. These solutions are valid only in the lowest order where the fluid velocity has a stream function. In order to investigate features of the multipole solutions more accurately, the effect of the higher order terms, for example the polarization drift in a plasma or the Coriolis force in a rotating planet, needs to be considered. It is shown that the higher order analysis through a new technique based on a transformation of variables is much easier than a straightforward iteration. The solutions in this analysis are obtained by inverse transformation to the original coordinates, where the profiles of potentials are distorted by the effects of higher order terms. (author)
Lagrangian averaging with geodesic mean.
Oliver, Marcel
2017-11-01
This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler- α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.
High-Order Hamilton's Principle and the Hamilton's Principle of High-Order Lagrangian Function
International Nuclear Information System (INIS)
Zhao Hongxia; Ma Shanjun
2008-01-01
In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton's principle. Finally, the Hamilton's principle of high-order Lagrangian function is given.
Relabeling symmetries in hydrodynamics and magnetohydrodynamics
International Nuclear Information System (INIS)
Padhye, N.; Morrison, P.J.
1996-04-01
Lagrangian symmetries and concomitant generalized Bianchi identities associated with the relabeling of fluid elements are found for hydrodynamics and magnetohydrodynamics (MHD). In hydrodynamics relabeling results in Ertel's theorem of conservation of potential vorticity, while in MHD it yields the conservation of cross helicity. The symmetries of the reduction from Lagrangian (material) to Eulerian variables are used to construct the Casimir invariants of the Hamiltonian formalism
Vorticity budget of a tornado-like vortex
Energy Technology Data Exchange (ETDEWEB)
Sassa, Koji; Takemura, Saki, E-mail: sassa@kochi-u.ac.jp [Department of Applied Science, Kochi University (Japan)
2011-12-22
We evaluated the vorticity budget of a tornado-like vortex by measuring vertical and horizontal circulations of it. Though spiral horizontal vortices are clearly observed to converge and tilted into the tornado-like vortex, their circulation is quite small. The conversion of the vertical vorticity concentrated at the side of the spiral horizontal vortices was found to mainly contribute to the maintenance of the tornado-like vortex.
Review of vortices in wildland fire
Jason M. Forthofer; Scott L. Goodrick
2011-01-01
Vortices are almost always present in the wildland fire environment and can sometimes interact with the fire in unpredictable ways, causing extreme fire behavior and safety concerns. In this paper, the current state of knowledge of the interaction of wildland fire and vortices is examined and reviewed. A basic introduction to vorticity is given, and the two common...
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.
Zheng, Yue; Chen, W J
2017-08-01
Topological defects in condensed matter are attracting e significant attention due to their important role in phase transition and their fascinating characteristics. Among the various types of matter, ferroics which possess a switchable physical characteristic and form domain structure are ideal systems to form topological defects. In particular, a special class of topological defects-vortices-have been found to commonly exist in ferroics. They often manifest themselves as singular regions where domains merge in large systems, or stabilize as novel order states instead of forming domain structures in small enough systems. Understanding the characteristics and controllability of vortices in ferroics can provide us with deeper insight into the phase transition of condensed matter and also exciting opportunities in designing novel functional devices such as nano-memories, sensors, and transducers based on topological defects. In this review, we summarize the recent experimental and theoretical progress in ferroic vortices, with emphasis on those spin/dipole vortices formed in nanoscale ferromagnetics and ferroelectrics, and those structural domain vortices formed in multiferroic hexagonal manganites. We begin with an overview of this field. The fundamental concepts of ferroic vortices, followed by the theoretical simulation and experimental methods to explore ferroic vortices, are then introduced. The various characteristics of vortices (e.g. formation mechanisms, static/dynamic features, and electronic properties) and their controllability (e.g. by size, geometry, external thermal, electrical, magnetic, or mechanical fields) in ferromagnetics, ferroelectrics, and multiferroics are discussed in detail in individual sections. Finally, we conclude this review with an outlook on this rapidly developing field.
Assessment of semi-empirical potentials for the U-Si system
Energy Technology Data Exchange (ETDEWEB)
Baskes, Michael I. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Andersson, Anders David [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-02-03
Accident tolerant fuels (ATF) are being developed in response to the Fukushima Daiichi accident in Japan. One of the options being pursued is U-Si fuels, such as the U_{3}Si_{2} and U_{3}Si_{5} compounds, which benefit from high thermal conductivity (metallic) compared to the UO2 fuel (semi-conductor) used in current Light Water Reactors (LWRs). The U-Si fuels also have higher fissile density. In order to perform meaningful engineering scale nuclear fuel performance simulations, the material properties of the fuel, including the response to irradiation environments, must be known. Unfortunately, the data available for U-Si fuels are rather limited, in particular for the temperature range where LWRs would operate. The ATF HIP is using multi-scale modeling and simulations to address this knowledge gap. Even though Density Functional Theory (DFT) calculations can provide useful answers to a subset of problems, they are computationally too costly for many others, including properties governing microstructure evolution and irradiation effects. For the latter, semi-empirical potentials are typically used. Unfortunately, there is currently no potential for the U-Si system. In this brief report we present initial results from the development of a U-Si semi-empirical potential based on the Modified Embedded Atom Method (MEAM). The potential should reproduce relevant parts of the U-Si phase diagram as well as defect properties important in irradiation environments. This work also serves as an assessment of the general challenges associated with the U-Si system, which will be valuable for the efforts to develop a U-Si Tersoff potential undertaken by Idaho National Laboratory (also part of the ATF HIP). Going forward the main potential development activity will reside at INL and the work presented here is meant to provide input data and guidelines for that activity. The main focus of our work is on the U_{3}Si_{2} and U3Si_{5}
Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds
Lehn, Christian
2011-01-01
We generalize Voisin's theorem on deformations of pairs of a symplectic manifold and a Lagrangian submanifold to the case of Lagrangian normal crossing subvarieties. Partial results are obtained for arbitrary Lagrangian subvarieties. We apply our results to the study of singular fibers of Lagrangian fibrations.
The shallow water equations in Lagrangian coordinates
International Nuclear Information System (INIS)
Mead, J.L.
2004-01-01
Recent advances in the collection of Lagrangian data from the ocean and results about the well-posedness of the primitive equations have led to a renewed interest in solving flow equations in Lagrangian coordinates. We do not take the view that solving in Lagrangian coordinates equates to solving on a moving grid that can become twisted or distorted. Rather, the grid in Lagrangian coordinates represents the initial position of particles, and it does not change with time. We apply numerical methods traditionally used to solve differential equations in Eulerian coordinates, to solve the shallow water equations in Lagrangian coordinates. The difficulty with solving in Lagrangian coordinates is that the transformation from Eulerian coordinates results in solving a highly nonlinear partial differential equation. The non-linearity is mainly due to the Jacobian of the coordinate transformation, which is a precise record of how the particles are rotated and stretched. The inverse Jacobian must be calculated, thus Lagrangian coordinates cannot be used in instances where the Jacobian vanishes. For linear (spatial) flows we give an explicit formula for the Jacobian and describe the two situations where the Lagrangian shallow water equations cannot be used because either the Jacobian vanishes or the shallow water assumption is violated. We also prove that linear (in space) steady state solutions of the Lagrangian shallow water equations have Jacobian equal to one. In the situations where the shallow water equations can be solved in Lagrangian coordinates, accurate numerical solutions are found with finite differences, the Chebyshev pseudospectral method, and the fourth order Runge-Kutta method. The numerical results shown here emphasize the need for high order temporal approximations for long time integrations
Renormalization and effective lagrangians
International Nuclear Information System (INIS)
Polchinski, J.
1984-01-01
There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional lambda PHI 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed. (orig.)
Crosswind Shear Gradient Affect on Wake Vortices
Proctor, Fred H.; Ahmad, Nashat N.
2011-01-01
Parametric simulations with a Large Eddy Simulation (LES) model are used to explore the influence of crosswind shear on aircraft wake vortices. Previous studies based on field measurements, laboratory experiments, as well as LES, have shown that the vertical gradient of crosswind shear, i.e. the second vertical derivative of the environmental crosswind, can influence wake vortex transport. The presence of nonlinear vertical shear of the crosswind velocity can reduce the descent rate, causing a wake vortex pair to tilt and change in its lateral separation. The LES parametric studies confirm that the vertical gradient of crosswind shear does influence vortex trajectories. The parametric results also show that vortex decay from the effects of shear are complex since the crosswind shear, along with the vertical gradient of crosswind shear, can affect whether the lateral separation between wake vortices is increased or decreased. If the separation is decreased, the vortex linking time is decreased, and a more rapid decay of wake vortex circulation occurs. If the separation is increased, the time to link is increased, and at least one of the vortices of the vortex pair may have a longer life time than in the case without shear. In some cases, the wake vortices may never link.
Lagrangian approach to the problem of the hydrodynamic instabilities of a spheical implosion
International Nuclear Information System (INIS)
Brun, L.; Sitt, B.
For the study of hydrodynamic instabilities of a spherical implosion, a very simple Lagrangian-type formulation is proposed, based on the introduction of a potential of transverse displacements, and on the decomposition of disturbances into spherical harmonics. The different modes are decoupled, and can be studied independently. The development of a numerical code utilizing this formulation can then be considered
Functional integral for non-Lagrangian systems
Kochan, Denis
2010-01-01
A novel functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The new approach, which we call "stringy quantization," is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force $-\\kappa[\\dot{q}]^A$. Results for $A = 1$ are compared with those obtained in the approaches by Caldirola-Kanai, Bateman and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.
An Augmented Lagrangian Method for a Class of Inverse Quadratic Programming Problems
International Nuclear Information System (INIS)
Zhang Jianzhong; Zhang Liwei
2010-01-01
We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semidefinite cone constraint and its dual is a linearly constrained semismoothly differentiable (SC 1 ) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/r, and the rate of multiplier iterates is proportional to 1/√r, where r is the penalty parameter in the augmented Lagrangian. As the objective function of the dual problem is a SC 1 function involving the projection operator onto the cone of symmetrically semi-definite matrices, the analysis requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and properties of the projection operator in the symmetric-matrix space. Furthermore, the semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Finally numerical results, implemented by the augmented Lagrangian method, are reported.
Analysis of vorticity dynamics for hump characteristics of a pump turbine model
Energy Technology Data Exchange (ETDEWEB)
Li, Deyou; Gong, Ruzhi; Wang, Hongjie; Han, Lei; Wei, Xianzhu; Qin, Daqing [School of Energy Science and Engineering, Harbin Institute of Technology, Harbin (China)
2016-08-15
Conventional parameters based on CFD methodology for the investigation on hump characteristics of a pump turbine cannot reflect the dynamic interaction mechanism between the runner and the fluid. This research presents a dynamic interaction mechanism of a pump turbine operating in the hump region. First, vorticity dynamic parameters were obtained based on the theory of vorticity dynamics. Second, 3-D unsteady flow simulations were performed in a full pump turbine model using the SST k-ω turbulence model, and numerical results have a good agreement with the experiments. Then, analysis was carried out to determine the relation between the vorticity dynamic parameters and hump characteristics. The results indicate that the theory of vorticity dynamics has an advantage in evaluating the dynamic performance of a pump turbine. The energy transfer between the runner and the fluid is through vorticity dynamic parameters-pressure and friction terms, in which the pressure term accounts for the most. Furthermore, vortex generation mainly results from the skin friction. Combining vorticity dynamic analysis with the method of Q-criterion indicates that hump characteristics are related to the reduction of the surface normal pressure work and vortex motion on the suction surfaces close to the leading edges in the runner, and the increase of skin friction work in the stay-guide vanes.
A thermodynamically general theory for convective vortices
Renno, Nilton O.
2008-08-01
Convective vortices are common features of atmospheres that absorb lower-entropy-energy at higher temperatures than they reject higher-entropy-energy to space. These vortices range from small to large-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective vortices is important to our understanding of some of the basic features of planetary atmospheres. The heat engine framework is a useful tool for studying convective vortices. However, current theories assume that convective vortices are reversible heat engines. Since there are questions about how reversible real atmospheric heat engines are, their usefulness for studying real atmospheric vortices is somewhat controversial. In order to reduce this problem, a theory for convective vortices that includes irreversible processes is proposed. The paper's main result is that the proposed theory provides an expression for the pressure drop along streamlines that includes the effects of irreversible processes. It is shown that a simplified version of this expression is a generalization of Bernoulli's equation to convective circulations. It is speculated that the proposed theory not only explains the intensity, but also sheds light on other basic features of convective vortices such as their physical appearance.
Sbii, Siham; Zazoui, Mimoun; Semane, Noureddine
2015-04-01
In the absence of observations covering the upper troposphere - lower stratophere, headquarters of several disturbances, and knowing that satellites are uniquely capable of providing uniform data coverage globally, a methodology is followed [1] to convert Total Column Ozone, observed by MetOp/GOME2, into pseudo-observations of Mean Potential Vorticity (MPV). The aim is to study the dynamical impact of Ozone data in the prediction of a Mediterranean Heavy Precipitation Event observed during 28-29 September 2012 in the context of HYMEX1. This study builds on a previously described methodology [2] that generates numerical weather prediction model initial conditions from ozone data. Indeed, the assimilation of MPV in a 3D-var framework is based on a linear regression between observed Ozone and vertical integrated Ertel PV. The latter is calculated using dynamical fields from the moroccan operational limited area model ALADIN-MAROC according to [3]: δθ fp p0 -R δU δV P V = - gξaδp- g-R-(p )Cp [(δp-)2 + (δp-)2] (1) Where ξa is the vertical component of the absolute vorticity, U and V the horizontal wind components, θ the potential temperature, R gas constant, Cp specific heat at constant pressure, p the pressure, p0 a reference pressure, g the gravity and f is the Coriolis parameter. The MPV is estimated using the following expression: --1--∫ P2 M PV = P1 - P2 P P V.δp 1 (2) With P1 = 500hPa and P2 = 100hPa In the present study, the linear regression is performed over September 2012 with a correlation coefficient of 0.8265 and is described as follows: M P V = 5.314610- 2 *O3 - 13.445 (3) where O3 and MPV are given in Dobson Unit (DU) and PVU (1 PV U = 10-6 m2 K kg-1 s-1), respectively. It is found that the ozone-influenced upper-level initializing fields affect the precipitation forecast, as diagnosed by a comparison with the ECMWF model. References [1] S. Sbii, N. Semane, Y. Michel, P. Arbogast and M. Zazoui (2012). Using METOP/GOME-2 data and MSG ozone
DEFF Research Database (Denmark)
Bjarløv, Søren Peter; Vladyková, Petra
2011-01-01
The paper gives an account of the potential and need for energy saving in standard family detached and semi-detached wooden houses in Greenland. It is based on studies of house construction compared with Building Regulation requirements and the spread of buildings over time. In the climatic...... conditions of Greenland, there is considerable potential for energy saving in houses due to their construction, shape and condition. To estimate the total potential for energy saving and thus reducing CO2 emissions, we carried out a detailed investigation of three typical standard semi-detached family houses...
Energy Technology Data Exchange (ETDEWEB)
Reithmeier, C.
2001-07-01
Investigating the chemical composition of the atmosphere and its influence on the global climate involves a large number of trace species. Therefore, the Lagrangian transport scheme ATTILA has been developed in this thesis. ATTILA runs online in the general circulation model ECHAM4 and, thus, can be used efficiently for studies involving many tracers. The present study discusses the problems which arise when applying Lagrangian methods on long range and global scale, and describes in detail the solutions developed for ATTILA. Transport experiments with both short-lived and long-lived tracers clearly show that ATTILA is numerically much less diffusive than the operational semi-Lagrangian scheme of ECHAM. It could be shown that the enhanced meridional transport in the tropopause region and the overestimated downward flux through the tropopause in ECHAM are rather due to the numerical properties of the semi-Lagrangian scheme than due to an incorrect circulation. Furthermore, the stratospheric dynamics has been investigated in this study by analysing trajectories and by calculating age spectra and mass fluxes. (orig.)
Vortices on hyperbolic surfaces
International Nuclear Information System (INIS)
Manton, Nicholas S; Rink, Norman A
2010-01-01
It is shown that Abelian Higgs vortices on a hyperbolic surface M can be constructed geometrically from holomorphic maps f: M → N, where N is also a hyperbolic surface. The fields depend on f and on the metrics of M and N. The vortex centres are the ramification points, where the derivative of f vanishes. The magnitude of the Higgs field measures the extent to which f is locally an isometry. Witten's construction of vortices on the hyperbolic plane is rederived, and new examples of vortices on compact surfaces and on hyperbolic surfaces of revolution are obtained. The interpretation of these solutions as SO(3)-invariant, self-dual SU(2) Yang-Mills fields on R 4 is also given.
The S-Lagrangian and a theory of homeostasis in living systems
Sandler, U.; Tsitolovsky, L.
2017-04-01
A major paradox of living things is their ability to actively counteract degradation in a continuously changing environment or being injured through homeostatic protection. In this study, we propose a dynamic theory of homeostasis based on a generalized Lagrangian approach (S-Lagrangian), which can be equally applied to physical and nonphysical systems. Following discoverer of homeostasis Cannon (1935), we assume that homeostasis results from tendency of the organisms to decrease of the stress and avoid of death. We show that the universality of homeostasis is a consequence of analytical properties of the S-Lagrangian, while peculiarities of the biochemical and physiological mechanisms of homeostasis determine phenomenological parameters of the S-Lagrangian. Additionally, we reveal that plausible assumptions about S-Lagrangian features lead to good agreement between theoretical descriptions and observed homeostatic behavior. Here, we have focused on homeostasis of living systems, however, the proposed theory is also capable of being extended to social systems.
Tracking Lagrangian trajectories in position–velocity space
International Nuclear Information System (INIS)
Xu, Haitao
2008-01-01
Lagrangian particle-tracking algorithms are susceptible to intermittent loss of particle images on the sensors. The measured trajectories are often interrupted into short segments and the long-time Lagrangian statistics are difficult to obtain. We present an algorithm to connect the segments of Lagrangian trajectories from common particle-tracking algorithms. Our algorithm tracks trajectory segments in the six-dimensional position and velocity space. We describe the approach to determine parameters in the algorithm and demonstrate the validity of the algorithm with data from numerical simulations and the improvement of long-time Lagrangian statistics on experimental data. The algorithm has important applications in measurements with high particle seeding density and in obtaining multi-particle Lagrangian statistics
Relativistic particle dynamics: Lagrangian proof of the no-interaction theorem
International Nuclear Information System (INIS)
Marmo, G.; Mukunda, N.; Sudarshan, E.C.G.
1983-11-01
An economical proof is given, in the Lagrangian framework, of the No Interaction Theorem of relativistic particle mechanics. It is based on the assumption that there is a Lagrangian, which if singular is allowed to lead at most to primary first class constraints. The proof works with Lagrange rather than Poisson brackets, leading to considerable simplifications compared to other proofs
Lagrangian viscoelastic flow computations using a generalized molecular stress function model
DEFF Research Database (Denmark)
Rasmussen, Henrik K.
2002-01-01
A new finite element technique for the numerical simulation of 3D time-dependent flow of viscoelastic fluid is presented. The technique is based on a Lagrangian kinematics description of the fluid flow. It represents a further development of the 3D Lagrangian integral method (3D-LIM) from a Rivlin...
Lagrangian velocity correlations in homogeneous isotropic turbulence
International Nuclear Information System (INIS)
Gotoh, T.; Rogallo, R.S.; Herring, J.R.; Kraichnan, R.H.
1993-01-01
The Lagrangian velocity autocorrelation and the time correlations for individual wave-number bands are computed by direct numerical simulation (DNS) using the passive vector method (PVM), and the accuracy of the method is studied. It is found that the PVM is accurate when K max /k d ≥2 where K max is the maximum wave number carried in the simulation and k d is the Kolmogorov wave number. The Eulerian and Lagrangian time correlations for various wave-number bands are compared. At moderate to high wave number the Eulerian time correlation decays faster than the Lagrangian, and the effect of sweep on the former is observed. The time scale of the Eulerian correlation is found to be (kU 0 ) -1 while that of the Lagrangian is [∫ 0 k p 2 E(p)dp] -1/2 . The Lagrangian velocity autocorrelation in a frozen turbulent field is computed using the DIA, ALHDIA, and LRA theories and is compared with DNS measurements. The Markovianized Lagrangian renormalized approximation (MLRA) is compared with the DNS, and good agreement is found for one-time quantities in decaying turbulence at low Reynolds numbers and for the Lagrangian velocity autocorrelation in stationary turbulence at moderate Reynolds number. The effect of non-Gaussianity on the Lagrangian correlation predicted by the theories is also discussed
Structure of pheomenological lagrangians for broken supersymmetry
International Nuclear Information System (INIS)
Uematsu, T.; Zachos, C.K.
1982-01-01
We consider the explicit connection between linear representations of supersymetry and the non-linear realizations associated with the generic effective lagrangians of the Volkov-Akulov type. We specify and illustrate a systematic approach for deriving the appropriate phenomenological lagrangian by transforming a pedagogical linear model, in which supersymmetry is broken at the tree level, into its corresponding non-linear lagrangian, in close analogy to the linear sigma model of pion dynamics. We discuss the significance and some properties of such phenomenological lagrangians. (orig.)
Flow structure and vorticity transport on a plunging wing
Eslam Panah, Azar
The structure and dynamics of the flow field created by a plunging flat plate airfoil are investigated at a chord Reynolds number of 10,000 while varying plunge amplitude and Strouhal number. Digital particle image velocimetry measurements are used to characterize the shedding patterns and the interactions between the leading and trailing edge vortex structures (LEV and TEV), resulting in the development of a wake classification system based on the nature and timing of interactions between the leading- and trailing-edge vortices. The convection speed of the LEV and its resulting interaction with the TEV is primarily dependent on reduced frequency; however, at Strouhal numbers above approximately 0.4, a significant influence of Strouhal number (or plunge amplitude) is observed in which LEV convection is retarded, and the contribution of the LEV to the wake is diminished. It is shown that this effect is caused by an enhanced interaction between the LEV and the airfoil surface, due to a significant increase in the strength of the vortices in this Strouhal number range, for all plunge amplitudes investigated. Comparison with low-Reynolds-number studies of plunging airfoil aerodynamics reveals a high degree of consistency and suggests applicability of the classification system beyond the range examined in the present work. Some important differences are also observed. The three-dimensional flow field was characterized for a plunging two-dimensional flat-plate airfoil using three-dimensional reconstructions of planar PIV data. Whereas the phase-averaged description of the flow field shows the secondary vortex penetrating the leading-edge shear layer to terminate LEV formation on the airfoil, time-resolved, instantaneous PIV measurements show a continuous and growing entrainment of secondary vorticity into the shear layer and LEV. A planar control volume analysis on the airfoil indicated that the generation of secondary vorticity produced approximately one half the
Lagrangian and Hamiltonian Formulation of Transmission Line Systems with Boundary Energy Flow
Jeltsema, Dimitri; Schaft, Arjan J. van der
The classical Lagrangian and Hamiltonian formulation of an electrical transmission line is reviewed and extended to allow for varying boundary conditions, The method is based on the definition of an infinite-dimensional analogue of the affine Lagrangian and Hamiltonian input-output systems
Budyansky, M. V.; Prants, S. V.; Samko, E. V.; Uleysky, M. Yu.
2017-09-01
Based on the AVISO velocity field, we compute daily synoptic Lagrangian maps in the South Kuril area for the fishery seasons of 1998, 1999, and 2001-2005 from available catching data on neon flying squid (NFS). With the help of drift maps for artificial particles, we found that the majority of NFS fishing grounds featuring maximum catches are situated near large-scale Lagrangian intrusions: tongues of water penetrating the surrounding water of other Lagrangian properties. It is shown that the NFS catch locations tend to accumulate at places where waters with different magnitudes of certain Lagrangian indicators converge, mix, and produce filaments, swirls, and tendrils typical of chaotic advection. Potential NFS fishing grounds are mainly located near (1) Lagrangian intrusions of the Subarctic front, (2) intrusions of Okhotsk Sea and Oyashio waters around mesoscale anticyclones east of Hokkaido with subsequent penetration of catch locations inside eddies and (3) intrusions of subtropical waters into the central part of the South Kuril area due to interaction with eddies of different size and polarity. Possible reasons for increased biological production and fishery in the vicinity of Lagrangian intrusions are discussed.
Uncovering the Geometry of Barrierless Reactions Using Lagrangian Descriptors.
Junginger, Andrej; Hernandez, Rigoberto
2016-03-03
Transition-state theories describing barrierless chemical reactions, or more general activated problems, are often hampered by the lack of a saddle around which the dividing surface can be constructed. For example, the time-dependent transition-state trajectory uncovering the nonrecrossing dividing surface in thermal reactions in the framework of the Langevin equation has relied on perturbative approaches in the vicinity of the saddle. We recently obtained an alternative approach using Lagrangian descriptors to construct time-dependent and recrossing-free dividing surfaces. This is a nonperturbative approach making no reference to a putative saddle. Here we show how the Lagrangian descriptor can be used to obtain the transition-state geometry of a dissipated and thermalized reaction across barrierless potentials. We illustrate the method in the case of a 1D Brownian motion for both barrierless and step potentials; however, the method is not restricted and can be directly applied to different kinds of potentials and higher dimensional systems.
Cushman-Roisin, B.
Following on a tradition of biannual meetings, the 5th Colloquium on the Modeling of Oceanic Vortices was held May 21-23, 1990, at the Thayer School of Engineering at Dartmouth College, Hanover, N.H. The colloquium series, sponsored by the Office of Naval Research, is intended to gather oceanographers who contribute to our understanding of oceanic mesoscale vortices via analytical, numerical and experimental modeling techniques.
A Lagrangian-dependent metric space
International Nuclear Information System (INIS)
El-Tahir, A.
1989-08-01
A generalized Lagrangian-dependent metric of the static isotropic spacetime is derived. Its behaviour should be governed by imposing physical constraints allowing to avert the pathological features of gravity at the strong field domain. This would restrict the choice of the Lagrangian form. (author). 10 refs
S-equivalents lagrangians in generalized mechanics
International Nuclear Information System (INIS)
Negri, L.J.; Silva, Edna G. da.
1985-01-01
The problem of s-equivalent lagrangians is considered in the realm of generalized mechanics. Some results corresponding to the ordinary (non-generalized) mechanics are extended to the generalized case. A theorem for the reduction of the higher order lagrangian description to the usual order is found to be useful for the analysis of generalized mechanical systems and leads to a new class of equivalence between lagrangian functions. Some new perspectives are pointed out. (Author) [pt
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Losano, L.; Marques, M.A.; Zafalan, I. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)
2017-02-15
We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that solve the equations of motion. We first deal with the asymptotic behavior of the field configurations, and then implement a numerical study of the solutions, the energy density and the magnetic field. We work with the generalized permeability having distinct profiles, giving rise to new models, and we investigate how the vortices behave, compared with the solutions of the corresponding standard models. In particular, we show how to build compact vortices, that is, vortex solutions with the energy density and magnetic field vanishing outside a compact region of the plane. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Grotjahn, Richard [University of California, Department of Land, Air and Water Resources, Davis, CA (United States); Pan, Lin-Lin; Tribbia, Joseph [National Center for Atmospheric Research, Boulder, CO (United States)
2011-06-15
CAM3 (Community Atmosphere Model version 3) simulation bias is diagnosed using the vorticity equation. The study compares CAM3 output with ECMWF (European Centre for Medium-Range Weather Forecasts) 40 year reanalysis (ERA-40) data. A time mean vorticity bias equation is also formulated and the terms are grouped into categories: linear terms, nonlinear terms, transient contributions, and friction (calculated as a residual). Frontal cyclone storms have much weaker band passed kinetic energy and enstrophy in CAM3. The downstream end of the North Atlantic storm track (NAST) has large location error. While the vorticity equation terms have similar amplitude ranking in CAM3 and ERA-40 at upper levels, the ranking differs notably in the lower troposphere. The linear and friction terms dominate the vorticity bias equation. The transient terms contribute along the storm track, but the nonlinear terms are generally much smaller, with the primary exception being over the Iberian peninsula. Friction is much stronger in CAM3. As evidence, nearly all wavelengths (including the longest planetary waves) have smaller amplitude in CAM3 than in ERA-40 vorticity data. Negative near surface vorticity tendency bias on the European side of the Arctic is linked to the NAST track error (evident in the divergence term). CAM3 misses the Beaufort high in sea level pressure (SLP) due to low level warm temperature bias, too little vortex compression, and to too little horizontal advection of negative vorticity compared with ERA-40. Generally lower SLP values in CAM3 over the entire Arctic follow from lower level warm bias in CAM3. (orig.)
Mass and momentum conservation for fluid simulation
Lentine, Michael; Aanjaneya, Mridul; Fedkiw, Ronald
2011-01-01
Momentum conservation has long been used as a design principle for solid simulation (e.g. collisions between rigid bodies, mass-spring elastic and damping forces, etc.), yet it has not been widely used for fluid simulation. In fact, semi-Lagrangian advection does not conserve momentum, but is still regularly used as a bread and butter method for fluid simulation. In this paper, we propose a modification to the semi-Lagrangian method in order to make it fully conserve momentum. While methods of this type have been proposed earlier in the computational physics literature, they are not necessarily appropriate for coarse grids, large time steps or inviscid flows, all of which are common in graphics applications. In addition, we show that the commonly used vorticity confinement turbulence model can be modified to exactly conserve momentum as well. We provide a number of examples that illustrate the benefits of this new approach, both in conserving fluid momentum and passively advected scalars such as smoke density. In particular, we show that our new method is amenable to efficient smoke simulation with one time step per frame, whereas the traditional non-conservative semi-Lagrangian method experiences serious artifacts when run with these large time steps, especially when object interaction is considered. Copyright © 2011 by the Association for Computing Machinery, Inc.
Potential Signatures of Semi-volatile Compounds Associated With Nuclear Processing
Energy Technology Data Exchange (ETDEWEB)
Probasco, Kathleen M.; Birnbaum, Jerome C.; Maughan, A. D.
2002-06-01
Semi-volatile chemicals associated with nuclear processes (e.g., the reprocessing of uranium to produce plutonium for nuclear weapons, or the separation of actinides from processing waste streams), can provide sticky residues or signatures that will attach to piping, ducting, soil, water, or other surface media. Volatile compounds, that are more suitable for electro-optical sensing, have been well studied. However, the semi-volatile compounds have not been well documented or studied. A majority of these semi-volatile chemicals are more robust than typical gaseous or liquid chemicals and can have lifetimes of several weeks, months, or years in the environment. However, large data gaps exist concerning these potential signature compounds and more research is needed to fill these data gaps so that important signature information is not overlooked or discarded. This report investigates key semi-volatile compounds associated with nuclear separations, identifies available chemical and physical properties, and discusses the degradation products that would result from hydrolysis, radiolysis and oxidation reactions on these compounds.
Aubry, R.; Oñate, E.; Idelsohn, S. R.
2006-09-01
The method presented in Aubry et al. (Comput Struc 83:1459-1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505-526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a Lagrangian description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. Numerical results are provided to assess the superiority of the modified algebraic splitting to the classical FS.
A Lagrangian analysis of mid-latitude stratospheric ozone variability and long-term trends.
Koch, G.; Wernli, H.; Staehelin, J.; Peter, T.
2002-05-01
A systematic Lagrangian investigation is performed of wintertime high-resolution stratospheric ozone soundings at Payerne, Switzerland, from January 1970 to March 2001. For every ozone sounding, 10-day backward trajectories have been calculated on 16 isentropic levels using NCEP reanalysis data. Both the minimum/maximum latitude and potential vorticity (PV) averaged along the trajectories are used as indicators of the air parcels' ``origin''. The importance of transport for the understandin g of single ozone profiles is confirmed by a statistical analysis which shows that negative/positive ozone deviations gener ally coincide with transport from regions with climatologically low/high ozone values. The stable relationship between PV and ozone for the 32 year period indicates either no direct chemical impact or no temporal change of this impact. In the upper layer the PV-ozone relationship changes significantly after 1987 and a separate trend analysis for air masses transported from the polar, midlatitude and subtropical regions shows negative ozone trends in all three categories (with a maximum for the polar region). This is not direct evidence for, but would be in agreement with, an increased chemical ozone depletion in the Arctic since the late 1980s. The reasons for the negative trend in the mid-stratospheric air masses with subtropical origin that are in qualitative agreement with recent satellite observations are presently unknown.
Option volatility and the acceleration Lagrangian
Baaquie, Belal E.; Cao, Yang
2014-01-01
This paper develops a volatility formula for option on an asset from an acceleration Lagrangian model and the formula is calibrated with market data. The Black-Scholes model is a simpler case that has a velocity dependent Lagrangian. The acceleration Lagrangian is defined, and the classical solution of the system in Euclidean time is solved by choosing proper boundary conditions. The conditional probability distribution of final position given the initial position is obtained from the transition amplitude. The volatility is the standard deviation of the conditional probability distribution. Using the conditional probability and the path integral method, the martingale condition is applied, and one of the parameters in the Lagrangian is fixed. The call option price is obtained using the conditional probability and the path integral method.
International Nuclear Information System (INIS)
Chang, Y.W.; Chu, H.Y.; Gvildys, J.; Wang, C.Y.
1979-01-01
The analysis of fluid-structure interaction involves the calculation of both fluid transient and structure dynamics. In the structural analysis, Lagrangian meshes have been used exclusively, whereas for the fluid transient, Lagrangian, Eulerian, and arbitrary Lagrangian-Eulerian (quasi-Eulerian) meshes have been used. This paper performs an evaluation on these three types of meshes. The emphasis is placed on the applicability of the method in analyzing fluid-structure interaction problems in HCDA analysis
Power corrections to the HTL effective Lagrangian of QED
Carignano, Stefano; Manuel, Cristina; Soto, Joan
2018-05-01
We present compact expressions for the power corrections to the hard thermal loop (HTL) Lagrangian of QED in d space dimensions. These are corrections of order (L / T) 2, valid for momenta L ≪ T, where T is the temperature. In the limit d → 3 we achieve a consistent regularization of both infrared and ultraviolet divergences, which respects the gauge symmetry of the theory. Dimensional regularization also allows us to witness subtle cancellations of infrared divergences. We also discuss how to generalize our results in the presence of a chemical potential, so as to obtain the power corrections to the hard dense loop (HDL) Lagrangian.
Assessing atmospheric bias correction for dynamical consistency using potential vorticity
International Nuclear Information System (INIS)
Rocheta, Eytan; Sharma, Ashish; Evans, Jason P
2014-01-01
Correcting biases in atmospheric variables prior to impact studies or dynamical downscaling can lead to new biases as dynamical consistency between the ‘corrected’ fields is not maintained. Use of these bias corrected fields for subsequent impact studies and dynamical downscaling provides input conditions that do not appropriately represent intervariable relationships in atmospheric fields. Here we investigate the consequences of the lack of dynamical consistency in bias correction using a measure of model consistency—the potential vorticity (PV). This paper presents an assessment of the biases present in PV using two alternative correction techniques—an approach where bias correction is performed individually on each atmospheric variable, thereby ignoring the physical relationships that exists between the multiple variables that are corrected, and a second approach where bias correction is performed directly on the PV field, thereby keeping the system dynamically coherent throughout the correction process. In this paper we show that bias correcting variables independently results in increased errors above the tropopause in the mean and standard deviation of the PV field, which are improved when using the alternative proposed. Furthermore, patterns of spatial variability are improved over nearly all vertical levels when applying the alternative approach. Results point to a need for a dynamically consistent atmospheric bias correction technique which results in fields that can be used as dynamically consistent lateral boundaries in follow-up downscaling applications. (letter)
Travelling water waves with compactly supported vorticity
International Nuclear Information System (INIS)
Shatah, Jalal; Walsh, Samuel; Zeng, Chongchun
2013-01-01
In this paper, we prove the existence of two-dimensional, travelling, capillary-gravity, water waves with compactly supported vorticity. Specifically, we consider the cases where the vorticity is a δ-function (a point vortex), or has small compact support (a vortex patch). Using a global bifurcation theoretic argument, we construct a continuum of finite-amplitude, finite-vorticity solutions for the periodic point vortex problem. For the non-periodic case, with either a vortex point or patch, we prove the existence of a continuum of small-amplitude, small-vorticity solutions. (paper)
Reducible gauge theories in local superfield Lagrangian BRST quantization
Energy Technology Data Exchange (ETDEWEB)
Gitman, D. M. [Universidade de Sao Paulo (USP), SP (Brazil). Inst. de Fisica; Moshin, P.Yu. [Tomsk State Pedagogical University (Russian Federation); Reshetnyak, A.A. [Inst. of Strength Physics and Materials Science, Tomsk (Russian Federation). Lab. of Non-equilibrium State Theory
2007-12-15
The construction of {theta}-local superfield Lagrangian BRST quantization in non-Abelian hyper gauges for generic gauge theories based on the action principle is examined in the case of reducible local superfield models (LSM) on the basis of embedding a gauge theory into a special {theta}-local superfield model with anti symplectic constraints and a Grassmann-odd time parameter {theta}. We examine the problem of establishing a new correspondence between the odd-Lagrangian and odd-Hamiltonian formulations of a local LSM in the case of degeneracy of the Lagrangian description with respect to derivatives over {theta} of generalized classical superfields A{sup I}({theta}). We also reveal the role of the nilpotent BRST-BFV charge for a formal dynamical system corresponding to the BV-BFV dual description of an LSM. (author)
Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: numerical testing
Rõõm, Rein; Männik, Aarne; Luhamaa, Andres; Zirk, Marko
2007-10-01
The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and non-hydrostatic effect presentation capability. Comparison demonstrates good (in strong primary wave generation) to satisfactory (in weak secondary wave reproduction in some cases) consistency of the numerical modelling results with known stationary linear test solutions. Numerical stability of the developed model is investigated with respect to the reference state choice, modelling dynamics of a stationary front. The horizontally area-mean reference temperature proves to be the optimal stability warrant. The numerical scheme with explicit residual in the vertical forcing term becomes unstable for cross-frontal temperature differences exceeding 30 K. Stability is restored, if the vertical forcing is treated implicitly, which enables to use time steps, comparable with the hydrostatic SISL.
The complete lowest order chiral Lagrangian from a little box
International Nuclear Information System (INIS)
DeGrand, T.; Schaefer, S.
2007-09-01
We recently performed a pilot study determining the parameters of the leading order chiral Lagrangian from distributions of the eigenvalues of a quenched Dirac operator coupled to an imaginary isospin chemical potential. (orig.)
International Nuclear Information System (INIS)
Tatekawa, Takayuki
2014-01-01
We study the initial conditions for cosmological N-body simulations for precision cosmology. In general, Zel'dovich approximation has been applied for the initial conditions of N-body simulations for a long time. These initial conditions provide incorrect higher-order growth. These error caused by setting up the initial conditions by perturbation theory is called transients. We investigated the impact of transient on non-Gaussianity of density field by performing cosmological N-body simulations with initial conditions based on first-, second-, and third-order Lagrangian perturbation theory in previous paper. In this paper, we evaluates the effect of the transverse mode in the third-order Lagrangian perturbation theory for several statistical quantities such as power spectrum and non-Gaussianty. Then we clarified that the effect of the transverse mode in the third-order Lagrangian perturbation theory is quite small
Aharonov-Bohm effect with many vortices
International Nuclear Information System (INIS)
Franchini, Fabio; Scharff Goldhaber, Alfred
2008-01-01
The Aharonov-Bohm (A-B) effect is the prime example of a zero-field-strength configuration where a nontrivial vector potential acquires physical significance, a typical quantum mechanical effect. We consider an extension of the traditional A-B problem, by studying a two-dimensional medium filled with many point-like vortices. Systems like this might be present within a type II superconducting layer in the presence of a strong magnetic field perpendicular to the layer, and have been studied in different limits. We construct an explicit solution for the wave function of a scalar particle moving within one such layer when the vortices occupy the sites of a square lattice and have all the same strength, equal to half of the flux quantum. From this construction, we infer some general characteristics of the spectrum, including the conclusion that such a flux array produces a repulsive barrier to an incident low-energy charged particle, so that the penetration probability decays exponentially with distance from the edge.
Aharonov-Bohm effect with many vortices
Franchini, Fabio; Scharff Goldhaber, Alfred
2008-12-01
The Aharonov-Bohm (A-B) effect is the prime example of a zero-field-strength configuration where a nontrivial vector potential acquires physical significance, a typical quantum mechanical effect. We consider an extension of the traditional A-B problem, by studying a two-dimensional medium filled with many point-like vortices. Systems like this might be present within a type II superconducting layer in the presence of a strong magnetic field perpendicular to the layer, and have been studied in different limits. We construct an explicit solution for the wave function of a scalar particle moving within one such layer when the vortices occupy the sites of a square lattice and have all the same strength, equal to half of the flux quantum. From this construction, we infer some general characteristics of the spectrum, including the conclusion that such a flux array produces a repulsive barrier to an incident low-energy charged particle, so that the penetration probability decays exponentially with distance from the edge.
Lagrangian relaxation technique in power systems operation planning: Multipliers updating problem
Energy Technology Data Exchange (ETDEWEB)
Ruzic, S. [Electric Power Utility of Serbia, Belgrade (Yugoslavia)
1995-11-01
All Lagrangian relaxation based approaches to the power systems operation planning have an important common part: the Lagrangian multipliers correction procedure. It is the subject of this paper. Different approaches presented in the literature are discussed and an original method for the Lagrangian multipliers updating is proposed. The basic idea of this new method is to update Lagrangian multipliers trying to satisfy Khun-Tucker optimality conditions. Instead of the dual function maximization the `distance of optimality function` is defined and minimized. If Khun-Tucker optimality conditions are satisfied the value of this function is in range (-1,0); otherwise the function has a big positive value. This method called `the distance of optimality method` takes into account future changes in planning generations due to the Lagrangian multipliers updating. The influence of changes in a multiplier associated to one system constraint to the satisfaction of some other system requirements is also considered. The numerical efficiency of the proposed method is analyzed and compared with results obtained using the sub-gradient technique. 20 refs, 2 tabs
Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.
Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun
2013-01-01
An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.
Phase locking of moving magnetic vortices in bridge-coupled nanodisks
International Nuclear Information System (INIS)
Zhu, Qiyuan; Zheng, Qi; Liu, Xianyin; Liu, Qingfang; Wang, Jianbo
2015-01-01
In this paper, phase locking dynamics of vortices induced by spin transfer torque in bridge-coupled nanodisks are studied by micromagnetic simulations. In the presence of the bridge coupling, the required time for the phase locking is dramatically reduced, and the phase difference between the two vortices keeps at a nonzero value after the phase locking. Moreover, the phase difference is affected significantly by bridge coupling, Oersted field distribution, nanodisk size, as well as in-plane bias magnetic field. In addition, the coupled gyrotropic frequency of vortices depends linearly on the perpendicular magnetic field. This systematic study of phase locking parameters, especially the phase difference, is important for the applications of vortex-based spin-torque nano-oscillators
Phase locking of moving magnetic vortices in bridge-coupled nanodisks
Energy Technology Data Exchange (ETDEWEB)
Zhu, Qiyuan; Zheng, Qi; Liu, Xianyin; Liu, Qingfang, E-mail: liuqf@lzu.edu.cn [Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000 (China); Wang, Jianbo [Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000 (China); Key Laboratory of Special Function Materials and Structure Design, Ministry of Education, Lanzhou University, Lanzhou 730000 (China)
2015-05-07
In this paper, phase locking dynamics of vortices induced by spin transfer torque in bridge-coupled nanodisks are studied by micromagnetic simulations. In the presence of the bridge coupling, the required time for the phase locking is dramatically reduced, and the phase difference between the two vortices keeps at a nonzero value after the phase locking. Moreover, the phase difference is affected significantly by bridge coupling, Oersted field distribution, nanodisk size, as well as in-plane bias magnetic field. In addition, the coupled gyrotropic frequency of vortices depends linearly on the perpendicular magnetic field. This systematic study of phase locking parameters, especially the phase difference, is important for the applications of vortex-based spin-torque nano-oscillators.
Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme
Rõõm, Rein; Männik, Aarne; Luhamaa, Andres
2007-10-01
Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.
Directory of Open Access Journals (Sweden)
M. Branicki
2010-03-01
Full Text Available In this work we discuss applications of Lagrangian techniques to study transport properties of flows generated by shallow water models of estuarine flows. We focus on the flow in the Chesapeake Bay generated by Quoddy (see Lynch and Werner, 1991, a finite-element (shallow water model adopted to the bay by Gross et al. (2001. The main goal of this analysis is to outline the potential benefits of using Lagrangian tools for both understanding transport properties of such flows, and for validating the model output and identifying model deficiencies. We argue that the currently available 2-D Lagrangian tools, including the stable and unstable manifolds of hyperbolic trajectories and techniques exploiting 2-D finite-time Lyapunov exponent fields, are of limited use in the case of partially mixed estuarine flows. A further development and efficient implementation of three-dimensional Lagrangian techniques, as well as improvements in the shallow-water modelling of 3-D velocity fields, are required for reliable transport analysis in such flows. Some aspects of the 3-D trajectory structure in the Chesapeake Bay, based on the Quoddy output, are also discussed.
Deconstructing field-induced ketene isomerization through Lagrangian descriptors.
Craven, Galen T; Hernandez, Rigoberto
2016-02-07
The time-dependent geometrical separatrices governing state transitions in field-induced ketene isomerization are constructed using the method of Lagrangian descriptors. We obtain the stable and unstable manifolds of time-varying transition states as dynamic phase space objects governing configurational changes when the ketene molecule is subjected to an oscillating electric field. The dynamics of the isomerization reaction are modeled through classical trajectory studies on the Gezelter-Miller potential energy surface and an approximate dipole moment model which is coupled to a time-dependent electric field. We obtain a representation of the reaction geometry, over varying field strengths and oscillation frequencies, by partitioning an initial phase space into basins labeled according to which product state is reached at a given time. The borders between these basins are in agreement with those obtained using Lagrangian descriptors, even in regimes exhibiting chaotic dynamics. Major outcomes of this work are: validation and extension of a transition state theory framework built from Lagrangian descriptors, elaboration of the applicability for this theory to periodically- and aperiodically-driven molecular systems, and prediction of regimes in which isomerization of ketene and its derivatives may be controlled using an external field.
On the stability of shear-Alfven vortices
International Nuclear Information System (INIS)
Jovanovic, D.; Horton, W.
1993-08-01
Linear stability of shear-Alfven vortices is studied analytically using the Lyapunov method. Instability is demonstrated for vortices belonging to the drift mode, which is a generalization of the standard Hasegawa-Mima vortex to the case of large parallel phase velocities. In the case of the convective-cell mode, short perpendicular-wavelength perturbations are stable for a broad class of vortices. Eventually, instability of convective-cell vortices may occur on the perpendicular scale comparable with the vortex size, but it is followed by a simultaneous excitation of coherent structures with better localization than the original vortex
Relating Lagrangian and Hamiltonian Formalisms of LC Circuits
Clemente-Gallardo, Jesús; Scherpen, Jacquelien M.A.
2003-01-01
The Lagrangian formalism earlier defined for (switching) electrical circuits, is adapted to the Lagrangian formalism defined on Lie algebroids. This allows us to define regular Lagrangians and consequently, well-defined Hamiltonian descriptions of arbitrary LC networks. The relation with other
Mean-Lagrangian formalism and covariance of fluid turbulence.
Ariki, Taketo
2017-05-01
Mean-field-based Lagrangian framework is developed for the fluid turbulence theory, which enables physically objective discussions, especially, of the history effect. Mean flow serves as a purely geometrical object of Lie group theory, providing useful operations to measure the objective rate and history integration of the general tensor field. The proposed framework is applied, on the one hand, to one-point closure model, yielding an objective expression of the turbulence viscoelastic effect. Application to two-point closure, on the other hand, is also discussed, where natural extension of known Lagrangian correlation is discovered on the basis of an extended covariance group.
Safe semi-supervised learning based on weighted likelihood.
Kawakita, Masanori; Takeuchi, Jun'ichi
2014-05-01
We are interested in developing a safe semi-supervised learning that works in any situation. Semi-supervised learning postulates that n(') unlabeled data are available in addition to n labeled data. However, almost all of the previous semi-supervised methods require additional assumptions (not only unlabeled data) to make improvements on supervised learning. If such assumptions are not met, then the methods possibly perform worse than supervised learning. Sokolovska, Cappé, and Yvon (2008) proposed a semi-supervised method based on a weighted likelihood approach. They proved that this method asymptotically never performs worse than supervised learning (i.e., it is safe) without any assumption. Their method is attractive because it is easy to implement and is potentially general. Moreover, it is deeply related to a certain statistical paradox. However, the method of Sokolovska et al. (2008) assumes a very limited situation, i.e., classification, discrete covariates, n(')→∞ and a maximum likelihood estimator. In this paper, we extend their method by modifying the weight. We prove that our proposal is safe in a significantly wide range of situations as long as n≤n('). Further, we give a geometrical interpretation of the proof of safety through the relationship with the above-mentioned statistical paradox. Finally, we show that the above proposal is asymptotically safe even when n(')
International Nuclear Information System (INIS)
Lyra, Wladimir; Lin, Min-Kai
2013-01-01
The Atacama Large Millimeter Array has returned images of transitional disks in which large asymmetries are seen in the distribution of millimeter sized dust in the outer disk. The explanation in vogue borrows from the vortex literature and suggests that these asymmetries are the result of dust trapping in giant vortices, excited via Rossby wave instabilities at planetary gap edges. Due to the drag force, dust trapped in vortices will accumulate in the center and diffusion is needed to maintain a steady state over the lifetime of the disk. While previous work derived semi-analytical models of the process, in this paper we provide analytical steady-steady solutions. Exact solutions exist for certain vortex models. The solution is determined by the vortex rotation profile, the gas scale height, the vortex aspect ratio, and the ratio of dust diffusion to gas-dust friction. In principle, all of these quantities can be derived from observations, which would validate the model and also provide constrains on the strength of the turbulence inside the vortex core. Based on our solution, we derive quantities such as the gas-dust contrast, the trapped dust mass, and the dust contrast at the same orbital location. We apply our model to the recently imaged Oph IRS 48 system, finding values within the range of the observational uncertainties
Meaning of the BRS Lagrangian theory
International Nuclear Information System (INIS)
Cheng, H.; Tsai, E.
1989-01-01
A simplified treatment of the Becchi-Rouet-Stora (BRS) Lagrangian theory is presented. With this treatment we show that the BRS Lagrangian theory in general, and the Feynman-gauge field theory in particular, are effective theories, not the physical theory, and the Feynman gauge is not, strictly speaking, a gauge. The relationship between the quantum states in the BRS Lagrangian theory and those in the physical theory is explicitly given. We also show that one may obtain matrix elements of gauge-invariant operators in the physical theory by calculating corresponding ones in the BRS Lagrangian theory. The formulas which equate such matrix elements are called correspondence formulas. The correspondence formula for the S matrix enables us to equate the scattering amplitudes in the physical theory with those in the BRS Lagrangian theory, thus a proof of the unitary of the Feynman-gauge (as well as other covariant gauges) Feynman rules is rendered unnecessary. This treatment can be applied to various gauge field theories and the examples of the pure Yang-Mills theory and a gauge field theory with a Higgs field is explicitly worked out
Hamilton-Jacobi equations and brane associated Lagrangians
International Nuclear Information System (INIS)
Baker, L.M.; Fairlie, D.B.
2001-01-01
This article seeks to relate a recent proposal for the association of a covariant Field Theory with a string or brane Lagrangian to the Hamilton-Jacobi formalism for strings and branes. It turns out that since in this special case, the Hamiltonian depends only upon the momenta of the Jacobi fields and not the fields themselves, it is the same as a Lagrangian, subject to a constancy constraint. We find that the associated Lagrangians for strings or branes have a covariant description in terms of the square root of the same Lagrangian. If the Hamilton-Jacobi function is zero, rather than a constant, then it is in in one dimension lower, reminiscent of the 'holographic' idea. In the second part of the paper, we discuss properties of these Lagrangians, which lead to what we have called 'Universal Field Equations', characteristic of covariant equations of motion
Lagrangian formulation of the general relativistic Poynting-Robertson effect
De Falco, Vittorio; Battista, Emmanuele; Falanga, Maurizio
2018-04-01
We propose the Lagrangian formulation for describing the motion of a test particle in a general relativistic, stationary, and axially symmetric spacetime. The test particle is also affected by a radiation field, modeled as a coherent flux of photons traveling along the null geodesics of the background spacetime, including the general relativistic Poynting-Robertson effect. The innovative part of this work is to prove the existence of the potential linked to the dissipative action caused by the Poynting-Robertson effect in general relativity through the help of an integrating factor, depending on the energy of the system. Generally, such kinds of inverse problems involving dissipative effects might not admit a Lagrangian formulation; especially, in general relativity, there are no examples of such attempts in the literature so far. We reduce this general relativistic Lagrangian formulation to the classic case in the weak-field limit. This approach facilitates further studies in improving the treatment of the radiation field, and it contains, for example, some implications for a deeper comprehension of the gravitational waves.
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.
Lagrangians for plasmas in drift-fluid approximation
International Nuclear Information System (INIS)
Pfirsch, D.; Correa-Restrepo, D.
1996-10-01
For drift waves and related instabilities conservation laws can play a crucial role. In an ideal theory these conservation laws are guaranteed when a Lagrangian can be found from which the equations for the various quantities result by Hamilton's principle. Such a Lagrangian for plasmas in drift-fluid approximation was obtained by a heuristic method in a recent paper by Pfirsch and Correa-Restrepo. In the present paper the same Lagrangian is derived from the exact multi-fluid Lagrangian via an iterative approximation procedure which resembles the standard method usually applied to the equations of motion. That method, however, does not guarantee all the conservation laws to hold. (orig.)
Uncertainty quantification in Eulerian-Lagrangian models for particle-laden flows
Fountoulakis, Vasileios; Jacobs, Gustaaf; Udaykumar, Hs
2017-11-01
A common approach to ameliorate the computational burden in simulations of particle-laden flows is to use a point-particle based Eulerian-Lagrangian model, which traces individual particles in their Lagrangian frame and models particles as mathematical points. The particle motion is determined by Stokes drag law, which is empirically corrected for Reynolds number, Mach number and other parameters. The empirical corrections are subject to uncertainty. Treating them as random variables renders the coupled system of PDEs and ODEs stochastic. An approach to quantify the propagation of this parametric uncertainty to the particle solution variables is proposed. The approach is based on averaging of the governing equations and allows for estimation of the first moments of the quantities of interest. We demonstrate the feasibility of our proposed methodology of uncertainty quantification of particle-laden flows on one-dimensional linear and nonlinear Eulerian-Lagrangian systems. This research is supported by AFOSR under Grant FA9550-16-1-0008.
Dynamics of vortices in superconductors
International Nuclear Information System (INIS)
Weinan, E.
1992-01-01
We study the dynamics of vortices in type-II superconductors from the point of view of time-dependent Ginzburg-Landau equations. We outline a proof of existence, uniqueness and regularity of strong solutions for these equations. We then derive reduced systems of ODEs governing the motion of the vortices in the asymptotic limit of large Ginzburg-Landau parameter
MMS Observations of Vorticity Near Sites of Magnetic Reconnection
Paterson, W. R.; Giles, B. L.; Avanov, L. A.; Boardsen, S. A.; Dorelli, J.; Gershman, D. J.; Mackler, D. A.; Moore, T. E.; Pollock, C. J.; Schiff, C.; Shuster, J. R.; Viñas, A. F.; Russell, C. T.; Strangeway, R. J.; Burch, J. L.; Torbert, R. B.
2017-12-01
With highly capable plasma instruments on four spacecraft flown in tetrahedral formation, it is possible for MMS investigators to approximate spatial derivatives of the plasma parameters observed. Here, we examine vorticity of the electron and ion components of the plasma computed from the curl of velocity as measured by the Fast Plasma Investigation (FPI). Vorticity of magnetospheric plasma has not previously been studied on scales of tens-of-km to less than 10 km, which are the typical inter-spacecraft separations for MMS. Nor has it been explored on time scales of 30 ms for electrons and 150 ms for ions, which are the burst data rates for the FPI spectrometers. Review of observations from the magnetopause and magnetotail phases of the mission finds increases in vorticity associated with near encounters with the electron diffusion region, with nearby regions of measurable current, and with elevated electron and ion temperatures. These are suggestive of a possible role for turbulence in magnetic reconnection. In this presentation we provide an assessment of the quality of these measurements and discuss their potential significance.
A comparative study of semi-empirical interionic potentials for alkali halides - II
International Nuclear Information System (INIS)
Khwaja, F.A.; Naqvi, S.H.
1985-08-01
A comprehensive study of some semi-empirical interionic potentials is carried out through the calculation of the cohesive energy, relative stability and pressure induced solid-solid phase transformations in alkali halides. The theoretical values of these properties of the alkali halides are obtained using a new set of van der Waals coefficients and zero-point energy in the expression for interionic potential. From the comparison of the present calculations with some previous sophisticated ab-initio quantum-mechanical calculations and other semi-empirical approaches, it is concluded that the present calculations in the simplest central pairwise interaction description with the new values of the van der Waals coefficients and zero-point energy are in better agreement with the experimental data than the previous calculations. It is also concluded that in some cases the better choice of the interionic potential alone in the simplest semi-empirical picture of interaction gives an agreement of the theoretical predictions with the experimental data much superior to the ab-initio quantum mechanical approaches. (author)
Quantizing non-Lagrangian gauge theories: an augmentation method
International Nuclear Information System (INIS)
Lyakhovich, Simon L.; Sharapov, Alexei A.
2007-01-01
We discuss a recently proposed method of quantizing general non-Lagrangian gauge theories. The method can be implemented in many different ways, in particular, it can employ a conversion procedure that turns an original non-Lagrangian field theory in d dimensions into an equivalent Lagrangian, topological field theory in d+1 dimensions. The method involves, besides the classical equations of motion, one more geometric ingredient called the Lagrange anchor. Different Lagrange anchors result in different quantizations of one and the same classical theory. Given the classical equations of motion and Lagrange anchor as input data, a new procedure, called the augmentation, is proposed to quantize non-Lagrangian dynamics. Within the augmentation procedure, the originally non-Lagrangian theory is absorbed by a wider Lagrangian theory on the same space-time manifold. The augmented theory is not generally equivalent to the original one as it has more physical degrees of freedom than the original theory. However, the extra degrees of freedom are factorized out in a certain regular way both at classical and quantum levels. The general techniques are exemplified by quantizing two non-Lagrangian models of physical interest
Lagrangian and Hamiltonian dynamics
Mann, Peter
2018-01-01
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding.
Krause, Katharina; Klopper, Wim
2016-01-28
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding
International Nuclear Information System (INIS)
Krause, Katharina; Klopper, Wim
2016-01-01
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian
A Chiang-type lagrangian in CP^2
Cannas da Silva, Ana
2018-03-01
We analyse a monotone lagrangian in CP^2 that is hamiltonian isotopic to the standard lagrangian RP^2, yet exhibits a distinguishing behaviour under reduction by one of the toric circle actions, namely it intersects transversally the reduction level set and it projects one-to-one onto a great circle in CP^1. This lagrangian thus provides an example of embedded composition fitting work of Wehrheim-Woodward and Weinstein.
A new proposal for Lagrangian correlation coefficient
International Nuclear Information System (INIS)
Altinsoy, N.; Tugrul, A.B.
2002-01-01
The statistical description of dispersion in turbulent flow was first considered by Taylor (Proc. London Math. Soc. 20 (1921) 196) and the statistical properties of the field were determined by Lagrangian correlation coefficient R L (τ). Frenkiel (Adv. Appl. Mech. 3 (1953) 61) has proposed several simple forms for R L (τ). Some workers have investigated for a proper form of the Lagrangian correlation coefficient. In this work, a new proposal for the Lagrangian correlation coefficient is proposed and discussed. It can be written in general form with the one of the Frenkiel's (Adv. Appl. Mech. 3 (1953) 61) Lagrangian correlation coefficient. There is very satisfactory agreement between the new correlation and the experiment
Propagation of the nonlinear plastic stress waves in semi-infinite bar
Directory of Open Access Journals (Sweden)
Edward Włodarczyk
2017-03-01
Full Text Available This paper presents the propagation longitudinal nonlinear plastic stress in thin semi-infinite rod or in wire. The rod is characterized by a nonlinear strain hardening model within the scope a plastic strain. The modulus of strain hardening is a decreasing function of the strain. The frontal bar end is suddenly launching to the velocity V, and subsequently moves with this one. General solution of this boundary value problem of the Lagrangian coordinate (material description and of the Eulerian one (spatial description has been presented. There has been carried out the physical interpretation of the obtained results by means of Lagrangian and Eulerian methods. The results of this paper may be utilized in scientific researches and in engineering practice.
Nuclear intrinsic vorticity and its coupling to global rotations
International Nuclear Information System (INIS)
Mikhailov, I.N.; Quentin, P.; Samsoen, D.
1997-01-01
Important collective modes which are generally neglected within current descriptions of nuclear excitations in terms of fluid dynamics, are studied here. The intrinsic vortical modes are defined in a general way from which a specific mode, both simple and versatile enough, is particularly discussed. In this paper the main emphasis is made on the coupling of the chosen intrinsic mode to the rotation of the nuclear principal axes frame with respect to the laboratory system. A semi-quantal description of such excitations is proposed which is a generalization of the so-called routhian approach of global rotations. The results of a semiclassical treatment of the corresponding variational problem are presented. A simple mean field approach where the one-body potential is mocked up by a harmonic oscillator is discussed in a somewhat detailed fashion. The broad range of validity of a quadratic approximation for the collective energy in terms of the relevant angular velocities, is hinted from the previous simple model approach. Some general consequences of the latter are then drawn which have bearing on some possible fingerprints for the existence of such excitations, as the staggering phenomenon observed in gamma transition energies in some superdeformed states and the occurrence of identical rotational bands in neighbouring nuclei. (orig.)
An efficient and general numerical method to compute steady uniform vortices
Luzzatto-Fegiz, Paolo; Williamson, Charles H. K.
2011-07-01
Steady uniform vortices are widely used to represent high Reynolds number flows, yet their efficient computation still presents some challenges. Existing Newton iteration methods become inefficient as the vortices develop fine-scale features; in addition, these methods cannot, in general, find solutions with specified Casimir invariants. On the other hand, available relaxation approaches are computationally inexpensive, but can fail to converge to a solution. In this paper, we overcome these limitations by introducing a new discretization, based on an inverse-velocity map, which radically increases the efficiency of Newton iteration methods. In addition, we introduce a procedure to prescribe Casimirs and remove the degeneracies in the steady vorticity equation, thus ensuring convergence for general vortex configurations. We illustrate our methodology by considering several unbounded flows involving one or two vortices. Our method enables the computation, for the first time, of steady vortices that do not exhibit any geometric symmetry. In addition, we discover that, as the limiting vortex state for each flow is approached, each family of solutions traces a clockwise spiral in a bifurcation plot consisting of a velocity-impulse diagram. By the recently introduced "IVI diagram" stability approach [Phys. Rev. Lett. 104 (2010) 044504], each turn of this spiral is associated with a loss of stability for the steady flows. Such spiral structure is suggested to be a universal feature of steady, uniform-vorticity flows.
Lagrangian ocean analysis : Fundamentals and practices
van Sebille, Erik; Deleersnijder, E.L.C.; Heemink, A.W.; Griffies, Stepehn M.; Abernathey, Ryan; Adams, Thomas P.; Berloff, Pavel; Biastoch, Arne; Blanke, Bruno; Chassignet, Eric P.; Authors, More
2018-01-01
Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several
Lagrangian ocean analysis : Fundamentals and practices
van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan; Adams, Thomas P.; Berloff, Pavel; Biastoch, Arne; Blanke, Bruno; Chassignet, Eric P.; Cheng, Yu; Cotter, Colin J.; Deleersnijder, Eric; Döös, Kristofer; Drake, Henri F.; Drijfhout, Sybren; Gary, Stefan F.; Heemink, Arnold W.; Kjellsson, Joakim; Koszalka, Inga Monika; Lange, Michael; Lique, Camille; MacGilchrist, Graeme A.; Marsh, Robert; Mayorga Adame, C. Gabriela; McAdam, Ronan; Nencioli, Francesco; Paris, Claire B.; Piggott, Matthew D.; Polton, Jeff A.; Rühs, Siren; Shah, Syed H.A.M.; Thomas, Matthew D.; Wang, Jinbo; Wolfram, Phillip J.; Zanna, Laure; Zika, Jan D.
2018-01-01
Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades,
Lagrangian properties of particles in turbulence
Toschi, F.; Bodenschatz, E.
2009-01-01
The Lagrangian description of turbulence is characterized by a unique conceptual simplicity and by an immediate connection with the physics of dispersion and mixing. In this article, we report some motivations behind the Lagrangian description of turbulence and focus on the statistical properties of
Theory of Concentrated Vortices
DEFF Research Database (Denmark)
Alekseenko, Sergey; Kuibin, Pavel; Okulov, Valery
This book presents comprehensive and authoritative coverage of the wide field of concentrated vortices observed in nature and technique. The methods for research of their kinematics and dynamics are considered. Special attention is paid to the flows with helical symmetry. The authors have describ...... models of vortex structures used for interpretation of experimental data which serve as a ground for development of theoretical and numerical approaches to vortex investigation. Achievements in the fields of stability analysis, waves on vortices and vortex breakdown are also presented....
Patra, Sarbani; Keshavamurthy, Srihari
2018-02-14
It has been known for sometime now that isomerization reactions, classically, are mediated by phase space structures called reactive islands (RI). RIs provide one possible route to correct for the nonstatistical effects in the reaction dynamics. In this work, we map out the reactive islands for the two dimensional Müller-Brown model potential and show that the reactive islands are intimately linked to the issue of rare event sampling. In particular, we establish the sensitivity of the so called committor probabilities, useful quantities in the transition path sampling technique, to the hierarchical RI structures. Mapping out the RI structure for high dimensional systems, however, is a challenging task. Here, we show that the technique of Lagrangian descriptors is able to effectively identify the RI hierarchy in the model system. Based on our results, we suggest that the Lagrangian descriptors can be useful for detecting RIs in high dimensional systems.
Chiral vortical effect from the compactified D4-branes with smeared D0-brane charge
Energy Technology Data Exchange (ETDEWEB)
Wu, Chao; Chen, Yidian [Institute of High Energy Physics, Chinese Academy of Sciences,Beijing 100049 (China); Huang, Mei [Institute of High Energy Physics, Chinese Academy of Sciences,Beijing 100049 (China); University of Chinese Academy of Sciences,Beijing 100049 (China); Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences,Beijing 100049 (China)
2017-03-15
By using the boundary derivative expansion formalism of fluid/gravity correspondence, we study the chiral vortical effect from the compactified D4-branes with smeared D0-brane charge. This background corresponds to a strongly coupled, nonconformal relativistic fluid with a conserved vector current. The presence of the chiral vortical effect is induced by the addition of a Chern-Simons term in the bulk action. Except that the non-dissipative anomalous viscous coefficient and the sound speed rely only on the chemical potential, most of the other thermal and hydrodynamical quantities of the first order depend both on the temperature and the chemical potential. According to our result, the way that the chiral vortical effect coefficient depends on the chemical potential seems irrelevant with whether the relativistic fluid is conformal or not. Stability analysis shows that this anomalous relativistic fluid is stable and the doping of the smeared D0-brane charge will slow down the sound speed.
Kinematical Compatibility Conditions for Vorticity Across Shock Waves
Baty, Roy
2015-11-01
This work develops the general kinematical compatibility conditions for vorticity across arbitrary shock waves in compressible, inviscid fluids. The vorticity compatibility conditions are derived from the curl of the momentum equation using singular distributions defined on two-dimensional shock wave surfaces embedded in three-dimensional flow fields. The singular distributions are represented as generalized differential operators concentrated on moving shock wave surfaces. The derivation of the compatibility conditions for vorticity requires the application of second-order generalized derivatives and elementary tensor algebra. The well-known vorticity jump conditions across a shock wave are then shown to follow from the general kinematical compatibility conditions for vorticity by expressing the flow field velocity in vectorial components normal and tangential to a shock surface.
Direct observation of rectified motion of vortices by Lorentz microscopy
Indian Academy of Sciences (India)
one-directional selective motion of field-gradient-driven vortices along fabricated channels. This results from ... was irradiated around etched holes to fabricate the asymmetric potential [19]. Fig- ures 1a .... The dotted line is a guide to the eye.
The generation of two-dimensional vortices by transverse oscillation of a soap film
International Nuclear Information System (INIS)
Afenchenko, V.O.; Ezersky, A.B.; Kiyashko, S.V.; Rabinovich, M.I.; Weidman, P.D.
1998-01-01
An experimental investigation of the dynamics of horizontal soap films stretched over circular or square boundaries undergoing periodic transverse oscillations at frequencies in the range 20 - 200 Hz is reported. Concomitant with modes of transverse flexural oscillations, it was observed that two-dimensional vortices in the plane of the film are excited. The vortices may be either (i) large, scaling with the size of the cavity or (ii) small, localized at a wavelength or half-wavelength of the membrane modes. In the experiments a stable generation of one, two, hor-ellipsis, ten pairs of counter-rotating vortices were observed in finite regions of amplitude-frequency parameter space. The circulation strength of vortices in a given vortex pattern increases with increasing external forcing and with decreasing soap film thickness. A theoretical model based on the wave-boundary interaction of excited Marangoni waves reveals a vorticity generation mechanism active in vibrating soap films. This model shows that vorticity is generated throughout the entire liquid volume by viscous diffusion, and qualitatively reproduces many steady vortex patterns observed in the experiment. However, the model cannot explain the existence of the sometimes intense vortices observed far from the film boundary that do not appear to be generated by diffusive processes. copyright 1998 American Institute of Physics
International Nuclear Information System (INIS)
Des Cloizeaux, J.
1976-01-01
The Lagrangian theory of a field with n components can be generalized for values of n which are not integers and in particular for n=0. This extension is made by introducing ordered Green's functions. It is shown how the zero components Lagrangian theory can be used to describe the behaviour of an isolated polymer or of a solution of polymers with large molecular masses. It is remarked that by analytic continuation with respect to the coupling constant, it should be possible to study the properties of electrons in a random potential and perhaps the nature of the mobility edges [fr
Quantized vortices in superfluids and superconductors
International Nuclear Information System (INIS)
Thoulessi, D.J.; Wexler, C.; Ping Ao, Ping; Niu, Qian; Geller, M.R.
1998-01-01
We give a general review of recent developments in the theory of vortices in superfluids and superconductors, discussing why the dynamics of vortices is important, and why some key results are still controversial. We discuss work that we have done on the dynamics of quantized vortices in a superfluid. Despite the fact that this problem has been recognized as important for forty years, there is still a lot of controversy about the forces on and masses of quantized vortices. We think that one can get unambiguous answers by considering a broken symmetry state that consists of one vortex in an infinite ideal system. We argue for a Magnus force that is proportional to the superfluid density, and we find that the effective mass density of a vortex in a neutral superfluid is divergent at low frequencies. We have generalized some of the results for a neutral superfluid to a charged system. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
The Theory of Vortical Gravitational Fields
Directory of Open Access Journals (Sweden)
Rabounski D.
2007-04-01
Full Text Available This paper treats of vortical gravitational fields, a tensor of which is the rotor of the general covariant gravitational inertial force. The field equations for a vortical gravitational field (the Lorentz condition, the Maxwell-like equations, and the continuity equation are deduced in an analogous fashion to electrodynamics. From the equations it is concluded that the main kind of vortical gravitational fields is “electric”, determined by the non-stationarity of the acting gravitational inertial force. Such a field is a medium for traveling waves of the force (they are different to the weak deformation waves of the space metric considered in the theory of gravitational waves. Standing waves of the gravitational inertial force and their medium, a vortical gravitational field of the “magnetic” kind, are exotic, since a non-stationary rotation of a space body (the source of such a field is a very rare phenomenon in the Universe.
Lagrangian Particle Tracking Simulation for Warm-Rain Processes in Quasi-One-Dimensional Domain
Kunishima, Y.; Onishi, R.
2017-12-01
Conventional cloud simulations are based on the Euler method and compute each microphysics process in a stochastic way assuming infinite numbers of particles within each numerical grid. They therefore cannot provide the Lagrangian statistics of individual particles in cloud microphysics (i.e., aerosol particles, cloud particles, and rain drops) nor discuss the statistical fluctuations due to finite number of particles. We here simulate the entire precipitation process of warm-rain, with tracking individual particles. We use the Lagrangian Cloud Simulator (LCS), which is based on the Euler-Lagrangian framework. In that framework, flow motion and scalar transportation are computed with the Euler method, and particle motion with the Lagrangian one. The LCS tracks particle motions and collision events individually with considering the hydrodynamic interaction between approaching particles with a superposition method, that is, it can directly represent the collisional growth of cloud particles. It is essential for trustworthy collision detection to take account of the hydrodynamic interaction. In this study, we newly developed a stochastic model based on the Twomey cloud condensation nuclei (CCN) activation for the Lagrangian tracking simulation and integrated it into the LCS. Coupling with the Euler computation for water vapour and temperature fields, the initiation and condensational growth of water droplets were computed in the Lagrangian way. We applied the integrated LCS for a kinematic simulation of warm-rain processes in a vertically-elongated domain of, at largest, 0.03×0.03×3000 (m3) with horizontal periodicity. Aerosol particles with a realistic number density, 5×107 (m3), were evenly distributed over the domain at the initial state. Prescribed updraft at the early stage initiated development of a precipitating cloud. We have confirmed that the obtained bulk statistics fairly agree with those from a conventional spectral-bin scheme for a vertical column
Cheng, Huai-yu; Long, Xin-ping; Ji, Bin; Liu, Qi; Bai, Xiao-rui
2018-02-01
In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model (FBDCM), a turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures (LCSs). Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet, the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage III, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.
On generating counter-rotating streamwise vortices
Winoto, S H
2015-09-23
Counter-rotating streamwise vortices are known to enhance the heat transfer rate from a surface and also to improve the aerodynamic performance of an aerofoil. In this paper, some methods to generate such counter-rotating vortices using different methods or physical conditions will be briefly considered and discussed.
On generating counter-rotating streamwise vortices
Winoto, S H; Mitsudharmadi, Hatsari; Budiman, A C; Hasheminejad, S M; Nadesan, T; Tandiono; Low, H T; Lee, T S
2015-01-01
Counter-rotating streamwise vortices are known to enhance the heat transfer rate from a surface and also to improve the aerodynamic performance of an aerofoil. In this paper, some methods to generate such counter-rotating vortices using different methods or physical conditions will be briefly considered and discussed.
Numerical and Experimental Study on Negative Buoyance Induced Vortices in N-Butane Jet Flames
Xiong, Yuan
2015-07-26
Near nozzle flow field in flickering n-butane diffusion jet flames was investigated with a special focus on transient flow patterns of negative buoyance induced vortices. The flow structures were obtained through Mie scattering imaging with seed particles in a fuel stream using continuous-wave (CW) Argon-ion laser. Velocity fields were also quantified with particle mage velocimetry (PIV) system having kHz repetition rate. The results showed that the dynamic motion of negative buoyance induced vortices near the nozzle exit was coupled strongly with a flame flickering instability. Typically during the flame flickering, the negative buoyant vortices oscillated at the flickering frequency. The vortices were distorted by the flickering motion and exhibited complicated transient vortical patterns, such as tilting and stretching. Numerical simulations were also implemented based on an open source C++ package, LaminarSMOKE, for further validations.
Effects of wing locations on wing rock induced by forebody vortices
Directory of Open Access Journals (Sweden)
Ma Baofeng
2016-10-01
Full Text Available Previous studies have shown that asymmetric vortex wakes over slender bodies exhibit a multi-vortex structure with an alternate arrangement along a body axis at high angle of attack. In this investigation, the effects of wing locations along a body axis on wing rock induced by forebody vortices was studied experimentally at a subcritical Reynolds number based on a body diameter. An artificial perturbation was added onto the nose tip to fix the orientations of forebody vortices. Particle image velocimetry was used to identify flow patterns of forebody vortices in static situations, and time histories of wing rock were obtained using a free-to-roll rig. The results show that the wing locations can affect significantly the motion patterns of wing rock owing to the variation of multi-vortex patterns of forebody vortices. As the wing locations make the forebody vortices a two-vortex pattern, the wing body exhibits regularly divergence and fixed-point motion with azimuthal variations of the tip perturbation. If a three-vortex pattern exists over the wing, however, the wing-rock patterns depend on the impact of the highest vortex and newborn vortex. As the three vortices together influence the wing flow, wing-rock patterns exhibit regularly fixed-points and limit-cycled oscillations. With the wing moving backwards, the newborn vortex becomes stronger, and wing-rock patterns become fixed-points, chaotic oscillations, and limit-cycled oscillations. With further backward movement of wings, the vortices are far away from the upper surface of wings, and the motions exhibit divergence, limit-cycled oscillations and fixed-points. For the rearmost location of the wing, the wing body exhibits stochastic oscillations and fixed-points.
Electrohydrodynamic (EHD) vortices in helical turbulence
International Nuclear Information System (INIS)
Kikuchi, H.
1996-01-01
The study of large-scale coherent hydrodynamic (HD) vortex generation has been extended to electrified charged dusty vortices to be termed as electrohydrodynamic (EHD) vortices, incorporating helical turbulence in electric and magnetic fields into that in fluid velocity, which are all created by an external DC electric field on the background. A new equation of EHD vortices is introduced on the basis of a set of EHD or electromagnetohydrodynamic (EMHD) equations, including equations of state and a full set of Maxwell's equations by using functional techniques for estimating equations for an ensemble average, turbulent background, and additional random field. In fact, EHD vortices for a charged dusty fluid can be more explosive with larger instabilities than HD vortices. In addition, it is inferred that an external DC electric field could provide the origin of additional self-organization to a coalescence of fluid vortex and electric field lines as a manifestation of a new frozen-in field concept for electric fields when the electric Reynolds number is sufficiently high. This is discussed on the basis of a set of general transport equations for fluid vorticity, magnetic and electric fields that are rederived concisely. In particular, a novel concept of electric field line merging-reconnection is developed in close relation to fluid vortex line merging, indicating a coalescence of fluid vortex breakdown or merging point and electric field line reconnection point, X-type or O-type with possible application to tornadic thunderstorms. In fact, a thundercloud charge distribution so as to provide a coalescence of fluid vortex and electric field lines is quite possible without theoretical inconsistency, and is thought most likely to occur from observations available so far. (orig.)
A Family of Vortices to Study Axisymmetric Vortex Breakdown and Reconnection
Young, Larry A.
2007-01-01
A new analytic model describing a family of vortices has been developed to study some of the axisymmetric vortex breakdown and reconnection fluid dynamic processes underlying body-vortex interactions that are frequently manifested in rotorcraft and propeller-driven fixed-wing aircraft wakes. The family of vortices incorporates a wide range of prescribed initial vorticity distributions -- including single or dual-core vorticity distributions. The result is analytical solutions for the vorticity and velocities for each member of the family of vortices. This model is of sufficient generality to further illustrate the dependence of vortex reconnection and breakdown on initial vorticity distribution as was suggested by earlier analytical work. This family of vortices, though laminar in nature, is anticipated to provide valuable insight into the vortical evolution of large-scale rotor and propeller wakes.
Perturbative QCD Lagrangian at large distances and stochastic dimensionality reduction. Pt. 2
International Nuclear Information System (INIS)
Shintani, M.
1986-11-01
Using the method of stochastic dimensional reduction, we derive a four-dimensional quantum effective Lagrangian for the classical Yang-Mills system coupled to the Gaussian white noise. It is found that the Lagrangian coincides with the perturbative QCD at large distances constructed in our previous paper. That formalism is based on the local covariant operator formalism which maintains the unitarity of the S-matrix. Furthermore, we show the non-perturbative equivalence between super-Lorentz invariant sectors of the effective Lagrangian and two dimensional QCD coupled to the adjoint pseudo-scalars. This implies that stochastic dimensionality reduction by two is approximately operative in QCD at large distances. (orig.)
Lane, John E.; Kasparis, Takis; Jones, W. Linwood; Metzger, Philip T.
2009-01-01
Methodologies to improve disdrometer processing, loosely based on mathematical techniques common to the field of particle flow and fluid mechanics, are examined and tested. The inclusion of advection and vertical wind field estimates appear to produce significantly improved results in a Lagrangian hydrometeor trajectory model, in spite of very strict assumptions of noninteracting hydrometeors, constant vertical air velocity, and time independent advection during the scan time interval. Wind field data can be extracted from each radar elevation scan by plotting and analyzing reflectivity contours over the disdrometer site and by collecting the radar radial velocity data to obtain estimates of advection. Specific regions of disdrometer spectra (drop size versus time) often exhibit strong gravitational sorting signatures, from which estimates of vertical velocity can be extracted. These independent wind field estimates become inputs and initial conditions to the Lagrangian trajectory simulation of falling hydrometeors.
Controlled Manipulation of Individual Vortices in a Superconductor
Energy Technology Data Exchange (ETDEWEB)
Straver, E.W.J.
2010-04-05
We report controlled local manipulation of single vortices by low temperature magnetic force microscope (MFM) in a thin film of superconducting Nb. We are able to position the vortices in arbitrary configurations and to measure the distribution of local depinning forces. This technique opens up new possibilities for the characterization and use of vortices in superconductors.
On the motion of multiple helical vortices
Wood, D. H.; Boersma, J.
2001-11-01
The analysis of the self-induced velocity of a single helical vortex (Boersma & Wood 1999) is extended to include equally spaced multiple vortices. This arrangement approximates the tip vortices in the far wake of multi-bladed wind turbines, propellers, or rotors in ascending, descending, or hovering flight. The problem is reduced to finding, from the Biot Savart law, the additional velocity of a helix due to an identical helix displaced azimuthally. The resulting Biot Savart integral is further reduced to a Mellin Barnes integral representation which allows the asymptotic expansions to be determined for small and for large pitch. The Biot Savart integral is also evaluated numerically for a total of two, three and four vortices over a range of pitch values. The previous finding that the self-induced velocity at small pitch is dominated by a term inversely proportional to the pitch carries over to multiple vortices. It is shown that a far wake dominated by helical tip vortices is consistent with the one-dimensional representation that leads to the Betz limit on the power output of wind turbines. The small-pitch approximation then allows the determination of the blade&s bound vorticity for optimum power extraction. The present analysis is shown to give reasonable estimates for the vortex circulation in experiments using a single hovering rotor and a four-bladed propeller.
Tunneling decay of self-gravitating vortices
Directory of Open Access Journals (Sweden)
Dupuis Éric
2018-01-01
Full Text Available We investigate tunneling decay of false vortices in the presence of gravity, in which vortices are trapped in the false vacuum of a theory of scalar electrodynamics in three dimensions. The core of the vortex contains magnetic flux in the true vacuum, while outside the vortex is the appropriate topologically nontrivial false vacuum. We numerically obtain vortex solutions which are classically stable; however, they could decay via tunneling. To show this phenomenon, we construct the proper junction conditions in curved spacetime. We find that the tunneling exponent for the vortices is half that for Coleman-de Luccia bubbles and discuss possible future applications.
Energy Technology Data Exchange (ETDEWEB)
Gaber, Tobias
2007-07-01
In this thesis static and dynamic properties of fractional vortices in long Josephson junctions are investigated. Fractional vortices are circulating supercurrents similar to the well-known Josephson fluxons. Yet, they show the distinguishing property of carrying only a fraction of the magnetic flux quantum. Fractional vortices are interesting non-linear objects. They spontaneously appear and are pinned at the phase discontinuity points of so called 0-{kappa} junctions but can be bend or flipped by external forces like bias currents or magnetic fields. 0-{kappa} junctions and fractional vortices are generalizations of the well-known 0-{pi} junctions and semifluxons, where not only phase jumps of pi but arbitrary values denoted by kappa are considered. By using so-called artificial 0-{kappa} junctions that are based on standard Nb-AlO{sub x}-Nb technology the classical dynamics of fractional vortices has been investigated experimentally for the very first time. Here, half-integer zero field steps could be observed. These voltage steps on the junction's current-voltage characteristics correspond to the periodic flipping/hopping of fractional vortices. In addition, the oscillatory eigenmodes of fractional vortices were investigated. In contrast to fluxons fractional vortices have an oscillatory eigenmode with a frequency within the plasma gap. Using resonance spectroscopy the dependence of the eigenmode frequency on the flux carried by the vortex and an applied bias current was determined. (orig.)
A functional LMO invariant for Lagrangian cobordisms
DEFF Research Database (Denmark)
Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël
2008-01-01
Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le–Murakami–Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category...... of Jacobi diagrams. We prove some properties of this functorial LMO invariant, including its universality among rational finite-type invariants of Lagrangian cobordisms. Finally, we apply the LMO functor to the study of homology cylinders from the point of view of their finite-type invariants....
Extended Lagrangian formulation of charge-constrained tight-binding molecular dynamics.
Cawkwell, M J; Coe, J D; Yadav, S K; Liu, X-Y; Niklasson, A M N
2015-06-09
The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [Niklasson, Phys. Rev. Lett., 2008, 100, 123004] has been applied to a tight-binding model under the constraint of local charge neutrality to yield microcanonical trajectories with both precise, long-term energy conservation and a reduced number of self-consistent field optimizations at each time step. The extended Lagrangian molecular dynamics formalism restores time reversal symmetry in the propagation of the electronic degrees of freedom, and it enables the efficient and accurate self-consistent optimization of the chemical potential and atomwise potential energy shifts in the on-site elements of the tight-binding Hamiltonian that are required when enforcing local charge neutrality. These capabilities are illustrated with microcanonical molecular dynamics simulations of a small metallic cluster using an sd-valent tight-binding model for titanium. The effects of weak dissipation on the propagation of the auxiliary degrees of freedom for the chemical potential and on-site Hamiltonian matrix elements that is used to counteract the accumulation of numerical noise during trajectories was also investigated.
International Nuclear Information System (INIS)
Giedt, Joel
2003-01-01
We compute the component field four-dimensional N = 1 supergravity Lagrangian that is obtained from a superfield Lagrangian in the U(1) K formalism with a linear dilaton multiplet. All fermionic terms are presented. In a variety of important ways, our results generalize those that have been reported previously, and are flexible enough to accommodate many situations of phenomenological interest in string-inspired effective supergravity, especially models based on orbifold compactifications of the weakly coupled heterotic string. We provide for an effective theory of hidden gaugino and matter condensation. We include supersymmetric Green-Schwarz counterterms associated with the cancellation of U(1) and modular duality anomalies; the modular duality counterterm is of a rather general form. Our assumed form for the dilaton Kaehler potential is quite general and can accommodate Kaehler stabilization methods. We note possible applications of our results. We also discuss the usefulness of the linear dilaton formulation as a complement to the chiral dilaton approach
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.
Topological vortices in gauge models of graphene
Zhang, Xin-Hui; Li, Xueqin; Hao, Jin-Bo
2018-06-01
Graphene-like structure possessing the topological vortices and knots, and the magnetic flux of the vortices configuration quantized, are proposed in this paper. The topological charges of the vortices are characterized by Hopf indices and Brower degrees. The Abelian background field action (BF action) is a topological invariant for the knot family, which is just the total sum of all the self-linking numbers and all the linking numbers. Flux quantization opens the possibility of having Aharonov-Bohm-type effects in graphene without external electromagnetic field.
Streamwise vortices destabilize swimming bluegill sunfish (Lepomis macrochirus).
Maia, Anabela; Sheltzer, Alex P; Tytell, Eric D
2015-03-01
In their natural environment, fish must swim stably through unsteady flows and vortices, including vertical vortices, typically shed by posts in a flow, horizontal cross-flow vortices, often produced by a step or a waterfall in a stream, and streamwise vortices, where the axis of rotation is aligned with the direction of the flow. Streamwise vortices are commonly shed by bluff bodies in streams and by ships' propellers and axial turbines, but we know little about their effects on fish. Here, we describe how bluegill sunfish use more energy and are destabilized more often in flow with strong streamwise vorticity. The vortices were created inside a sealed flow tank by an array of four turbines with similar diameter to the experimental fish. We measured oxygen consumption for seven sunfish swimming at 1.5 body lengths (BL) s(-1) with the turbines rotating at 2 Hz and with the turbines off (control). Simultaneously, we filmed the fish ventrally and recorded the fraction of time spent maneuvering side-to-side and accelerating forward. Separately, we also recorded lateral and ventral video for a combination of swimming speeds (0.5, 1.5 and 2.5 BL s(-1)) and turbine speeds (0, 1, 2 and 3 Hz), immediately after turning the turbines on and 10 min later to test for accommodation. Bluegill sunfish are negatively affected by streamwise vorticity. Spills (loss of heading), maneuvers and accelerations were more frequent when the turbines were on than in the control treatment. These unsteady behaviors, particularly acceleration, correlated with an increase in oxygen consumption in the vortex flow. Bluegill sunfish are generally fast to recover from roll perturbations and do so by moving their pectoral fins. The frequency of spills decreased after the turbines had run for 10 min, but was still markedly higher than in the control, showing that fish partially adapt to streamwise vorticity, but not completely. Coping with streamwise vorticity may be an important energetic
Probing dynamics and pinning of single vortices in superconductors at nanometer scales
Embon, L.; Anahory, Y.; Suhov, A.; Halbertal, D.; Cuppens, J.; Yakovenko, A.; Uri, A.; Myasoedov, Y.; Rappaport, M. L.; Huber, M. E.; Gurevich, A.; Zeldov, E.
2015-01-01
The dynamics of quantized magnetic vortices and their pinning by materials defects determine electromagnetic properties of superconductors, particularly their ability to carry non-dissipative currents. Despite recent advances in the understanding of the complex physics of vortex matter, the behavior of vortices driven by current through a multi-scale potential of the actual materials defects is still not well understood, mostly due to the scarcity of appropriate experimental tools capable of tracing vortex trajectories on nanometer scales. Using a novel scanning superconducting quantum interference microscope we report here an investigation of controlled dynamics of vortices in lead films with sub-Angstrom spatial resolution and unprecedented sensitivity. We measured, for the first time, the fundamental dependence of the elementary pinning force of multiple defects on the vortex displacement, revealing a far more complex behavior than has previously been recognized, including striking spring softening and broken-spring depinning, as well as spontaneous hysteretic switching between cellular vortex trajectories. Our results indicate the importance of thermal fluctuations even at 4.2 K and of the vital role of ripples in the pinning potential, giving new insights into the mechanisms of magnetic relaxation and electromagnetic response of superconductors.
Jovian Vortices and Barges: HST observations 1994-1998
Morales, R.; Sanchez-Lavega, A.; Lecacheux, J.; Colas, F.; Miyazaki, I.
2000-10-01
We have used the HST-WFPC2 archived images of Jupiter in the period 1994-1998 to study the zonal and meridional distributions, long-term motions, lifetimes, interactions and other properties of the vortices larger than 2 degrees. The latitude range covered spans from +75 to -75 degrees. High-resolution images obtained with the 890nm, 410nm and 953nm wavelength filters allowed us to make a morphological classification based on their appearance in each filter. The vortices are anticyclones, and their long-term motions have been completed with ground-based images and are compared to the mean Jovian zonal wind profile. Significant differences are found between the vortex velocities and the mean zonal winds. Some vortices exhibited important drift changes in short period times. We analyze a possible correlation between their size and zonal wind velocity. On the other hand, the "barges" lie in the cyclone domains of the wind-profile and have been identified in several latitudes. Their latitudinal size is similar in all of them (typically 1.6 degrees) but their longitudinal size ranges from 1 to 32 degrees. We discuss the temporal evolution of some of these cyclonic regions. The Spanish team was supported by Gobierno Vasco PI 034/97. The French team was supported by the "Programme National de Planetologie." RM acknowledges a fellowship from Universidad Pais Vasco.
Experimental Observations of Ion Phase-Space Vortices
DEFF Research Database (Denmark)
Pécseli, Hans; Armstrong, R. J.; Trulsen, J.
1981-01-01
Experimental observations of ion phase-space vortices are reported. The ion phase-space vortices form in the region of heated ions behind electrostatic ion acoustic shocks. The results are in qualitative agreement with numerical and analytic studies....
On the Eulerian-Lagrangian Transform in the Statistical Theory of Turbulence
DEFF Research Database (Denmark)
Wandel, C. F:; Kofoed-Hansen, O.
1962-01-01
"Fundamental Problems in Turbulence" Conference Paper (see Abstr. 1962A024007). Two important types of probing of a turbulent velocity field droarr/dtoarr = voarr (voarr constant) and the Lagrangian probing defined by droarr/dtoarr = roarr (roarr t). Explicit expressions are derived for the trans......"Fundamental Problems in Turbulence" Conference Paper (see Abstr. 1962A024007). Two important types of probing of a turbulent velocity field droarr/dtoarr = voarr (voarr constant) and the Lagrangian probing defined by droarr/dtoarr = roarr (roarr t). Explicit expressions are derived...... for the transformation of autocorrelations and power spectra obtained by Eulerian and Lagrangian probing in the case of fully developed isotropic and homogeneous turbulence. The derivations are based on a statistical representation of the turbulent velocity field using the results of the equilibrium theory of turbulence....... The Taylor (1921) hypothesis is verified in the limit of high probing velocities. The Hay-Pasquill (1960) conjecture relating the Lagrangian and Eulerian power spectra results as an approximation to the transformation equations. Application of the results to the theory of turbulent diffusion is indicated....
International Nuclear Information System (INIS)
Theodorakis, S.
1988-01-01
This paper presents a phenomenological Lagrangian that fully describes the dynamics of any homogeneous phase of superfluid 3 He, unitary or not, omitting relaxation. This Lagrangian is built by using the concept of a local SO(3) x SO(3) x U(1) symmetry. The spin and angular momentum play the role of gauge fields. We derive the Leggett equations for spin and orbital dynamics from the equations of motion, for both the A and the B phase. This Lagrangian not only enables us to describe both the spin and orbital dynamics of superfluid 3 He in a unified fashion, but can also be used for finding the dynamics in any experimental situation. Furthermore, it can describe the dynamics of the magnitude, as well as of the orientation of the order parameter, and thus it can be used to describe the dynamics of the A-B phase transition
Kieokaew, Rungployphan; Foullon, Claire; Lavraud, Benoit
2018-01-01
Four-spacecraft missions are probing the Earth's magnetospheric environment with high potential for revealing spatial and temporal scales of a variety of in situ phenomena. The techniques allowed by these four spacecraft include the calculation of vorticity and the magnetic curvature analysis (MCA), both of which have been used in the study of various plasma structures. Motivated by curved magnetic field and vortical structures induced by Kelvin- Helmholtz (KH) waves, we investigate the robustness of the MCA and vorticity techniques when increasing (regular) tetrahedron sizes, to interpret real data. Here for the first time, we test both techniques on a 2.5-D MHD simulation of KH waves at the magnetopause. We investigate, in particular, the curvature and flow vorticity across KH vortices and produce time series for static spacecraft in the boundary layers. The combined results of magnetic curvature and vorticity further help us to understand the development of KH waves. In particular, first, in the trailing edge, the magnetic curvature across the magnetopause points in opposite directions, in the wave propagation direction on the magnetosheath side and against it on the magnetospheric side. Second, the existence of a "turnover layer" in the magnetospheric side, defined by negative vorticity for the duskside magnetopause, which persists in the saturation phase, is reminiscent of roll-up history. We found significant variations in the MCA measures depending on the size of the tetrahedron. This study lends support for cross-scale observations to better understand the nature of curvature and its role in plasma phenomena.
Interaction of vortices with flexible piezoelectric beams
Goushcha, Oleg; Akaydin, Huseyin Dogus; Elvin, Niell; Andreopoulos, Yiannis
2012-11-01
A cantilever piezoelectric beam immersed in a flow is used to harvest fluidic energy. Pressure distribution induced by naturally present vortices in a turbulent fluid flow can force the beam to oscillate producing electrical output. Maximizing the power output of such an electromechanical fluidic system is a challenge. In order to understand the behavior of the beam in a fluid flow where vortices of different scales are present, an experimental facility was set up to study the interaction of individual vortices with the beam. In our set up, vortex rings produced by an audio speaker travel at specific distances from the beam or impinge on it, with a frequency varied up to the natural frequency of the beam. Depending on this frequency both constructive and destructive interactions between the vortices and the beam are observed. Vortices traveling over the beam with a frequency multiple of the natural frequency of the beam cause the beam to resonate and larger deflection amplitudes are observed compared to excitation from a single vortex. PIV is used to compute the flow field and circulation of each vortex and estimate the effect of pressure distribution on the beam deflection. Sponsored by NSF Grant: CBET #1033117.
Dynamics of Chern-Simons vortices
International Nuclear Information System (INIS)
Collie, Benjamin; Tong, David
2008-01-01
We study vortex dynamics in three-dimensional theories with Chern-Simons interactions. The dynamics is governed by motion on the moduli space M in the presence of a magnetic field. For Abelian vortices, the magnetic field is shown to be the Ricci form over M; for non-Abelian vortices, it is the first Chern character of a suitable index bundle. We derive these results by integrating out massive fermions and following the fate of their zero modes.
Stability of two-dimensional vorticity filaments
International Nuclear Information System (INIS)
Elhmaidi, D.; Provenzale, A.; Lili, T.; Babiano, A.
2004-01-01
We discuss the results of a numerical study on the stability of two-dimensional vorticity filaments around a circular vortex. We illustrate how the stability of the filaments depends on the balance between the strain associated with the far field of the vortex and the local vorticity of the filament, and we discuss an empirical criterion for filament stability
Why does gravitational radiation produce vorticity?
International Nuclear Information System (INIS)
Herrera, L; Barreto, W; Carot, J; Prisco, A Di
2007-01-01
We calculate the vorticity of worldlines of observers at rest in a Bondi-Sachs frame, produced by gravitational radiation, in a general Sachs metric. We claim that such an effect is related to the super-Poynting vector, in a similar way as the existence of the electromagnetic Poynting vector is related to the vorticity in stationary electrovacuum spacetimes
Lagrangian Timescales of Southern Ocean Upwelling in a Hierarchy of Model Resolutions
Drake, Henri F.; Morrison, Adele K.; Griffies, Stephen M.; Sarmiento, Jorge L.; Weijer, Wilbert; Gray, Alison R.
2018-01-01
In this paper we study upwelling pathways and timescales of Circumpolar Deep Water (CDW) in a hierarchy of models using a Lagrangian particle tracking method. Lagrangian timescales of CDW upwelling decrease from 87 years to 31 years to 17 years as the ocean resolution is refined from 1° to 0.25° to 0.1°. We attribute some of the differences in timescale to the strength of the eddy fields, as demonstrated by temporally degrading high-resolution model velocity fields. Consistent with the timescale dependence, we find that an average Lagrangian particle completes 3.2 circumpolar loops in the 1° model in comparison to 0.9 loops in the 0.1° model. These differences suggest that advective timescales and thus interbasin merging of upwelling CDW may be overestimated by coarse-resolution models, potentially affecting the skill of centennial scale climate change projections.
Lagrangian model of conformal invariant interacting quantum field theory
International Nuclear Information System (INIS)
Lukierski, J.
1976-01-01
A Lagrangian model of conformal invariant interacting quantum field theory is presented. The interacting Lagrangian and free Lagrangian are derived replacing the canonical field phi by the field operator PHIsub(d)sup(c) and introducing the conformal-invariant interaction Lagrangian. It is suggested that in the conformal-invariant QFT with the dimensionality αsub(B) obtained from the bootstrep equation, the normalization constant c of the propagator and the coupling parametery do not necessarily need to satisfy the relation xsub(B) = phi 2 c 3
A Survey of Factors Affecting Blunt Leading-Edge Separation for Swept and Semi-Slender Wings
Luckring, James M.
2010-01-01
A survey is presented of factors affecting blunt leading-edge separation for swept and semi-slender wings. This class of separation often results in the onset and progression of separation-induced vortical flow over a slender or semi-slender wing. The term semi-slender is used to distinguish wings with moderate sweeps and aspect ratios from the more traditional highly-swept, low-aspect-ratio slender wing. Emphasis is divided between a selection of results obtained through literature survey a section of results from some recent research projects primarily being coordinated through NATO s Research and Technology Organization (RTO). An aircraft context to these studies is included.
Gas transfer under breaking waves: experiments and an improved vorticity-based model
Directory of Open Access Journals (Sweden)
V. K. Tsoukala
2008-07-01
Full Text Available In the present paper a modified vorticity-based model for gas transfer under breaking waves in the absence of significant wind forcing is presented. A theoretically valid and practically applicable mathematical expression is suggested for the assessment of the oxygen transfer coefficient in the area of wave-breaking. The proposed model is based on the theory of surface renewal that expresses the oxygen transfer coefficient as a function of both the wave vorticity and the Reynolds wave number for breaking waves. Experimental data were collected in wave flumes of various scales: a small-scale experiments were carried out using both a sloping beach and a rubble-mound breakwater in the wave flume of the Laboratory of Harbor Works, NTUA, Greece; b large-scale experiments were carried out with a sloping beach in the wind-wave flume of Delft Hydraulics, the Netherlands, and with a three-layer rubble mound breakwater in the Schneideberg Wave Flume of the Franzius Institute, University of Hannover, Germany. The experimental data acquired from both the small- and large-scale experiments were in good agreement with the proposed model. Although the apparent transfer coefficients from the large-scale experiments were lower than those determined from the small-scale experiments, the actual oxygen transfer coefficients, as calculated using a discretized form of the transport equation, are in the same order of magnitude for both the small- and large-scale experiments. The validity of the proposed model is compared to experimental results from other researchers. Although the results are encouraging, additional research is needed, to incorporate the influence of bubble mediated gas exchange, before these results are used for an environmental friendly design of harbor works, or for projects involving waste disposal at sea.
VO2-based radiative thermal transistor with a semi-transparent base
Prod'homme, Hugo; Ordonez-Miranda, Jose; Ezzahri, Younès; Drévillon, Jérémie; Joulain, Karl
2018-05-01
We study a radiative thermal transistor analogous to an electronic one made of a VO2 base placed between two silica semi-infinite plates playing the roles of the transistor collector and emitter. The fact that VO2 exhibits an insulator to metal transition is exploited to modulate and/or amplify heat fluxes between the emitter and the collector, by applying a thermal current on the VO2 base. We extend the work of precedent studies considering the case where the base can be semi-transparent so that heat can be exchanged directly between the collector and the emitter. Both near and far field cases are considered leading to 4 typical regimes resulting from the fact that the emitter-base and base-collector separation distances can be larger or smaller than the thermal wavelength for a VO2 layer opaque or semi-transparent. Thermal currents variations with the base temperatures are calculated and analyzed. It is found that the transistor can operate in an amplification mode as already stated in [1] or in a switching mode as seen in [2]. An optimum configuration for the base thickness and separation distance maximizing the thermal transistor modulation factor is found.
Stability of relative equilibria of three vortices
DEFF Research Database (Denmark)
Aref, Hassan
2009-01-01
Three point vortices on the unbounded plane have relative equilibria wherein the vortices either form an equilateral triangle or are collinear. While the stability analysis of the equilateral triangle configurations is straightforward, that of the collinear relative equilibria is considerably mor...
Collision dynamics of two-dimensional non-Abelian vortices
Mawson, Thomas; Petersen, Timothy C.; Simula, Tapio
2017-09-01
We study computationally the collision dynamics of vortices in a two-dimensional spin-2 Bose-Einstein condensate. In contrast to Abelian vortex pairs, which annihilate or pass through each other, we observe non-Abelian vortex pairs to undergo rungihilation—an event that converts the colliding vortices into a rung vortex. The resulting rung defect subsequently decays to another pair of non-Abelian vortices of different type, accompanied by a magnetization reversal.
Why superconducting vortices follow to moving hot sport?
Sergeev, Andrei; Michael, Reizer
Recent experiments reported in Nature Comm. 7, 12801, 2016 show that superconducting vortices follow to the moving hot sport created by a focused laser beam, i.e. vortices move from the cold area to the moving hot area. This behavior is opposite to the vortex motion observed in numerous measurements of the vortex Nernst effect, where vortices always move against the temperature gradient. Taking into account that superconducting magnetization currents do not transfer entropy, we analyze the balance of forces acting on a vortex in stationary and dynamic temperature gradients. We show that the dynamic measurements may be described by a single vortex approximation, while in stationary measurements interaction between vortices is critical. Supported by NRC.
On the canonical treatment of Lagrangian constraints
International Nuclear Information System (INIS)
Barbashov, B.M.
2001-01-01
The canonical treatment of dynamic systems with manifest Lagrangian constraints proposed by Berezin is applied to concrete examples: a special Lagrangian linear in velocities, relativistic particles in proper time gauge, a relativistic string in orthonormal gauge, and the Maxwell field in the Lorentz gauge
On the canonical treatment of Lagrangian constraints
International Nuclear Information System (INIS)
Barbashov, B.M.
2001-01-01
The canonical treatment of dynamic systems with manifest Lagrangian constraints proposed by Berezin is applied to concrete examples: a specific Lagrangian linear in velocities, relativistic particles in proper time gauge, a relativistic string in orthonormal gauge, and the Maxwell field in the Lorentz gauge
On trailing vortices: A short review
International Nuclear Information System (INIS)
Jacquin, Laurent
2005-01-01
This paper reviews some mechanisms involved in the dynamics of vortices in fluid flows. The topic is first introduced by pointing out its importance in aerodynamics. Several basic notions useful to appraise experimental observations are then surveyed, namely: centrifugal instabilities, inertial waves, cooperative instabilities, vortex merger, vortex breakdown and turbulence in vortices. Each topic is illustrated with experimental or numerical results
Machine learning vortices at the Kosterlitz-Thouless transition
Beach, Matthew J. S.; Golubeva, Anna; Melko, Roger G.
2018-01-01
Efficient and automated classification of phases from minimally processed data is one goal of machine learning in condensed-matter and statistical physics. Supervised algorithms trained on raw samples of microstates can successfully detect conventional phase transitions via learning a bulk feature such as an order parameter. In this paper, we investigate whether neural networks can learn to classify phases based on topological defects. We address this question on the two-dimensional classical XY model which exhibits a Kosterlitz-Thouless transition. We find significant feature engineering of the raw spin states is required to convincingly claim that features of the vortex configurations are responsible for learning the transition temperature. We further show a single-layer network does not correctly classify the phases of the XY model, while a convolutional network easily performs classification by learning the global magnetization. Finally, we design a deep network capable of learning vortices without feature engineering. We demonstrate the detection of vortices does not necessarily result in the best classification accuracy, especially for lattices of less than approximately 1000 spins. For larger systems, it remains a difficult task to learn vortices.
International Nuclear Information System (INIS)
Blanchet, Y.; Obry, P.; Louvet, J.; Graveleau, J.
1981-04-01
Two different numerical methods have been implemented in two computer codes developed in CEA/DRNR, Cadarache, to predict the dynamic response of the containment of Super-Phenix reactor after a hypothetical energy excursion. Both codes are 2D-axisymmetric and solve the time-dependent flow of compressible fluids in the presence of deformable thin structures. The first one, called SIRIUS, uses only Lagrangian meshes; in the second one, called CASSIOPEE, the thick elastic-plastic materials are calculated in Lagrangian coordinates while fluids can be calculated either in Lagrangian or in Eulerian coordinates. The treatment of hydrodynamic, elastic-plastic thick domains then the thin shells models and the fluid-structure couplings are described in parallel for both codes. The efficiency and the limits of the previous methods are finally illustrated by comparison of measured and predicted strains of a vessel issued from one of the MARA experiments which are being purposely performed in Cadarache for validation of these codes in Super-Phenix scale models. These comparisons are encouraging and justify that the Super-Phenix reactor vessel response can be determined using the SIRIUS and CASSIOPEE codes
Lagrangian particle method for compressible fluid dynamics
Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang
2018-06-01
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface/multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic-elliptic systems. Numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.
Lagrangian ocean analysis: Fundamentals and practices
van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan; Adams, Thomas P.; Berloff, Pavel; Biastoch, Arne; Blanke, Bruno; Chassignet, Eric P.; Cheng, Yu; Cotter, Colin J.; Deleersnijder, Eric; Döös, Kristofer; Drake, Henri F.; Drijfhout, Sybren; Gary, Stefan F.; Heemink, Arnold W.; Kjellsson, Joakim; Koszalka, Inga Monika; Lange, Michael; Lique, Camille; MacGilchrist, Graeme A.; Marsh, Robert; Mayorga Adame, C. Gabriela; McAdam, Ronan; Nencioli, Francesco; Paris, Claire B.; Piggott, Matthew D.; Polton, Jeff A.; Rühs, Siren; Shah, Syed H. A. M.; Thomas, Matthew D.; Wang, Jinbo; Wolfram, Phillip J.; Zanna, Laure; Zika, Jan D.
2018-01-01
Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.
Reaction enhancement of initially distant scalars by Lagrangian coherent structures
International Nuclear Information System (INIS)
Pratt, Kenneth R.; Crimaldi, John P.; Meiss, James D.
2015-01-01
Turbulent fluid flows have long been recognized as a superior means of diluting initial concentrations of scalars due to rapid stirring. Conversely, experiments have shown that the structures responsible for this rapid dilution can also aggregate initially distant reactive scalars and thereby greatly enhance reaction rates. Indeed, chaotic flows not only enhance dilution by shearing and stretching but also organize initially distant scalars along transiently attracting regions in the flow. To show the robustness of this phenomenon, a hierarchical set of three numerical flows is used: the periodic wake downstream of a stationary cylinder, a chaotic double gyre flow, and a chaotic, aperiodic flow consisting of interacting Taylor vortices. We demonstrate that Lagrangian coherent structures (LCS), as identified by ridges in finite time Lyapunov exponents, are directly responsible for this coalescence of reactive scalar filaments. When highly concentrated filaments coalesce, reaction rates can be orders of magnitude greater than would be predicted in a well-mixed system. This is further supported by an idealized, analytical model that was developed to quantify the competing effects of scalar dilution and coalescence. Chaotic flows, known for their ability to efficiently dilute scalars, therefore have the competing effect of organizing initially distant scalars along the LCS at timescales shorter than that required for dilution, resulting in reaction enhancement
A Lagrangian framework for deriving triples and quadruples corrections to the CCSD energy
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Kristensen, Kasper; Kjærgaard, Thomas
2014-01-01
Using the coupled cluster Lagrangian technique, we have determined perturbative corrections to the coupled cluster singles and doubles (CCSD) energy that converge towards the coupled cluster singles, doubles, and triples (CCSDT) and coupled cluster singles, doubles, triples, and quadruples (CCSDTQ......) energies, considering the CCSD state as the unperturbed reference state and the fluctua- tion potential as the perturbation. Since the Lagrangian technique is utilized, the energy corrections satisfy Wigner’s 2n + 1 rule for the cluster amplitudes and the 2n + 2 rule for the Lagrange multi- pliers...
Thick vortices in SU(2) lattice gauge theory
Cheluvaraja, Srinath
2004-01-01
Three dimensional SU(2) lattice gauge theory is studied after eliminating thin monopoles and the smallest thick monopoles. Kinematically this constraint allows the formation of thick vortex loops which produce Z(2) fluctuations at longer length scales. The thick vortex loops are identified in a three dimensional simulation. A condensate of thick vortices persists even after the thin vortices have all disappeared. The thick vortices decouple at a slightly lower temperature (higher beta) than t...
Geometry of Lagrangian first-order classical field theories
International Nuclear Information System (INIS)
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N.
1996-01-01
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Nueesch, F. A. [EMPA, Duebendorf (Switzerland)
2010-07-01
This is a popularization article that describes basic properties of semi-conductors and reports on the status of research and development of organic semi-conductors. In a first part, fundamentals of semi-conductors are recalled. Comparisons are made between inorganic and organic (i.e. based on carbon polymers) compounds. Indications are given on how semi-conducting polymers are obtained. Potential applications are listed: flexible organic solar cells, light emitting diodes, flexible organic displays, intelligent cards for ticketing, etc. Research on organic semi-conductors is of great interest for industry, worldwide, and several companies are widely investing in this area.
Transitions between Taylor vortices and spirals via wavy Taylor vortices and wavy spirals
International Nuclear Information System (INIS)
Hoffmann, Ch; Altmeyer, S; Pinter, A; Luecke, M
2009-01-01
We present numerical simulations of closed wavy Taylor vortices and of helicoidal wavy spirals in the Taylor-Couette system. These wavy structures appearing via a secondary bifurcation out of Taylor vortex flow and out of spiral vortex flow, respectively, mediate transitions between Taylor and spiral vortices and vice versa. Structure, dynamics, stability and bifurcation behaviour are investigated in quantitative detail as a function of Reynolds numbers and wave numbers for counter-rotating as well as corotating cylinders. These results are obtained by solving the Navier-Stokes equations subject to axial periodicity for a radius ratio η=0.5 with a combination of a finite differences method and a Galerkin method.
Electroweak chiral Lagrangian from a natural topcolor-assisted technicolor model
International Nuclear Information System (INIS)
Lang Junyi; Jiang Shaozhou; Wang Qing
2009-01-01
Based on previous studies on computing coefficients of the electroweak chiral Lagrangian from C. T. Hill's schematic topcolor-assisted technicolor model, we generalize the calculation to K. Lane's prototype natural topcolor-assisted technicolor model. We find that typical features of the model are qualitatively similar to those of Hill's, but Lane's model prefers a smaller technicolor group and the Z ' mass must be smaller than 400 GeV. Furthermore, the S parameter is around the order of +1, mainly due to the existence of three doublets of techniquarks. We obtain the values for all coefficients of the electroweak chiral Lagrangian up to the order p 4 . Apart from large negative four-fermion coupling values, the extended technicolor impacts on the electroweak chiral Lagrangian coefficients are small, since the techniquark self energy, which determines these coefficients, in general receives almost no influence from the extended technicolor induced four-fermion interactions except for its large momentum tail.
Observation of Polarization Vortices in Momentum Space
Zhang, Yiwen; Chen, Ang; Liu, Wenzhe; Hsu, Chia Wei; Wang, Bo; Guan, Fang; Liu, Xiaohan; Shi, Lei; Lu, Ling; Zi, Jian
2018-05-01
The vortex, a fundamental topological excitation featuring the in-plane winding of a vector field, is important in various areas such as fluid dynamics, liquid crystals, and superconductors. Although commonly existing in nature, vortices were observed exclusively in real space. Here, we experimentally observed momentum-space vortices as the winding of far-field polarization vectors in the first Brillouin zone of periodic plasmonic structures. Using homemade polarization-resolved momentum-space imaging spectroscopy, we mapped out the dispersion, lifetime, and polarization of all radiative states at the visible wavelengths. The momentum-space vortices were experimentally identified by their winding patterns in the polarization-resolved isofrequency contours and their diverging radiative quality factors. Such polarization vortices can exist robustly on any periodic systems of vectorial fields, while they are not captured by the existing topological band theory developed for scalar fields. Our work provides a new way for designing high-Q plasmonic resonances, generating vector beams, and studying topological photonics in the momentum space.
Geometry of Lagrangian first-order classical field theories
Energy Technology Data Exchange (ETDEWEB)
Echeverria-Enriquez, A. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Munoz-Lecanda, M.C. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Roman-Roy, N. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica
1996-10-01
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether`s theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied. (orig.)
Simulation of Venus polar vortices with the non-hydrostatic general circulation model
Rodin, Alexander V.; Mingalev, Oleg; Orlov, Konstantin
2012-07-01
The dynamics of Venus atmosphere in the polar regions presents a challenge for general circulation models. Numerous images and hyperspectral data from Venus Express mission shows that above 60 degrees latitude atmospheric motion is substantially different from that of the tropical and extratropical atmosphere. In particular, extended polar hoods composed presumably of fine haze particles, as well as polar vortices revealing mesoscale wave perturbations with variable zonal wavenumbers, imply the significance of vertical motion in these circulation elements. On these scales, however, hydrostatic balance commonly used in the general circulation models is no longer valid, and vertical forces have to be taken into account to obtain correct wind field. We present the first non-hydrostatic general circulation model of the Venus atmosphere based on the full set of gas dynamics equations. The model uses uniform grid with the resolution of 1.2 degrees in horizontal and 200 m in the vertical direction. Thermal forcing is simulated by means of relaxation approximation with specified thermal profile and time scale. The model takes advantage of hybrid calculations on graphical processors using CUDA technology in order to increase performance. Simulations show that vorticity is concentrated at high latitudes within planetary scale, off-axis vortices, precessing with a period of 30 to 40 days. The scale and position of these vortices coincides with polar hoods observed in the UV images. The regions characterized with high vorticity are surrounded by series of small vortices which may be caused by shear instability of the zonal flow. Vertical velocity component implies that in the central part of high vorticity areas atmospheric flow is downwelling and perturbed by mesoscale waves with zonal wavenumbers 1-4, resembling observed wave structures in the polar vortices. Simulations also show the existence of areas with strong vertical flow, concentrated in spiral branches extending
Extended Lagrangian formalism for rheonomic systems with variable mass
Directory of Open Access Journals (Sweden)
Mušicki Đorđe
2017-01-01
Full Text Available In this paper the extended Lagrangian formalism for the rheonomic systems (Dj. Mušicki, 2004, which began with the modification of the mechanics of such systems (V. Vujičić, 1987, is extended to the systems with variable mass, with emphasis on the corresponding energy relations. This extended Lagrangian formalism is based on the extension of the set of chosen generalized coordinates by new quantities, suggested by the form of nonstationary constraints, which determine the position of the frame of reference in respect to which these generalized coordinates refer. As a consequence, an extended system of the Lagrangian equations is formulated, accommodated to the variability of the masses of particles, where the additional ones correspond to the additional generalized coordinates. By means of these equations, the energy relations of such systems have been studied, where it is demonstrated that here there are four types of energy conservation laws. The obtained energy laws are more complete and natural than the corresponding ones in the usual Lagrangian formulation for such systems. It is demonstrated that the obtained energy laws, are in full accordance with the energy laws in the corresponding vector formulation, if they are expressed in terms of the quantities introduced in this formulation of mechanics. The obtained results are illustrated by an example: the motion of a rocket, which ejects the gasses backwards, while this rocket moves up a straight line on an oblique plane, which glides uniformly in a horizontal direction.
Fast Lagrangian relaxation for constrained generation scheduling in a centralized electricity market
International Nuclear Information System (INIS)
Ongsakul, Weerakorn; Petcharaks, Nit
2008-01-01
This paper proposes a fast Lagrangian relaxation (FLR) for constrained generation scheduling (CGS) problem in a centralized electricity market. FLR minimizes the consumer payment rather than the total supply cost subject to the power balance, spinning reserve, transmission line, and generator operating constraints. FLR algorithm is improved by new initialization of Lagrangian multipliers and adaptive adjustment of Lagrangian multipliers. The adaptive subgradient method using high quality initial feasible multipliers requires much less number of iterations to converge, leading to a faster computational time. If congestion exists, the alleviating congestion index is proposed for congestion management. Finally, the unit decommitment is performed to prevent excessive spinning reserve. The FLR for CGS is tested on the 4 unit and the IEEE 24 bus reliability test systems. The proposed uniform electricity price results in a lower consumer payment than system marginal price based on uniformly fixed cost amortized allocation, non-uniform price, and electricity price incorporating side payment, leading to a lower electricity price. In addition, observations on objective functions, pricing scheme comparison and interpretation of Lagrangian multipliers are provided. (author)
Doppler Velocity Signatures of Idealized Elliptical Vortices
Directory of Open Access Journals (Sweden)
Wen-Chau Lee
2006-01-01
Full Text Available Doppler radar observations have revealed a class of atmospheric vortices (tropical cyclones, tornadoes, dust devils that possess elliptical radar reflectivity signatures. One famous example is Typhoon Herb (1996 that maintained its elliptical reflectivity structure over a 40-hour period. Theoretical work and dual-Doppler analyses of observed tropical cyclones have suggested two physical mechanisms that can explain the formation of two types of elliptical vortices observed in nature, namely, the combination of a circular vortex with either a wavenumber two vortex Rossby wave or a deformation field. The characteristics of these two types of elliptical vortices and their corresponding Doppler velocity signatures have not been previously examined.
CFD model of diabatic annular two-phase flow using the Eulerian–Lagrangian approach
International Nuclear Information System (INIS)
Li, Haipeng; Anglart, Henryk
2015-01-01
Highlights: • A CFD model of annular two-phase flow with evaporating liquid film has been developed. • A two-dimensional liquid film model is developed assuming that the liquid film is sufficiently thin. • The liquid film model is coupled to the gas core flow, which is represented using the Eulerian–Lagrangian approach. - Abstract: A computational fluid dynamics (CFD) model of annular two-phase flow with evaporating liquid film has been developed based on the Eulerian–Lagrangian approach, with the objective to predict the dryout occurrence. Due to the fact that the liquid film is sufficiently thin in the diabatic annular flow and at the pre-dryout conditions, it is assumed that the flow in the wall normal direction can be neglected, and the spatial gradients of the dependent variables tangential to the wall are negligible compared to those in the wall normal direction. Subsequently the transport equations of mass, momentum and energy for liquid film are integrated in the wall normal direction to obtain two-dimensional equations, with all the liquid film properties depth-averaged. The liquid film model is coupled to the gas core flow, which currently is represented using the Eulerian–Lagrangian technique. The mass, momentum and energy transfers between the liquid film, gas, and entrained droplets have been taken into account. The resultant unified model for annular flow has been applied to the steam–water flow with conditions typical for a Boiling Water Reactor (BWR). The simulation results for the liquid film flow rate show favorable agreement with the experimental data, with the potential to predict the dryout occurrence based on criteria of critical film thickness or critical film flow rate
Robust Prediction of High Lift Using Surface Vorticity, Phase II
National Aeronautics and Space Administration — FlightStream has been developed a fast, accurate, aerodynamic prediction code based on vorticity computations on the surface of an aircraft. The code, though still a...
Lagrangian-based Backtracking of Oil Spill Dynamics from SAR Images: Application to Montara Case
Gautama, Budhi Gunadharma; Mercier, Gregoire; Fablet, Ronan; Longepe, Nicolas
2016-08-01
Within the framework of INDESO project (Infrastructure Development Space Oceanography), we address the issue of oilspill and aim at developing an operational SAR- based system for monitoring this issue in Indonesian waters from space. In this work, we focus on the backtrack- ing of an oilspill detected from SAR observations. As a case-study, we consider one large oil spill event that happened in Indonesian waters in 2009, referred to as the Montara oilspill. On 21 August 2009, the Montara Wellhead Platform had an uncontrolled release of hydrocarbons from one of the platform wells. It was estimated that 400 barrels (or approximately 64 tonnes) of crude oil were being lost per day. The uncontrolled release continued until 3 November 2009 and response operations continued until 3 December 2009. In this work, we develop a Langragian analysis and associated numerical inversion tools with a view to further analyzing the oil spread due to the Montara Wellhead Platform. Our model relies on a 2D Lagrangian transport model developed by CLS (Collecte Localisation Satellite). Our model involves four main parameters : the weights of wind- related and current-related advection, the origin and the duration of the oil leakage. Given SAR oilspill detections, we propose a numerical inversion of the parameters of the Lagrangian model, so that the simulated drift match the SAR observations of the oil spill. We demonstrate the relevance of the proposed model and numerical scheme for the Montara oilspill and further discuss their operational interest for the space-based oilspill backtracking and forecasting.
An investigation of singular Lagrangians as field systems
International Nuclear Information System (INIS)
Rabei, E.M.
1995-07-01
The link between the treatment of singular Lagrangians as field systems and the general approach is studied. It is shown that singular Lagrangians as field systems are always in exact agreement with the general approach. Two examples and the singular Lagrangian with zero rank Hessian matrix are studied. The equations of motion in the field systems are equivalent to the equations which contain acceleration, and the constraints are equivalent to the equations which do not contain acceleration in the general approach treatment. (author). 10 refs
Liu, Chunsen; Yan, Xiao; Song, Xiongfei; Ding, Shijin; Zhang, David Wei; Zhou, Peng
2018-04-09
As conventional circuits based on field-effect transistors are approaching their physical limits due to quantum phenomena, semi-floating gate transistors have emerged as an alternative ultrafast and silicon-compatible technology. Here, we show a quasi-non-volatile memory featuring a semi-floating gate architecture with band-engineered van der Waals heterostructures. This two-dimensional semi-floating gate memory demonstrates 156 times longer refresh time with respect to that of dynamic random access memory and ultrahigh-speed writing operations on nanosecond timescales. The semi-floating gate architecture greatly enhances the writing operation performance and is approximately 10 6 times faster than other memories based on two-dimensional materials. The demonstrated characteristics suggest that the quasi-non-volatile memory has the potential to bridge the gap between volatile and non-volatile memory technologies and decrease the power consumption required for frequent refresh operations, enabling a high-speed and low-power random access memory.
Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS3 space
International Nuclear Information System (INIS)
Buchbinder, I.L.; Snegirev, T.V.; Zinoviev, Yu.M.
2012-01-01
We develop the frame-like formulation of massive bosonic higher spin fields in the case of three-dimensional (A)dS space with the arbitrary cosmological constant. The formulation is based on gauge invariant description by involving the Stueckelberg auxiliary fields. The explicit form of the Lagrangians and the gauge transformation laws are found. The theory can be written in terms of gauge invariant objects similar to the massless theories, thus allowing us to hope to use the same methods for investigation of interactions. In the massive spin 3 field example we are able to rewrite the Lagrangian using the new the so-called separated variables, so that the study of Lagrangian formulation reduces to finding the Lagrangian containing only half of the fields. The same construction takes places for arbitrary integer spin field as well. Further working in terms of separated variables, we build Lagrangian for arbitrary integer spin and write it in terms of gauge invariant objects. Also, we demonstrate how to restore the full set of variables, thus receiving Lagrangian for the massive fields of arbitrary spin in the terms of initial fields.
Statistical balance of vorticity and a new scale for vortical structures in turbulence
International Nuclear Information System (INIS)
Novikov, E.A.
1993-01-01
The balance of one-point and two-point statistical characterics of vorticity, is considered on the basis of the Navier-Stokes equations. It is shown that within the inertial range of scales (L Re -3/4 much-lt r much-lt L, L external scale, Re Reynolds number) there is a physically distinguished scale l s ∼L Re -3/10 . The balance of vortical correlations with scales r≥l s is directly affected by the large-scale motion. l s is a natural length scale for the ''vortex strings,'' observed experimentally and numerically in three-dimensional turbulent flows. The twist of vortex lines in the internal structure of vortex strings is also briefly discussed
Evans, John; Coley, Christopher; Aronson, Ryan; Nelson, Corey
2017-11-01
In this talk, a large eddy simulation methodology for turbulent incompressible flow will be presented which combines the best features of divergence-conforming discretizations and the residual-based variational multiscale approach to large eddy simulation. In this method, the resolved motion is represented using a divergence-conforming discretization, that is, a discretization that preserves the incompressibility constraint in a pointwise manner, and the unresolved fluid motion is explicitly modeled by subgrid vortices that lie within individual grid cells. The evolution of the subgrid vortices is governed by dynamical model equations driven by the residual of the resolved motion. Consequently, the subgrid vortices appropriately vanish for laminar flow and fully resolved turbulent flow. As the resolved velocity field and subgrid vortices are both divergence-free, the methodology conserves mass in a pointwise sense and admits discrete balance laws for energy, enstrophy, and helicity. Numerical results demonstrate the methodology yields improved results versus state-of-the-art eddy viscosity models in the context of transitional, wall-bounded, and rotational flow when a divergence-conforming B-spline discretization is utilized to represent the resolved motion.
Behaviour of Lagrangian triangular mixed fluid finite elements
Indian Academy of Sciences (India)
The behaviour of mixed fluid finite elements, formulated based on the Lagrangian frame of reference, is investigated to understand the effects of locking due to incompressibility and irrotational constraints. For this purpose, both linear and quadratic mixed triangular fluid elements are formulated. It is found that there exists a ...
Transitions in turbulent rotating convection: A Lagrangian perspective : A Lagrangian perspective
Rajaei, H.; Joshi, P.R.; Alards, K.M.J.; Kunnen, R.P.J.; Toschi, F.; Clercx, H.J.H.
2016-01-01
Using measurements of Lagrangian acceleration in turbulent rotating convection and accompanying direct numerical simulations, we show that the transition between turbulent states reported earlier [e.g., S. Weiss et al., Phys. Rev. Lett. 105, 224501 (2010)] is a boundary-layer transition between the
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.
Modulation of leading edge vorticity and aerodynamic forces in flexible flapping wings.
Zhao, Liang; Deng, Xinyan; Sane, Sanjay P
2011-09-01
In diverse biological flight systems, the leading edge vortex has been implicated as a flow feature of key importance in the generation of flight forces. Unlike fixed wings, flapping wings can translate at higher angles of attack without stalling because their leading edge vorticity is more stable than the corresponding fixed wing case. Hence, the leading edge vorticity has often been suggested as the primary determinant of the high forces generated by flapping wings. To test this hypothesis, it is necessary to modulate the size and strength of the leading edge vorticity independently of the gross kinematics while simultaneously monitoring the forces generated by the wing. In a recent study, we observed that forces generated by wings with flexible trailing margins showed a direct dependence on the flexural stiffness of the wing. Based on that study, we hypothesized that trailing edge flexion directly influences leading edge vorticity, and thereby the magnitude of aerodynamic forces on the flexible flapping wings. To test this hypothesis, we visualized the flows on wings of varying flexural stiffness using a custom 2D digital particle image velocimetry system, while simultaneously monitoring the magnitude of the aerodynamic forces. Our data show that as flexion decreases, the magnitude of the leading edge vorticity increases and enhances aerodynamic forces, thus confirming that the leading edge vortex is indeed a key feature for aerodynamic force generation in flapping flight. The data shown here thus support the hypothesis that camber influences instantaneous aerodynamic forces through modulation of the leading edge vorticity.
Bayesian Lagrangian Data Assimilation and Drifter Deployment Strategies
Dutt, A.; Lermusiaux, P. F. J.
2017-12-01
Ocean currents transport a variety of natural (e.g. water masses, phytoplankton, zooplankton, sediments, etc.) and man-made materials and other objects (e.g. pollutants, floating debris, search and rescue, etc.). Lagrangian Coherent Structures (LCSs) or the most influential/persistent material lines in a flow, provide a robust approach to characterize such Lagrangian transports and organize classic trajectories. Using the flow-map stochastic advection and a dynamically-orthogonal decomposition, we develop uncertainty prediction schemes for both Eulerian and Lagrangian variables. We then extend our Bayesian Gaussian Mixture Model (GMM)-DO filter to a joint Eulerian-Lagrangian Bayesian data assimilation scheme. The resulting nonlinear filter allows the simultaneous non-Gaussian estimation of Eulerian variables (e.g. velocity, temperature, salinity, etc.) and Lagrangian variables (e.g. drifter/float positions, trajectories, LCSs, etc.). Its results are showcased using a double-gyre flow with a random frequency, a stochastic flow past a cylinder, and realistic ocean examples. We further show how our Bayesian mutual information and adaptive sampling equations provide a rigorous efficient methodology to plan optimal drifter deployment strategies and predict the optimal times, locations, and types of measurements to be collected.
Scale-by-scale contributions to Lagrangian particle acceleration
Lalescu, Cristian C.; Wilczek, Michael
2017-11-01
Fluctuations on a wide range of scales in both space and time are characteristic of turbulence. Lagrangian particles, advected by the flow, probe these fluctuations along their trajectories. In an effort to isolate the influence of the different scales on Lagrangian statistics, we employ direct numerical simulations (DNS) combined with a filtering approach. Specifically, we study the acceleration statistics of tracers advected in filtered fields to characterize the smallest temporal scales of the flow. Emphasis is put on the acceleration variance as a function of filter scale, along with the scaling properties of the relevant terms of the Navier-Stokes equations. We furthermore discuss scaling ranges for higher-order moments of the tracer acceleration, as well as the influence of the choice of filter on the results. Starting from the Lagrangian tracer acceleration as the short time limit of the Lagrangian velocity increment, we also quantify the influence of filtering on Lagrangian intermittency. Our work complements existing experimental results on intermittency and accelerations of finite-sized, neutrally-buoyant particles: for the passive tracers used in our DNS, feedback effects are neglected such that the spatial averaging effect is cleanly isolated.
Lagrangian statistics in compressible isotropic homogeneous turbulence
Yang, Yantao; Wang, Jianchun; Shi, Yipeng; Chen, Shiyi
2011-11-01
In this work we conducted the Direct Numerical Simulation (DNS) of a forced compressible isotropic homogeneous turbulence and investigated the flow statistics from the Lagrangian point of view, namely the statistics is computed following the passive tracers trajectories. The numerical method combined the Eulerian field solver which was developed by Wang et al. (2010, J. Comp. Phys., 229, 5257-5279), and a Lagrangian module for tracking the tracers and recording the data. The Lagrangian probability density functions (p.d.f.'s) have then been calculated for both kinetic and thermodynamic quantities. In order to isolate the shearing part from the compressing part of the flow, we employed the Helmholtz decomposition to decompose the flow field (mainly the velocity field) into the solenoidal and compressive parts. The solenoidal part was compared with the incompressible case, while the compressibility effect showed up in the compressive part. The Lagrangian structure functions and cross-correlation between various quantities will also be discussed. This work was supported in part by the China's Turbulence Program under Grant No.2009CB724101.
Generalized large-scale semigeostrophic approximations for the f-plane primitive equations
Oliver, Marcel; Vasylkevych, Sergiy
2016-05-01
We derive a family of balance models for rotating stratified flow in the primitive equation (PE) setting. By construction, the models possess conservation laws for energy and potential vorticity and are formally of the same order of accuracy as Hoskins’ semigeostrophic equations. Our construction is based on choosing a new coordinate frame for the PE variational principle in such a way that the consistently truncated Lagrangian degenerates. We show that the balance relations so obtained are elliptic when the fluid is stably stratified and certain smallness assumptions are satisfied. Moreover, the potential temperature can be recovered from the potential vorticity via inversion of a non-standard Monge-Ampère problem which is subject to the same ellipticity condition. While the present work is entirely formal, we conjecture, based on a careful rewriting of the equations of motion and a straightforward derivative count, that the Cauchy problem for the balance models is well posed subject to conditions on the initial data. Our family of models includes, in particular, the stratified analog of the L 1 balance model of Salmon.
Generalized large-scale semigeostrophic approximations for the f-plane primitive equations
International Nuclear Information System (INIS)
Oliver, Marcel; Vasylkevych, Sergiy
2016-01-01
We derive a family of balance models for rotating stratified flow in the primitive equation (PE) setting. By construction, the models possess conservation laws for energy and potential vorticity and are formally of the same order of accuracy as Hoskins’ semigeostrophic equations. Our construction is based on choosing a new coordinate frame for the PE variational principle in such a way that the consistently truncated Lagrangian degenerates. We show that the balance relations so obtained are elliptic when the fluid is stably stratified and certain smallness assumptions are satisfied. Moreover, the potential temperature can be recovered from the potential vorticity via inversion of a non-standard Monge–Ampère problem which is subject to the same ellipticity condition. While the present work is entirely formal, we conjecture, based on a careful rewriting of the equations of motion and a straightforward derivative count, that the Cauchy problem for the balance models is well posed subject to conditions on the initial data. Our family of models includes, in particular, the stratified analog of the L 1 balance model of Salmon. (paper)
Lagrangian solution of supersonic real gas flows
International Nuclear Information System (INIS)
Loh, Chingyuen; Liou, Mengsing
1993-01-01
This paper details the procedure of the real gas Riemann solution in the Lagrangian approach originally proposed by Loh and Hui for perfect gases. The extension to real gases is nontrivial and requires substantial development of an exact real-gas Riemann solver for the Lagrangian form of conservation laws. The first-order Gudonov scheme is enhanced for accuracy by adding limited anti-diffusive terms according to Sweby. Extensive calculations were made to test the accuracy and robustness of the present real gas Lagrangian approach, including complex wave interactions of different types. The accuracy for capturing 2D oblique waves and slip line is clearly demonstrated. In addition, we also show the real gas effect in a generic engine nozzle
Aerodynamics and vortical structures in hovering fruitflies
Meng, Xue Guang; Sun, Mao
2015-03-01
We measure the wing kinematics and morphological parameters of seven freely hovering fruitflies and numerically compute the flows of the flapping wings. The computed mean lift approximately equals to the measured weight and the mean horizontal force is approximately zero, validating the computational model. Because of the very small relative velocity of the wing, the mean lift coefficient required to support the weight is rather large, around 1.8, and the Reynolds number of the wing is low, around 100. How such a large lift is produced at such a low Reynolds number is explained by combining the wing motion data, the computed vortical structures, and the theory of vorticity dynamics. It has been shown that two unsteady mechanisms are responsible for the high lift. One is referred as to "fast pitching-up rotation": at the start of an up- or downstroke when the wing has very small speed, it fast pitches down to a small angle of attack, and then, when its speed is higher, it fast pitches up to the angle it normally uses. When the wing pitches up while moving forward, large vorticity is produced and sheds at the trailing edge, and vorticity of opposite sign is produced near the leading edge and on the upper surface, resulting in a large time rate of change of the first moment of vorticity (or fluid impulse), hence a large aerodynamic force. The other is the well known "delayed stall" mechanism: in the mid-portion of the up- or downstroke the wing moves at large angle of attack (about 45 deg) and the leading-edge-vortex (LEV) moves with the wing; thus, the vortex ring, formed by the LEV, the tip vortices, and the starting vortex, expands in size continuously, producing a large time rate of change of fluid impulse or a large aerodynamic force.
The Bach-Lanczos Lagrangian in matrix relativity
International Nuclear Information System (INIS)
Maluf, J.W.
1987-01-01
The author examines the generalisation of the Bach-Lanczos Lagrangian in matrix relativity where it is no longer a topological invariant, and find that for certain structures of the matrix affine connection a Yang-Mills type Lagrangian is obtained. Thus the possibility is considered of interpreting non-Abelian gauge fields as arising from an otherwise topological invariant. (author)
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...
A numerical study of vorticity-enhanced heat transfer
Wang, Xiaolin; Alben, Silas
2012-11-01
The Glezer lab at Georgia Tech has found that vorticity produced by vibrated reeds can improve heat transfer in electronic hardware. Vortices enhance forced convection by boundary layer separation and thermal mixing in the bulk flow. In this work, we simulate the heat transfer process in a 3-dimensional plate-fin heat sink. We propose a simplified model by considering flow and temperature in a 2-D channel, and extend the model to the third dimension using a 1-D heat fin model. We simulate periodically steady-state solutions. We determine how the global Nusselt number is increased, depending on the vortices' strengths and spacings, in the parameter space of Reynolds and Peclet numbers. We find a surprising spatial oscillation of the local Nusselt number due to the vortices. Support from NSF-DMS grant 1022619 is acknowledged.
Multiple gamma lines from semi-annihilation
International Nuclear Information System (INIS)
D'Eramo, Francesco; McCullough, Matthew; Thaler, Jesse
2013-01-01
Hints in the Fermi data for a 130 GeV gamma line from the galactic center have ignited interest in potential gamma line signatures of dark matter. Explanations of this line based on dark matter annihilation face a parametric tension since they often rely on large enhancements of loop-suppressed cross sections. In this paper, we pursue an alternative possibility that dark matter gamma lines could arise from ''semi-annihilation'' among multiple dark sector states. The semi-annihilation reaction ψ i ψ j → ψ k γ with a single final state photon is typically enhanced relative to ordinary annihilation ψ i ψ-bar i → γγ into photon pairs. Semi-annihilation allows for a wide range of dark matter masses compared to the fixed mass value required by annihilation, opening the possibility to explain potential dark matter signatures at higher energies. The most striking prediction of semi-annihilation is the presence of multiple gamma lines, with as many as order N 3 lines possible for N dark sector states, allowing for dark sector spectroscopy. A smoking gun signature arises in the simplest case of degenerate dark matter, where a strong semi-annihilation line at 130 GeV would be accompanied by a weaker annihilation line at 173 GeV. As a proof of principle, we construct two explicit models of dark matter semi-annihilation, one based on non-Abelian vector dark matter and the other based on retrofitting Rayleigh dark matter
Guo, Jian; Wei, Zhongchao; Liu, Yuebo; Huang, Aili
2015-02-01
Two amplitude modulation methods, including modified Bessel-like function modulation structure and trapezoid annulus structure, for suppressing sidelobes of optical vortices are studied. In the former approach, we propose that the order of the Bessel-like function can be an additional parameter to modulate diffraction patterns of optical vortices motivated by the idea of conventional annulus structures. Furthermore, new Bessel-like modulation functions are introduced to solve the problem of low diffraction efficiency of the original one. Trapezoid annulus structure is proposed as a compromise structure between the modified Bessel-like modulation structure and the conventional annulus one, and has advantages of both. It is demonstrated that these two approaches can achieve high-quality optical vortices with suppressed sidelobes effectively, and the relative structures behave as more flexible and applicable structures for producing optical vortices with large coverage of topological charges, which suggests great potential in simplifying the structure designing procedure. These reliable and generalized structures for generating high-quality optical vortices will help to promote the development of future optical communication and optical manipulation significantly.
Lagrangian analysis of multiscale particulate flows with the particle finite element method
Oñate, Eugenio; Celigueta, Miguel Angel; Latorre, Salvador; Casas, Guillermo; Rossi, Riccardo; Rojek, Jerzy
2014-05-01
We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories
Buican, Matthew; Laczko, Zoltan
2018-02-01
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.
Buican, Matthew; Laczko, Zoltan
2018-02-23
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
Near field vorticity distributions from a sharp-edged rectangular jet
International Nuclear Information System (INIS)
Vouros, Alexandros P.; Panidis, Thrassos; Pollard, Andrew; Schwab, Rainer R.
2015-01-01
Highlights: • Axial mean vorticity equation terms are calculated from experimental data. • Appearance of ridges, dumbbell shape and saddleback velocity profiles is highlighted. • Explanations are provided using terms from the vorticity equation. - Abstract: Experimental results on the near field development of a free rectangular jet with aspect ratio 10 are presented. The jet issues from a sharp-edged orifice attached to a rectangular settling chamber at Re h ∼ 23,000, based on slot width, h. Measurements on cross plane grids were obtained with a two-component hot wire anemometry probe, which provided information on the three dimensional characteristics of the flow field. Two key features of this type of jet are mean axial velocity profiles presenting two off axis peaks, commonly mentioned as saddleback profiles, and a predominant dumbbell shape as described by, for example, a contour of the axial mean velocity. The saddleback shape is found to be significantly influenced by the vorticity distribution in the transverse plane of the jet, while the dumbbell is traced to two terms in the axial mean vorticity transport equation that diffuse fluid from the centre of the jet towards its periphery. At the farthest location where measurements were taken, 30 slot widths from the jet exit, the flow field resembles that of an axisymmetric jet
Geometric Lagrangian approach to the physical degree of freedom count in field theory
Díaz, Bogar; Montesinos, Merced
2018-05-01
To circumvent some technical difficulties faced by the geometric Lagrangian approach to the physical degree of freedom count presented in the work of Díaz, Higuita, and Montesinos [J. Math. Phys. 55, 122901 (2014)] that prevent its direct implementation to field theory, in this paper, we slightly modify the geometric Lagrangian approach in such a way that its resulting version works perfectly for field theory (and for particle systems, of course). As in previous work, the current approach also allows us to directly get the Lagrangian constraints, a new Lagrangian formula for the counting of the number of physical degrees of freedom, the gauge transformations, and the number of first- and second-class constraints for any action principle based on a Lagrangian depending on the fields and their first derivatives without performing any Dirac's canonical analysis. An advantage of this approach over the previous work is that it also allows us to handle the reducibility of the constraints and to get the off-shell gauge transformations. The theoretical framework is illustrated in 3-dimensional generalized general relativity (Palatini and Witten's exotic actions), Chern-Simons theory, 4-dimensional BF theory, and 4-dimensional general relativity given by Palatini's action with a cosmological constant.
A Bernstein type result for special Lagrangian submanifolds
Tsui, Mao-Pei; Wang, Mu-Tao
2002-01-01
Let \\Sigma be a complete minimal Lagrangian submanifold of \\C^n. We identify regions in the Grassmannian of Lagrangian subspaces so that whenever the image of the Gauss map of \\Sigma lies in one of these regions, then \\Sigma is an affine space.
Simultaneous Buffer-sizing and Wire-sizing for Clock Trees Based on Lagrangian Relaxation
Directory of Open Access Journals (Sweden)
Yu-Min Lee
2002-01-01
Full Text Available Delay, power, skew, area and sensitivity are the most important concerns in current clock-tree design. We present in this paper an algorithm for simultaneously optimizing the above objectives by sizing wires and buffers in clock trees. Our algorithm, based on Lagrangian relaxation method, can optimally minimize delay, power and area simultaneously with very low skew and sensitivity. With linear storage overall and linear runtime per iteration, our algorithm is extremely economical, fast and accurate; for example, our algorithm can solve a 6201-wire-segment clock-tree problem using about 1-minute runtime and 1.3-MB memory and still achieve pico-second precision on an IBM RS/6000 workstation.
A study on relativistic lagrangian field theories with non-topological soliton solutions
International Nuclear Information System (INIS)
Diaz-Alonso, J.; Rubiera-Garcia, D.
2009-01-01
We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call 'admissible' models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite
Capecelatro, Jesse
2018-03-01
It has long been suggested that a purely Lagrangian solution to global-scale atmospheric/oceanic flows can potentially outperform tradition Eulerian schemes. Meanwhile, a demonstration of a scalable and practical framework remains elusive. Motivated by recent progress in particle-based methods when applied to convection dominated flows, this work presents a fully Lagrangian method for solving the inviscid shallow water equations on a rotating sphere in a smooth particle hydrodynamics framework. To avoid singularities at the poles, the governing equations are solved in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the surface of the sphere. An underlying grid in spherical coordinates is used to facilitate efficient neighbor detection and parallelization. The method is applied to a suite of canonical test cases, and conservation, accuracy, and parallel performance are assessed.
International Nuclear Information System (INIS)
Gaida, R.P.; Kluchkousky, Ya.B.; Tretyak, V.I.
1987-01-01
In the present report the main attention is paid to the interrelations of various three-dimensional approaches and to the relation of the latter to the Fokker-type action formalism; the problem of the correspondence between three-dimensional descriptions and singular Lagrangian formalism will be shortly concerned. The authors start with the three-dimensional Lagrangian formulation of the classical RDIT. The generality of this formalism enables, similarly as in the non-relativistic case, to consider it as a central link explaining naturally a number of features of other three-dimensional approaches, namely Newtonian (based directly on second order equations of motion) and Hamiltonian ones). It is also capable of describing four-dimensional manifestly covariant models using Fokker action integrals and singular Lagrangians
Dynamics of quantised vortices in superfluids
Sonin, Edouard B
2016-01-01
A comprehensive overview of the basic principles of vortex dynamics in superfluids, this book addresses the problems of vortex dynamics in all three superfluids available in laboratories (4He, 3He, and BEC of cold atoms) alongside discussions of the elasticity of vortices, forces on vortices, and vortex mass. Beginning with a summary of classical hydrodynamics, the book guides the reader through examinations of vortex dynamics from large scales to the microscopic scale. Topics such as vortex arrays in rotating superfluids, bound states in vortex cores and interaction of vortices with quasiparticles are discussed. The final chapter of the book considers implications of vortex dynamics to superfluid turbulence using simple scaling and symmetry arguments. Written from a unified point of view that avoids complicated mathematical approaches, this text is ideal for students and researchers working with vortex dynamics in superfluids, superconductors, magnetically ordered materials, neutron stars and cosmological mo...
Direct Lagrangian tracking simulations of particles in vertically-developing atmospheric clouds
Onishi, Ryo; Kunishima, Yuichi
2017-11-01
We have been developing the Lagrangian Cloud Simulator (LCS), which follows the so-called Euler-Lagrangian framework, where flow motion and scalar transportations (i.e., temperature and humidity) are computed with the Euler method and particle motion with the Lagrangian method. The LCS simulation considers the hydrodynamic interaction between approaching particles for robust collision detection. This leads to reliable simulations of collision growth of cloud droplets. Recently the activation process, in which aerosol particles become tiny liquid droplets, has been implemented in the LCS. The present LCS can therefore consider the whole warm-rain precipitation processes -activation, condensation, collision and drop precipitation. In this talk, after briefly introducing the LCS, we will show kinematic simulations using the LCS for quasi-one dimensional domain, i.e., vertically elongated 3D domain. They are compared with one-dimensional kinematic simulations using a spectral-bin cloud microphysics scheme, which is based on the Euler method. The comparisons show fairly good agreement with small discrepancies, the source of which will be presented. The Lagrangian statistics, obtained for the first time for the vertical domain, will be the center of discussion. This research was supported by MEXT as ``Exploratory Challenge on Post-K computer'' (Frontiers of Basic Science: Challenging the Limits).
Lagrangian formulation and symmetrical description of liquid dynamics.
Trachenko, K
2017-12-01
Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.
Effective lagrangian description on discrete gauge symmetries
International Nuclear Information System (INIS)
Banks, T.
1989-01-01
We exhibit a simple low-energy lagrangian which describes a system with a discrete remnant of a spontaneously broken continuous gauge symmetry. The lagrangian gives a simple description of the effects ascribed to such systems by Krauss and Wilczek: black holes carry discrete hair and interact with cosmic strings, and wormholes cannot lead to violation of discrete gauge symmetries. (orig.)
Cohomology for Lagrangian systems and Noetherian symmetries
International Nuclear Information System (INIS)
Popp, O.T.
1989-06-01
Using the theory of sheaves we find some exact sequences describing the locally Lagrangian systems. Using cohomology theory of groups with coefficients in sheaves we obtain some exact sequences describing the Noetherian symmetries. It is shown how the results can be used to find all locally Lagrangian dynamics Noetherian invariant with respect to a given group of kinematical symmetries.(author)
A Combined Eulerian-Lagrangian Data Representation for Large-Scale Applications.
Sauer, Franz; Xie, Jinrong; Ma, Kwan-Liu
2017-10-01
The Eulerian and Lagrangian reference frames each provide a unique perspective when studying and visualizing results from scientific systems. As a result, many large-scale simulations produce data in both formats, and analysis tasks that simultaneously utilize information from both representations are becoming increasingly popular. However, due to their fundamentally different nature, drawing correlations between these data formats is a computationally difficult task, especially in a large-scale setting. In this work, we present a new data representation which combines both reference frames into a joint Eulerian-Lagrangian format. By reorganizing Lagrangian information according to the Eulerian simulation grid into a "unit cell" based approach, we can provide an efficient out-of-core means of sampling, querying, and operating with both representations simultaneously. We also extend this design to generate multi-resolution subsets of the full data to suit the viewer's needs and provide a fast flow-aware trajectory construction scheme. We demonstrate the effectiveness of our method using three large-scale real world scientific datasets and provide insight into the types of performance gains that can be achieved.
Magnetic Vortices in Nanodisks: What are the implications in macroscopic magnetic properties?
Gelvez Pedroza, Ciro Fernando; Patino, Edgar J.; Superconductivity; Nanodevices Laboratory Team
The study of nanodevices is of great importance nowadays. In particular nanodisks present extraordinary properties when varying their size, shape and materials. One of the most interesting ones has been the presence of magnetic vortices which are normally not present in continuous films or bulk materials. For that reason, these constitute of great interest in potential applications such as data storage, binary logic gates or nano-plasmonics. Although there are many high cost methods for fabrication we have chosen a low cost technique based on Colloidal Lithography. Using Polystyrene Nanoparticles (100nm) nanodisks of about 180 nm in diameter have been grown using Electron Beam evaporation. The fabrication technique requires a number of steps such as spin coating, oxygen plasma and Ion Beam Etching. The samples obtained with this method were Ti/Co/Nb nanodisks with various thickness of the Co layer. Micromagnetic simulations were carried out in OOMMF giving magnetic domain structure and hysteresis loops which were later compared with those obtained experimentally using Vibrating Sample Magnetometry. Simulation results suggest a critical thickness for the appearance of magnetic vortices, revealed by hysteresis loops with substantially lower coercive fields. Facultad de Ciencias,Vicerrectoria de Investigaciones - Universidad de los Andes.
Hairpin vortices in turbulent boundary layers
International Nuclear Information System (INIS)
Eitel-Amor, G; Schlatter, P; Flores, O
2014-01-01
The present work addresses the question whether hairpin vortices are a dominant feature of near-wall turbulence and which role they play during transition. First, the parent-offspring mechanism is investigated in temporal simulations of a single hairpin vortex introduced in a mean shear flow corresponding to turbulent channels and boundary layers up to Re τ = 590. Using an eddy viscosity computed from resolved simulations, the effect of a turbulent background is also considered. Tracking the vortical structure downstream, it is found that secondary hairpins are created shortly after initialization. Thereafter, all rotational structures decay, whereas this effect is enforced in the presence of an eddy viscosity. In a second approach, a laminar boundary layer is tripped to transition by insertion of a regular pattern of hairpins by means of defined volumetric forces representing an ejection event. The idea is to create a synthetic turbulent boundary layer dominated by hairpin-like vortices. The flow for Re τ < 250 is analysed with respect to the lifetime of individual hairpin-like vortices. Both the temporal and spatial simulations demonstrate that the regeneration process is rather short-lived and may not sustain once a turbulent background has formed. From the transitional flow simulations, it is conjectured that the forest of hairpins reported in former DNS studies is an outer layer phenomenon not being connected to the onset of near-wall turbulence.
Tight focusing properties of linearly polarized Gaussian beam with a pair of vortices
Energy Technology Data Exchange (ETDEWEB)
Chen, Ziyang [Department of Physics, Zhejiang University, Hangzhou 310027 (China); College of Information Science and Engineering, Institute of Optics and Photonics, Huaqiao University, Xiamen, Fujian 361021 (China); Pu, Jixiong [College of Information Science and Engineering, Institute of Optics and Photonics, Huaqiao University, Xiamen, Fujian 361021 (China); Zhao, Daomu, E-mail: zhaodaomu@yahoo.com [Department of Physics, Zhejiang University, Hangzhou 310027 (China)
2011-07-25
The properties of a pair of vortices embedded in a Gaussian beam focused by a high numerical-aperture are studied on the basis of vector Debye integral. The vortices move and rotate in the vicinity of the focal plane for a pair of vortices with equal topological charges. For incident beam with a pair of vortices with opposite topological charges, the vortices move toward each other, annihilate and revive in the vicinity of focal plane. -- Highlights: → The properties of a pair of vortices focused by a high numerical-aperture are studied. → It is shown that the focusing vortices with equal topological charges move toward and rotate. → It is shown that the focusing vortices with opposite topological charges move toward each other, annihilate and revive.
Marensi, Elena; Ricco, Pierre
2017-11-01
The generation, nonlinear evolution, and wall-transpiration control of unsteady Görtler vortices in an incompressible boundary layer over a concave plate is studied theoretically and numerically. Görtler rolls are initiated and driven by free-stream vortical perturbations of which only the low-frequency components are considered because they penetrate the most into the boundary layer. The formation and development of the disturbances are governed by the nonlinear unsteady boundary-region equations with the centrifugal force included. These equations are subject to appropriate initial and outer boundary conditions, which account for the influence of the upstream and free-stream forcing in a rigorous and mutually consistent manner. Numerical solutions show that the stabilizing effect on nonlinearity, which also occurs in flat-plate boundary layers, is significantly enhanced in the presence of centrifugal forces. Sufficiently downstream, the nonlinear vortices excited at different free-stream turbulence intensities Tu saturate at the same level, proving that the initial amplitude of the forcing becomes unimportant. At low Tu, the disturbance exhibits a quasi-exponential growth with the growth rate being intensified for more curved plates and for lower frequencies. At higher Tu, in the typical range of turbomachinery applications, the Görtler vortices do not undergo a modal stage as nonlinearity saturates rapidly, and the wall curvature does not affect the boundary-layer response. Good quantitative agreement with data from direct numerical simulations and experiments is obtained. Steady spanwise-uniform and spanwise-modulated zero-mass-flow-rate wall transpiration is shown to attenuate the growth of the Görtler vortices significantly. A novel modified version of the Fukagata-Iwamoto-Kasagi identity, used for the first time to study a transitional flow, reveals which terms in the streamwise momentum balance are mostly affected by the wall transpiration, thus
Physical properties corresponding to vortical flow geometry
Energy Technology Data Exchange (ETDEWEB)
Nakayama, K, E-mail: nakayama@aitech.ac.jp [Department of Mechanical Engineering, Aichi Institute of Technology, Toyota, Aichi 470-0392 (Japan)
2014-10-01
We examine a vortical flow geometry specified by the velocity gradient tensor ∇v, and derive properties representing the symmetry (axisymmetry or skewness) of the vortical flow in the swirl plane and a property specifying inflowing (outflowing) motion in all directions around the point. We focus on the radial and azimuthal velocities in a plane nonparallel to the eigenvector corresponding to the real eigenvalue of ∇v and show that these components are expressed as specific quadratic forms. The real and imaginary parts of the complex eigenvalues of ∇v represent averages of these eigenvalues of the quadratic forms, and are inadequate to specify the detailed flow geometry uniquely. The new properties complement specifying the precise flow geometry of the vortical flow.
Pallas Sanz, E.; García-Carrillo, P.; Garcia Gomez, B. I.; Lilly, J. M.; Perez-Brunius, P.
2016-02-01
The time-average horizontal distribution of the near-inertial waves (NIWs) on the western Gulf of Mexico (GoM) is investigated using horizontal velocity data obtained from Lagrangian trajectories of 200 surface drifters drogued at 50m and deployed between September 2008 and September 2012. Preliminary results suggest maximum time-averaged near-inertial circle radius of 2.6km located in the southern Campeche bay near [22N,95W]; implying an inertial velocity of about 0.14m/s. Similar conclusions are delineated using horizontal velocity data obtained from 21 moorings deployed in the western GoM during the same time period. Maximum near-inertial kinetic energy and clockwise spectral energy is found in the mooring LNK3500 located at 21.850N and 94.028W. Maximum inertial circles measured with mooring data, however, are of about 1.6km leading to inertial currents of 0.087m/s, approximately a 40% smaller. This discrepancy seems to be due to the different depth level of the measurements and the bandwidth used to extract the near-inertial oscillations from the total flow. The time-average horizontal distributions of wind work computed from Lagrangian and Eulerian data are compared and they are not consistent with the time-averaged NIW field. The differences are not well understood but we speculate they may be due to the different time scales of wind fluctuations in the northwestern GoM compared to those observed in the Bay of Campeche, together with the change of sign of the background vorticity in the region; being negative (anticyclonic) in the northern GoM and positive (cyclonic) in the Bay of Campeche.
Equivalence of Lagrangian and Hamiltonian BRST quantizations
International Nuclear Information System (INIS)
Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.
1992-01-01
Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme
Cheng, Shaobo
2017-04-06
We report structural transformation of sixfold vortex domains into two-, four-, and eightfold vortices via a different type of topological defect in hexagonal manganites. Combining high-resolution electron microscopy and Landau-theory-based numerical simulations, we investigate the remarkable atomic arrangement and the intertwined relationship between the vortex structures and the topological defects. The roles of their displacement field, formation temperature, and nucleation sites are revealed. All conceivable vortices in the system are topologically classified using homotopy group theory, and their origins are identified.
Towards laboratory detection of topological vortices in superfluid phases of QCD
Das, Arpan; Dave, Shreyansh S.; de, Somnath; Srivastava, Ajit M.
2017-10-01
Topological defects arise in a variety of systems, e.g. vortices in superfluid helium to cosmic strings in the early universe. There is an indirect evidence of neutron superfluid vortices from the glitches in pulsars. One also expects that the topological defects may arise in various high baryon density phases of quantum chromodynamics (QCD), e.g. superfluid topological vortices in the color flavor locked (CFL) phase. Though vastly different in energy/length scales, there are universal features in the formation of all these defects. Utilizing this universality, we investigate the possibility of detecting these topological superfluid vortices in laboratory experiments, namely heavy-ion collisions (HICs). Using hydrodynamic simulations, we show that vortices can qualitatively affect the power spectrum of flow fluctuations. This can give an unambiguous signal for superfluid transition resulting in vortices, allowing for the check of defect formation theories in a relativistic quantum field theory system, and the detection of superfluid phases of QCD. Detection of nucleonic superfluid vortices in low energy HICs will give opportunity for laboratory controlled study of their properties, providing crucial inputs for the physics of pulsars.
Lagrangian mass-flow investigations of inorganic contaminants in wastewater-impacted streams
Barber, L.B.; Antweiler, Ronald C.; Flynn, J.L.; Keefe, S.H.; Kolpin, D.W.; Roth, D.A.; Schnoebelen, D.J.; Taylor, Howard E.; Verplanck, P.L.
2011-01-01
Understanding the potential effects of increased reliance on wastewater treatment plant (WWTP) effluents to meet municipal, agricultural, and environmental flow requires an understanding of the complex chemical loading characteristics of the WWTPs and the assimilative capacity of receiving waters. Stream ecosystem effects are linked to proportions of WWTP effluent under low-flow conditions as well as the nature of the effluent chemical mixtures. This study quantifies the loading of 58 inorganic constituents (nutrients to rare earth elements) from WWTP discharges relative to upstream landscape-based sources. Stream assimilation capacity was evaluated by Lagrangian sampling, using flow velocities determined from tracer experiments to track the same parcel of water as it moved downstream. Boulder Creek, Colorado and Fourmile Creek, Iowa, representing two different geologic and hydrologic landscapes, were sampled under low-flow conditions in the summer and spring. One-half of the constituents had greater loads from the WWTP effluents than the upstream drainages, and once introduced into the streams, dilution was the predominant assimilation mechanism. Only ammonium and bismuth had significant decreases in mass load downstream from the WWTPs during all samplings. The link between hydrology and water chemistry inherent in Lagrangian sampling allows quantitative assessment of chemical fate across different landscapes. ?? 2011 American Chemical Society.
Hasheminejad, S. M.
2016-01-05
A series of flow visualizations were conducted to qualitatively study the development of streamwise counter-rotating vortices over a flat plate induced by triangular patterns at the leading edge of a flat plate. The experiments were carried out for a Reynolds number based on the pattern wavelength (λ) of 3080. The results depict the onset, development and breakdown of the vortical structures within the flat plate boundary layer. Moreover, the effect of one spanwise array of holes with diameter of 0.2λ (=3 mm) was examined. This investigation was done on two different flat plates with holes placed at the location x/λ = 2 downstream of the troughs and peaks. The presence of holes after troughs does not show any significant effect on the vortical structures. However, the plate with holes after peaks noticeably delays the vortex breakdown. In this case, the “mushroom-like” vortices move away from the wall and propagate downstream with stable vortical structures. The vortex growth is halted further downstream but start to tilt aside.
Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data
2015-09-30
Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...coastal ocean fields, both in Eulerian and Lagrangian forms. - Further develop and implement our GMM-DO schemes for robust Bayesian nonlinear estimation
Driven motion of vortices in superconductors
International Nuclear Information System (INIS)
Crabtree, G.W.; Leaf, G.K.; Kaper, H.G.; Vinokur, V.M.; Koshelev, A.E.; Braun, D.W.; Levine, D.M.
1995-09-01
The driven motion of vortices in the solid vortex state is analyzed with the time-dependent Ginzburg-Landau equations. In large-scale numerical simulations, carried out on the IBM Scalable POWERparallel (SP) system at Argonne National Laboratory, many hundreds of vortices are followed as they move under the influence of a Lorentz force induced by a transport current in the presence of a planar defect (similar to a twin boundary in YBa 2 CU 3 O 7 ). Correlations in the positions and velocities of the vortices in plastic and elastic motion are identified and compared. Two types of plastic motion are observed. Organized plastic motion displaying long-range orientational correlation and shorter-range velocity correlation occurs when the driving forces are small compared to the pinning forces in the twin boundary. Disorganized plastic motion displaying no significant correlation in either the velocities or orientation of the vortex system occurs when the driving and pinning forces axe of the same order
Helicity conservation and twisted Seifert surfaces for superfluid vortices.
Salman, Hayder
2017-04-01
Starting from the continuum definition of helicity, we derive from first principles its different contributions for superfluid vortices. Our analysis shows that an internal twist contribution emerges naturally from the mathematical derivation. This reveals that the spanwise vector that is used to characterize the twist contribution must point in the direction of a surface of constant velocity potential. An immediate consequence of the Seifert framing is that the continuum definition of helicity for a superfluid is trivially zero at all times. It follows that the Gauss-linking number is a more appropriate definition of helicity for superfluids. Despite this, we explain how a quasi-classical limit can arise in a superfluid in which the continuum definition for helicity can be used. This provides a clear connection between a microscopic and a macroscopic description of a superfluid as provided by the Hall-Vinen-Bekarevich-Khalatnikov equations. This leads to consistency with the definition of helicity used for classical vortices.
Coulomb energy, vortices, and confinement
International Nuclear Information System (INIS)
Greensite, Jeff; Olejnik, Stefan
2003-01-01
We estimate the Coulomb energy of static quarks from a Monte Carlo calculation of the correlator of timelike link variables in the Coulomb gauge. We find, in agreement with Cucchieri and Zwanziger, that this energy grows linearly with distance at large quark separations. The corresponding string tension, however, is several times greater than the accepted asymptotic string tension, indicating that a state containing only static sources, with no constituent gluons, is not the lowest energy flux tube state. The Coulomb energy is also measured on thermalized lattices with center vortices removed by the de Forcrand-D'Elia procedure. We find that when vortices are removed, the Coulomb string tension vanishes
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 ...
General conditions for the existence of non-standard Lagrangians for dissipative dynamical systems
International Nuclear Information System (INIS)
Musielak, Z.E.
2009-01-01
Equations of motion describing dissipative dynamical systems with coefficients varying either in time or in space are considered. To identify the equations that admit a Lagrangian description, two classes of non-standard Lagrangians are introduced and general conditions required for the existence of these Lagrangians are determined. The conditions are used to obtain some non-standard Lagrangians and derive equations of motion resulting from these Lagrangians.
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.)
Control of a three-dimensional turbulent shear layer by means of oblique vortices
Jürgens, Werner; Kaltenbach, Hans-Jakob
2018-04-01
The effect of local forcing on the separated, three-dimensional shear layer downstream of a backward-facing step is investigated by means of large-eddy simulation for a Reynolds number based on the step height of 10,700. The step edge is either oriented normal to the approaching turbulent boundary layer or swept at an angle of 40°. Oblique vortices with different orientation and spacing are generated by wavelike suction and blowing of fluid through an edge parallel slot. The vortices exhibit a complex three-dimensional structure, but they can be characterized by a wavevector in a horizontal section plane. In order to determine the step-normal component of the wavevector, a method is developed based on phase averages. The dependence of the wavevector on the forcing parameters can be described in terms of a dispersion relation, the structure of which indicates that the disturbances are mainly convected through the fluid. The introduced vortices reduce the size of the recirculation region by up to 38%. In both the planar and the swept case, the most efficient of the studied forcings consists of vortices which propagate in a direction that deviates by more than 50° from the step normal. These vortices exhibit a spacing in the order of 2.5 step heights. The upstream shift of the reattachment line can be explained by increased mixing and momentum transport inside the shear layer which is reflected in high levels of the Reynolds shear stress -ρ \\overline{u'v'}. The position of the maximum of the coherent shear stress is found to depend linearly on the wavelength, similar to two-dimensional free shear layers.
Jakovetic, Dusan; Xavier, João; Moura, José M. F.
2011-08-01
We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x=x^\\star. The objective function of the corresponding optimization problem is the sum of private (known only by a node,) convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, decentralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l_1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.
Numerical analysis of propeller induced ground vortices by actuator disk model
Yang, Y.; Veldhuis, L.L.M.; Eitelberg, G.
2017-01-01
Abstract: During the ground operation of aircraft, the interaction between the propulsor-induced flow field and the ground may lead to the generation of ground vortices. Utilizing numerical approaches, the source of vorticity entering ground vortices is investigated. The results show that the
Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations
International Nuclear Information System (INIS)
Mestdag, T; Crampin, M
2008-01-01
We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated with Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper, we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincare equations in a new fashion and we show how solutions of the Euler-Lagrange equations can be reconstructed with the help of the mechanical connection. Illustrative examples confirm the theory
GAUGE PRINCIPLE AND VARIATIONAL FORMULATION FOR FLOWS OF AN IDEAL FLUID
Institute of Scientific and Technical Information of China (English)
KAMBE Tsutomu
2003-01-01
A gauge principle is applied to mass flows of an ideal compressible fluid subject to Galilei transformation. A free-field Lagrangian defined at the outset is invariant with respect to global SO(3) gauge transformations as well as Galilei transformations. The action principle leads to the equation of potential flows under constraint of a continuity equation. However, the irrotational flow is not invariant with respect to local SO(3) gauge transformations. According to the gauge principle,a gauge-covariant derivative is defined by introducing a new gauge field. Galilei invariance of the derivative requires the gauge field to coincide with the vorticity, i.e. the curl of the velocity field. A full gauge-covariant variational formulation is proposed on the basis of the Hamilton's principle and an assoicated Lagrangian. By means of an isentropic material variation taking into account individual particle motion, the Euler's equation of motion is derived for isentropic flows by using the covariant derivative. Noether's law associated with global SO(3) gauge invariance leads to the conservation of total angular momentum. In addition, the Lagrangian has a local symmetry of particle permutation which results in local conservation law equivalent to the vorticity equation.
A Laboratory Study of Vortical Structures in Rotating Convection Plumes
Fu, Hao; Sun, Shiwei; Wang, Yuan; Zhou, Bowen; Thermal Turbulence Research Team
2015-11-01
A laboratory study of the columnar vortex structure in rotating Rayleigh-Bénard convection is conducted. A rectangular water tank is uniformly heated from below and cooled from above, with Ra = (6 . 35 +/- 0 . 77) ×107 , Ta = 9 . 84 ×107 , Pr = 7 . 34 . The columnar vortices are vertically aligned and quasi steady. Two 2D PIV systems were used to measure velocity field. One system performs horizontal scans at 9 different heights every 13.6s, covering 62% of the total depth. The other system scans vertically to obtain the vertical velocity profile. The measured vertical vorticity profiles of most vortices are quasi-linear with height while the vertical velocities are nearly uniform with only a small curvature. A simple model to deduce vertical velocity profile from vertical vorticity profile is proposed. Under quasi-steady and axisymmetric conditions, a ``vortex core'' assumption is introduced to simplify vertical vorticity equation. A linear ODE about vertical velocity is obtained whenever a vertical vorticity profile is given and solved with experimental data as input. The result is approximately in agreement with the measurement. This work was supported by Undergraduates Training Project (J1103410).
Bethuel, Fabrice; Helein, Frederic
2017-01-01
This book is concerned with the study in two dimensions of stationary solutions of uɛ of a complex valued Ginzburg-Landau equation involving a small parameter ɛ. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ɛ has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ɛ tends to zero. One of the main results asserts that the limit u-star of minimizers uɛ exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree – or winding number – of the boundary condition. Each singularity has degree one – or as physicists would say, vortices are quantized. The singularities have infinite energy, but after removing the core energy we are lead to a concept of finite renormalized energy. The location of the singularities is completely determined by minimiz...
Lagrangian formalism for constrained systems. 2. Gauge symmetries
International Nuclear Information System (INIS)
Pyatov, P.N.
1990-01-01
Using the Lagrangian formalism for constrained systems all gauge symmetries peculiar for a given Lagrangian system and in establishing the relation between them and the constraints are constructed. Besides, the question about the possible dependence of gauge transformations on accelerations and other higher order time derivatives of coordinates is clarified. 14 refs
Three dimensional vortices and interfaces in Hele-Shaw cells
International Nuclear Information System (INIS)
Pumir, A.
1987-06-01
A model of nonviscous flow, based on the Biot-Savart equations is used to examine the existence of singularities in three dimensional, incompressible, hydrodynamic equations. The results suggest a fairly simple physical mechanism, which could lead to the formation of singularities in the nonviscous case: two vortex tubes with opposite circulations pair up and stretch each other, until the radii of the vortex cores become extremely small, causing a divergence of the vorticity. The cases of a perfect and a slightly viscous fluid are considered. The results are unclear as to whether the vorticity of a slightly viscous fluid can become infinite or not, and whether singularities exist. The dynamics of hydrodynamic interfaces are also investigated. The propagation of bubbles in a slightly viscous fluid, in a Hele-Shaw cell are described [fr
Lattice vortices in the two-dimensional Abelian Higgs model
International Nuclear Information System (INIS)
Grunewald, S.; Ilgenfritz, E.-M.; Mueller-Preussker, M.
1986-01-01
Multi-vortices of the 2D Abelian Higgs model on a finite lattice by relaxation of Monte-Carlo equilibrium configurations are generated and identified. The lattice vortices have action and a uniquely defined topological charge corresponding to the continuum ones. They exhibit the expected exponential decay behaviour and satisfy approximately the classical equations of motion. Vortex-antivortex superpositions are seen as well, supporting the dilute gas picture. Single vortices finally relax into ''dislocations'' and dissapear. A background charge construction turns out nearly insensitive with respect to dislocations
Between Laws and Models: Some Philosophical Morals of Lagrangian Mechanics
Butterfield, Jeremy
2004-01-01
I extract some philosophical morals from some aspects of Lagrangian mechanics. (A companion paper will present similar morals from Hamiltonian mechanics and Hamilton-Jacobi theory.) One main moral concerns methodology: Lagrangian mechanics provides a level of description of phenomena which has been largely ignored by philosophers, since it falls between their accustomed levels--``laws of nature'' and ``models''. Another main moral concerns ontology: the ontology of Lagrangian mechanics is bot...
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
Laboratory experiments on multipolar vortices in a rotating fluid
Trieling, R.R.; Heijst, van G.J.F.; Kizner, Ziv
2010-01-01
The instability properties of isolated monopolar vortices have been investigated experimentally and the corresponding multipolar quasisteady states have been compared with semianalytical vorticity-distributed solutions to the Euler equations in two dimensions. A novel experimental technique was
Approximate Noether symmetries and collineations for regular perturbative Lagrangians
Paliathanasis, Andronikos; Jamal, Sameerah
2018-01-01
Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.
The 3D Lagrangian Integral Method. Henrik Koblitz Rasmussen
DEFF Research Database (Denmark)
Rasmussen, Henrik Koblitz
2003-01-01
. This are processes such as thermo-forming, gas-assisted injection moulding and all kind of simultaneous multi-component polymer processing operations. Though, in all polymer processing operations free surfaces (or interfaces) are present and the dynamic of these surfaces are of interest. In the "3D Lagrangian...... Integral Method" to simulate viscoelastic flow, the governing equations are solved for the particle positions (Lagrangian kinematics). Therefore, the transient motion of surfaces can be followed in a particularly simple fashion even in 3D viscoelastic flow. The "3D Lagrangian Integral Method" is described...
Borneo Vortices: A case study and its relation to climatology
Braesicke, P.; Ooi, S. H.; Samah, A. A.
2012-04-01
Borneo vortices (BVs) develop over the South China Sea and are main drivers for the formation of deep convection and heavy rainfall in East Malaysia. We present a case study of a cold-surge-induced BV during January 2010 in which the export of potential energy lead to a strengthening of the subtropical jet. Potential vorticity (PV) and water vapour analyses confirm a significant impact of the BV on upper tropospheric composition. Dry, high PV air is found far below 100 hPa in the vicinty of the vortex. Using a PV threshold analysis of ERA-Interim data we construct a climatological composite of similar events and characterise the thermal, dynamical and composition structure of a 'typical' BV. We note the preferential formation of BVs during ENSO cold conditions and show that two effects contribute to the formation of the dry upper layer above a BV: Air is vertically transported upwards in the BV whilst precipitating and the large scale flow in which the BV is embedded advect dry, ozone rich air from the equatorial TTL over the BV. Thus the occurence frequency of BVs is important for the regional variability of upper tropospheric/lower stratospheric composition.
A coherent structure approach for parameter estimation in Lagrangian Data Assimilation
Maclean, John; Santitissadeekorn, Naratip; Jones, Christopher K. R. T.
2017-12-01
We introduce a data assimilation method to estimate model parameters with observations of passive tracers by directly assimilating Lagrangian Coherent Structures. Our approach differs from the usual Lagrangian Data Assimilation approach, where parameters are estimated based on tracer trajectories. We employ the Approximate Bayesian Computation (ABC) framework to avoid computing the likelihood function of the coherent structure, which is usually unavailable. We solve the ABC by a Sequential Monte Carlo (SMC) method, and use Principal Component Analysis (PCA) to identify the coherent patterns from tracer trajectory data. Our new method shows remarkably improved results compared to the bootstrap particle filter when the physical model exhibits chaotic advection.
Extended hamiltonian formalism and Lorentz-violating lagrangians
Directory of Open Access Journals (Sweden)
Don Colladay
2017-09-01
Full Text Available A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler–Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.
Extended hamiltonian formalism and Lorentz-violating lagrangians
Colladay, Don
2017-09-01
A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.
CSIR Research Space (South Africa)
Roux, FS
2014-02-01
Full Text Available Optical vortices are always created or annihilated in pairs with opposite topological charges. However, the presence of such a vortex dipole does not directly indicate whether they are associated with a creation or an annihilation event. Here we...
Semi-classical signal analysis
Laleg-Kirati, Taous-Meriem; Cré peau, Emmanuelle; Sorine, Michel
2012-01-01
This study introduces a new signal analysis method, based on a semi-classical approach. The main idea in this method is to interpret a pulse-shaped signal as a potential of a Schrödinger operator and then to use the discrete spectrum
The universal lagrangian and the cosmic evolution
International Nuclear Information System (INIS)
El Tahir, A.
1984-08-01
By geometrizing Mach's Universe, we derive the most rational form of a Lagrangian which we, hence, call Universal. It contains both linear and nonlinear terms of the scalar curvature R, with constant coefficients which underlie a certain physical meaning. The metric derivable from this Lagrangian is believed to be far advanced from those derived from general relativity. A wave equation describing the overall evolution of the Universe is obtained and discussed. (author)
Problems of vector Lagrangians in field theories
International Nuclear Information System (INIS)
Krivsky, I.Yu.; Simulik, V.M.
1997-01-01
A vector Lagrange approach to the Dirac spinor field and the relationship between the vector Lagrangians for the spinor and electromagnetic fields are considered. A vector Lagrange approach for the system of interacting electromagnetic B=(B μ υ)=(E-bar,H-bar) and spinor Ψ fields is constructed. New Lagrangians (scalar and vector) for electromagnetic field in terms of field strengths are found. The foundations of two new QED models are formulated
Carbon storage capacity of semi-arid grassland soils and sequestration potentials in northern China.
Wiesmeier, Martin; Munro, Sam; Barthold, Frauke; Steffens, Markus; Schad, Peter; Kögel-Knabner, Ingrid
2015-10-01
Organic carbon (OC) sequestration in degraded semi-arid environments by improved soil management is assumed to contribute substantially to climate change mitigation. However, information about the soil organic carbon (SOC) sequestration potential in steppe soils and their current saturation status remains unknown. In this study, we estimated the OC storage capacity of semi-arid grassland soils on the basis of remote, natural steppe fragments in northern China. Based on the maximum OC saturation of silt and clay particles soils (grazing land, arable land, eroded areas) were estimated. The analysis of natural grassland soils revealed a strong linear regression between the proportion of the fine fraction and its OC content, confirming the importance of silt and clay particles for OC stabilization in steppe soils. This relationship was similar to derived regressions in temperate and tropical soils but on a lower level, probably due to a lower C input and different clay mineralogy. In relation to the estimated OC storage capacity, degraded steppe soils showed a high OC saturation of 78-85% despite massive SOC losses due to unsustainable land use. As a result, the potential of degraded grassland soils to sequester additional OC was generally low. This can be related to a relatively high contribution of labile SOC, which is preferentially lost in the course of soil degradation. Moreover, wind erosion leads to substantial loss of silt and clay particles and consequently results in a direct loss of the ability to stabilize additional OC. Our findings indicate that the SOC loss in semi-arid environments induced by intensive land use is largely irreversible. Observed SOC increases after improved land management mainly result in an accumulation of labile SOC prone to land use/climate changes and therefore cannot be regarded as contribution to long-term OC sequestration. © 2015 John Wiley & Sons Ltd.
Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices.
Mehmood, M Q; Mei, Shengtao; Hussain, Sajid; Huang, Kun; Siew, S Y; Zhang, Lei; Zhang, Tianhang; Ling, Xiaohui; Liu, Hong; Teng, Jinghua; Danner, Aaron; Zhang, Shuang; Qiu, Cheng-Wei
2016-04-06
A multifocus optical vortex metalens, with enhanced signal-to-noise ratio, is presented, which focuses three longitudinal vortices with distinct topological charges at different focal planes. The design largely extends the flexibility of tuning the number of vortices and their focal positions for circularly polarized light in a compact device, which provides the convenience for the nanomanipulation of optical vortices. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.
Huang, Yongxiang; Biferale, Luca; Calzavarini, Enrico; Sun, Chao; Toschi, Federico
2013-04-01
The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)].
The Lagrangians and Hamiltonians of damped coupled vibrations
International Nuclear Information System (INIS)
Ding Guangtao; Gan Huilan; Zheng Xianfeng; Cui Zhifeng
2012-01-01
In this paper, the analytical mechanization of two kinds of damped coupled vibrations is studied. First, by use of coordinate transformations the equations of motion are transformed into the self-ad- joint form. Secondly, the Lagrangians are obtained according to Engels method. Finally the Lagrangians and Hamiltonians of the original equations are deduced by using the inverse transformation. (authors)
Lagrangian 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...
Role of centre vortices in dynamical mass generation
International Nuclear Information System (INIS)
Leinweber, Derek B.; Bowman, Patrick O.; Heller, Urs M.; Kusterer, Daniel-Jens; Langfeld, Kurt; Williams, Anthony G.
2006-01-01
The mass and renormalization functions of the nonperturbative quark propagator are studied in SU(3) gauge field theory with a Symanzik-improved gluon action and the AsqTad fermion action. Centre vortices in the gauge field are identified by fixing to maximal centre gauge. The role of centre vortices in dynamical mass generation is explored by removing centre vortices from the gauge fields and studying the associated changes in the quark propagator. We find that dynamical mass generation survives in the vortex-removed SU(3) gauge field theory despite the vanishing of the string tension and suppression of the gluon propagator in the infrared suggesting the possibility of decoupling dynamical mass generation from confinement
Vortices and nanostructured superconductors
2017-01-01
This book provides expert coverage of modern and novel aspects of the study of vortex matter, dynamics, and pinning in nanostructured and multi-component superconductors. Vortex matter in superconducting materials is a field of enormous beauty and intellectual challenge, which began with the theoretical prediction of vortices by A. Abrikosov (Nobel Laureate). Vortices, vortex dynamics, and pinning are key features in many of today’s human endeavors: from the huge superconducting accelerating magnets and detectors at the Large Hadron Collider at CERN, which opened new windows of knowledge on the universe, to the tiny superconducting transceivers using Rapid Single Flux Quanta, which have opened a revolutionary means of communication. In recent years, two new features have added to the intrinsic beauty and complexity of the subject: nanostructured/nanoengineered superconductors, and the discovery of a range of new materials showing multi-component (multi-gap) superconductivity. In this book, leading researche...
Unambiguous formalism for higher order Lagrangian field theories
International Nuclear Information System (INIS)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn; Vankerschaver, Joris
2009-01-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Magnetic monopoles, center vortices, confinement and topology of gauge fields
International Nuclear Information System (INIS)
Reinhardt, H.; Engelhardt, M.; Langfeld, K.; Quandt, M.; Schaefke, A.
2000-01-01
The vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario. Furthermore the topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills-theory. For this purpose the continuum analog of the maximum center gauge is constructed
Magnetic Monopoles, Center Vortices, Confinement and Topology of Gauge Fields
Reinhardt, H.; Engelhardt, M.; Langfeld, K.; Quandt, M.; Sch"afke, A.
1999-01-01
The vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario. Furthermore the topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills-theory. For this purpose the continuum analog of the maximum center gauge is constructed.
Process development of starch hydrolysis using mixing characteristics of Taylor vortices.
Masuda, Hayato; Horie, Takafumi; Hubacz, Robert; Ohmura, Naoto; Shimoyamada, Makoto
2017-04-01
In food industries, enzymatic starch hydrolysis is an important process that consists of two steps: gelatinization and saccharification. One of the major difficulties in designing the starch hydrolysis process is the sharp change in its rheological properties. In this study, Taylor-Couette flow reactor was applied to continuous starch hydrolysis process. The concentration of reducing sugar produced via enzymatic hydrolysis was evaluated by varying operational variables: rotational speed of the inner cylinder, axial velocity (reaction time), amount of enzyme, and initial starch content in the slurry. When Taylor vortices were formed in the annular space, efficient hydrolysis occurred because Taylor vortices improved the mixing of gelatinized starch with enzyme. Furthermore, a modified inner cylinder was proposed, and its mixing performance was numerically investigated. The modified inner cylinder showed higher potential for enhanced mixing of gelatinized starch and the enzyme than the conventional cylinder.
International Nuclear Information System (INIS)
Massacret, Nicolas; Moysan, Joseph; Ploix, Marie-Aude; Chaouch, Naim; Jeannot, Jean-Philippe
2016-01-01
Ultrasonic monitoring in high temperature fluids with turbulences requires the knowledge of wave propagation in such media and the development of simulation tools. Applications could be the monitoring of sodium-cooled fast reactors. The objectives are mainly acoustic telemetry and thermometry, which involve the propagation of ultrasounds in turbulent and heated sodium flows. We developed a ray-tracing model to simulate the wave propagation and to determine wave deviations and delays due to an inhomogeneous medium. In previous work we demonstrated the sensitivity of ultrasounds to temperature gradients in liquid sodium. To complete that study, we need to investigate the sensitivity of ultrasounds to vortices created in a moving fluid. We designed a specific experimental setup called IKHAR (Instabilities of Kelvin-Helmholtz for Acoustic Research) in order to assess the validity of the ray-tracing model and the potential of ultrasounds for monitoring such fluid. In this experiment, Von Karman instabilities were created in a flow of water. Fluid temperature was homogeneous in our experimental setup. Through a careful choice of the parameters, periodic vortices were generated. The experiment was also simulated using Comsol registered to allow discussion about repeatability. The throughtransmission method was used to measure wave delays due to the vortices. Arrays of transducers were used to measure time of flight variations of several nanoseconds with a high spatial resolution. Results were similar to simulation results. They demonstrate that beam delays due to vortices can be measured and confirm the potential of ultrasounds in monitoring very inhomogeneous fluid media such as liquid sodium used as coolant fluid in nuclear fast reactors.
Theory of Concentrated Vortices
DEFF Research Database (Denmark)
Alekseenko, Sergey; Kuibin, Pavel; Okulov, Valery
This book presents comprehensive and authoritative coverage of the wide field of concentrated vortices observed in nature and technique. The methods for research of their kinematics and dynamics are considered. Special attention is paid to the flows with helical symmetry. The authors have describ...
Diffusion coefficient adaptive correction in Lagrangian puff model
International Nuclear Information System (INIS)
Tan Wenji; Wang Dezhong; Ma Yuanwei; Ji Zhilong
2014-01-01
Lagrangian puff model is widely used in the decision support system for nuclear emergency management. The diffusion coefficient is one of the key parameters impacting puff model. An adaptive method was proposed in this paper, which could correct the diffusion coefficient in Lagrangian puff model, and it aimed to improve the accuracy of calculating the nuclide concentration distribution. This method used detected concentration data, meteorological data and source release data to estimate the actual diffusion coefficient with least square method. The diffusion coefficient adaptive correction method was evaluated by Kincaid data in MVK, and was compared with traditional Pasquill-Gifford (P-G) diffusion scheme method. The results indicate that this diffusion coefficient adaptive correction method can improve the accuracy of Lagrangian puff model. (authors)
Potential-vorticity inversion and the wave-turbulence jigsaw: some recent clarifications
Directory of Open Access Journals (Sweden)
M. E. McIntyre
2008-06-01
Full Text Available Two key ideas stand out as crucial to understanding atmosphere-ocean dynamics, and the dynamics of other planets including the gas giants. The first key idea is the invertibility principle for potential vorticity (PV. Without it, one can hardly give a coherent account of even so important and elementary a process as Rossby-wave propagation, going beyond the simplest textbook cases. Still less can one fully understand nonlinear processes like the self-sharpening or narrowing of jets – the once-mysterious "negative viscosity" phenomenon. The second key idea, also crucial to understanding jets, might be summarized in the phrase "there is no such thing as turbulence without waves", meaning Rossby waves especially. Without this idea one cannot begin to make sense of, for instance, momentum budgets and eddy momentum transports in complex large-scale flows. Like the invertibility principle the idea has long been recognized, or at least adumbrated. However, it is worth articulating explicitly if only because it can be forgotten when, in the usual way, we speak of "turbulence" and "turbulence theory" as if they were autonomous concepts. In many cases of interest, such as the well-studied terrestrial stratosphere, reality is more accurately described as a highly inhomogeneous "wave-turbulence jigsaw puzzle" in which wavelike and turbulent regions fit together and crucially affect each other's evolution. This modifies, for instance, formulae for the Rhines scale interpreted as indicating the comparable importance of wavelike and turbulent dynamics. Also, weakly inhomogeneous turbulence theory is altogether inapplicable. For instance there is no scale separation. Eddy scales are not much smaller than the sizes of the individual turbulent regions in the jigsaw. Here I review some recent progress in clarifying these ideas and their implications.
Effective lagrangian for Kaon-nucleon scattering
International Nuclear Information System (INIS)
Andrade, S.C.B. de; Ferreira, E.M.
1980-11-01
A model for the Kaon-nucleon interaction is investigated, based on a lagrangian which includes the Yukawa interactions of hyperons, kaons and nucleons plus contact terms representing short range interactions in each isospin state. All diagrams up to fourth order are evaluated and the partial wave S matrix elements are unitarized through diagonal Pade approximants. The results of the calculations with this model give a good description of all experimental data on both I = O and I = 1 states of the KN system at low and intermediate energies. (Author) [pt
Sharp vorticity gradients in two-dimensional turbulence and the energy spectrum
DEFF Research Database (Denmark)
Kuznetsov, E.A.; Naulin, Volker; Nielsen, Anders Henry
2010-01-01
Formation of sharp vorticity gradients in two-dimensional (2D) hydrodynamic turbulence and their influence on the turbulent spectra are considered. The analog of the vortex line representation as a transformation to the curvilinear system of coordinates moving together with the di-vorticity lines...... is developed and compressibility of this mapping appears as the main reason for the formation of the sharp vorticity gradients at high Reynolds numbers. In the case of strong anisotropy the sharp vorticity gradients can generate spectra which fall off as k −3 at large k, which appear to take the same form...
Identifying finite-time coherent sets from limited quantities of Lagrangian data
Energy Technology Data Exchange (ETDEWEB)
Williams, Matthew O. [Program in Applied and Computational Mathematics, Princeton University, New Jersey 08544 (United States); Rypina, Irina I. [Department of Physical Oceanography, Woods Hole Oceanographic Institute, Massachusetts 02543 (United States); Rowley, Clarence W. [Department of Mechanical and Aerospace Engineering, Princeton University, New Jersey 08544 (United States)
2015-08-15
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.
Identifying finite-time coherent sets from limited quantities of Lagrangian data
International Nuclear Information System (INIS)
Williams, Matthew O.; Rypina, Irina I.; Rowley, Clarence W.
2015-01-01
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea
Identifying finite-time coherent sets from limited quantities of Lagrangian data.
Williams, Matthew O; Rypina, Irina I; Rowley, Clarence W
2015-08-01
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or "mesh-free" methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.
Influence of artificial tip perturbation on asymmetric vortices flow over a chined fuselage
Directory of Open Access Journals (Sweden)
Shi Wei
2015-08-01
Full Text Available An experimental study was conducted with the aim of understanding behavior of asymmetric vortices flow over a chined fuselage. The tests were carried out in a wind tunnel at Reynolds number of 1.87 × 105 under the conditions of high angles of attack and zero angle of sideslip. The results show that leeward vortices flow becomes asymmetric vortices flow when angle of attack increases over 20°. The asymmetric vortices flow is asymmetry of two forebody vortices owing to the increase of angle of attack but not asymmetry of vortex breakdown which appears when angle of attack is above 35°. Asymmetric vortices flow is sensitive to tip perturbation and is non-deterministic due to randomly distributed natural minute geometrical irregularities on the nose tip within machining tolerance. Deterministic asymmetric vortices flow can be obtained by attaching artificial tip perturbation which can trigger asymmetric vortices flow and decide asymmetric vortices flow pattern. Triggered by artificial tip perturbation, the vortex on the same side with perturbation is in a higher position, and the other vortex on the opposite side is in a lower position. Vortex suction on the lower vortex side is larger, which corresponds to a side force pointing to the lower vortex side.
On hairpin vortices in a transitional boundary layer
Directory of Open Access Journals (Sweden)
Uruba Václav
2012-04-01
Full Text Available In the presented paper the results of experiments on transitional boundary layer are presented. The boundary layer was generated on smooth flat wall with zero pressure gradient forming one side of the channel of rectangular cross section. The hairpin vortices, packets of hairpin vortices, turbulent spots and calmed regions were experimentally investigated using time-resolved PIV technique.
Vortices and domain walls: 'Wormholes' in unconventional superconductors
International Nuclear Information System (INIS)
Bessarab, P F; Radievsky, A V
2010-01-01
In the framework of the 2D and 3D time-dependent Ginzburg-Landau model we study superconductors with multicomponent order parameter (d-pairing). We argue that topological defects inside the sample do affect its thermodynamic properties such as hysteresis loop, susceptibility, etc. Along with earlier known topological defects such as Abrikosov vortices, domain walls (DWs) which separate different magnetic phases and even vortices inside the DW, we found an interesting combination of DWs and vortices. Namely we show that equivalent magnetic phases may be linked together with a vortex going through the other magnetic phase. This configuration may correspond to a stable state even in a zero external magnetic field. We also mention that this configuration is topologically similar to the 'wormholes' in the quantum gravity.
Dowling, Timothy E.; Stanley, Geoff; Bradley, Mary Elizabeth; Marshall, David P.
2017-10-01
We are working to expand the comparative planetology of vorticity-streamfunction correlations established for the atmospheres of Earth, Mars, Jupiter and Saturn to include Earth’s Antarctic Circumpolar Current (ACC), which is the only oceanic jet that encircles the planet. Interestingly, the ACC and its eddies scale like atmospheric jets and eddies on Jupiter and Saturn---the Southern Ocean is a “giant planet” with a zonal jet stream. Our input is the Southern Ocean State Estimate (SOSE; Mazloff et al 2010, J. Phys. Ocean. 40, 880-899), an optimal combination of observations and primitive-equation model that spans 2005-2010. Two hurdles not encountered in atmospheric work arise from the nonlinear equation of state of ocean water: non-zero helicity, which prevents the existence of truly neutral (analogous to adiabatic) surfaces, and the lack of a geostrophic streamfunction in general. We follow de Szoeke et al (2000, J. Phys. Ocean. 30, 2830-2852) to overcome these hurdles, regionally, by using orthobaric density as the vertical coordinate. In agreement with results for all atmospheres analyzed to date, scatter plots of Ertel potential vorticity, Q, versus Bernoulli streamfunction, B, on orthobaric density surfaces in the Southern Ocean are well correlated. The general shape of the correlation is like a hockey stick, with the “blade” corresponding to a broad horizontal region that spans the ACC, and the “handle” corresponding to shallow water. The same linear-regression Q versus B model employed for Mars is applied to the ACC (“blade”) signal. Results include that the deeper water on the equatorward side of the ACC is most prone to shear instability, and elsewhere the ACC is “supersonic” such that the net propagation of vorticity waves is eastward, not the usual westward. During the 6-year span of the SOSE data, there is a steady drift of the correlation to larger values at the top of the vertical profile, and to smaller values in the middle of
Hard wall - soft wall - vorticity scattering in shear flow
Rienstra, S.W.; Singh, D.K.
2014-01-01
An analytically exact solution, for the problem of lowMach number incident vorticity scattering at a hard-soft wall transition, is obtained in the form of Fourier integrals by using theWiener-Hopf method. Harmonic vortical perturbations of inviscid linear shear flow are scattered at the wall
Hard wall - soft wall - vorticity scattering in shear flow
Rienstra, S.W.; Singh, D.K.
2014-01-01
An analytically exact solution, for the problem of low Mach number incident vorticity scattering at a hard-soft wall transition, is obtained in the form of Fourier integrals by using the Wiener-Hopf method. Harmonic vortical perturbations of inviscid linear shear flow are scattered at the wall
LONG-TERM EVOLUTION OF PLANET-INDUCED VORTICES IN PROTOPLANETARY DISKS
International Nuclear Information System (INIS)
Fu, Wen; Li, Hui; Li, Shengtai; Lubow, Stephen
2014-01-01
Recent observations of large-scale asymmetric features in protoplanetary disks suggest that large-scale vortices exist in such disks. Massive planets are known to be able to produce deep gaps in protoplanetary disks. The gap edges could become hydrodynamically unstable to the Rossby wave/vortex instability and form large-scale vortices. In this study we examine the long-term evolution of these vortices by carrying out high-resolution two-dimensional hydrodynamic simulations that last more than 10 4 orbits (measured at the planet's orbit). We find that the disk viscosity has a strong influence on both the emergence and lifetime of vortices. In the outer disk region where asymmetric features are observed, our simulation results suggest that the disk viscous α needs to be low, ∼10 –5 -10 –4 , to sustain vortices to thousands and up to 10 4 orbits in certain cases. The chance of finding a vortex feature in a disk then decreases with smaller planet orbital radius. For α ∼ 10 –3 or larger, even planets with masses of 5 M J will have difficulty either producing or sustaining vortices. We have also studied the effects of different disk temperatures and planet masses. We discuss the implications of our findings on current and future protoplanetary disk observations
Lagrangian Curves on Spectral Curves of Monopoles
International Nuclear Information System (INIS)
Guilfoyle, Brendan; Khalid, Madeeha; Ramon Mari, Jose J.
2010-01-01
We study Lagrangian points on smooth holomorphic curves in TP 1 equipped with a natural neutral Kaehler structure, and prove that they must form real curves. By virtue of the identification of TP 1 with the space LE 3 of oriented affine lines in Euclidean 3-space, these Lagrangian curves give rise to ruled surfaces in E 3 , which we prove have zero Gauss curvature. Each ruled surface is shown to be the tangent lines to a curve in E 3 , called the edge of regression of the ruled surface. We give an alternative characterization of these curves as the points in E 3 where the number of oriented lines in the complex curve Σ that pass through the point is less than the degree of Σ. We then apply these results to the spectral curves of certain monopoles and construct the ruled surfaces and edges of regression generated by the Lagrangian curves.
Minimal local Lagrangians for higher-spin geometry
International Nuclear Information System (INIS)
Francia, Dario; Sagnotti, Augusto
2005-01-01
The Fronsdal Lagrangians for free totally symmetric rank-s tensors φ μ 1 ...μ s rest on suitable trace constraints for their gauge parameters and gauge fields. Only when these constraints are removed, however, the resulting equations reflect the expected free higher-spin geometry. We show that geometric equations, in both their local and non-local forms, can be simply recovered from local Lagrangians with only two additional fields, a rank-(s-3) compensator α μ 1 ...μ s-3 and a rank-(s-4) Lagrange multiplier β μ 1 ...μ s-4 . In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors ψ μ 1 ...μ n can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n-2) compensator ξ μ 1 ...μ n-2 and a rank-(n-3) Lagrange multiplier λ μ 1 ...μ n-3
Inward propagating chemical waves in Taylor vortices.
Thompson, Barnaby W; Novak, Jan; Wilson, Mark C T; Britton, Melanie M; Taylor, Annette F
2010-04-01
Advection-reaction-diffusion (ARD) waves in the Belousov-Zhabotinsky reaction in steady Taylor-Couette vortices have been visualized using magnetic-resonance imaging and simulated using an adapted Oregonator model. We show how propagating wave behavior depends on the ratio of advective, chemical and diffusive time scales. In simulations, inward propagating spiral flamelets are observed at high Damköhler number (Da). At low Da, the reaction distributes itself over several vortices and then propagates inwards as contracting ring pulses--also observed experimentally.
Influence of Initial Vorticity Distribution on Axisymmetric Vortex Breakdown and Reconnection
Young, Larry A.
2007-01-01
An analytical treatment has been developed to study some of the axisymmetric vortex breakdown and reconnection fluid dynamic processes underlying body-vortex interactions that are frequently manifested in rotorcraft and propeller-driven fixed-wing aircraft wakes. In particular, the presence of negative vorticity in the inner core of a vortex filament (one example of which is examined in this paper) subsequent to "cutting" by a solid body has a profound influence on the vortex reconnection, leading to analog flow behavior similar to vortex breakdown phenomena described in the literature. Initial vorticity distributions (three specific examples which are examined) without an inner core of negative vorticity do not exhibit vortex breakdown and instead manifest diffusion-like properties while undergoing vortex reconnection. Though this work focuses on laminar vortical flow, this work is anticipated to provide valuable insight into rotary-wing aerodynamics as well as other types of vortical flow phenomena.
4D-flat compactifications with brane vorticities
International Nuclear Information System (INIS)
Randjbar Daemi, S.; Rubakov, V.
2004-07-01
We present solutions in six-dimensional gravity coupled to a sigma model, in the presence of three-brane sources. The space transverse to the branes is a compact non-singular manifold. The example of O(3) sigma model in the presence of two three-branes is worked out in detail. We show that the four-dimensional flatness is obtained with a single condition involving the brane tensions, which are in general different and may be both positive, and another characteristic of the branes, vorticity. We speculate that the adjustment of the effective four- dimensional cosmological constant may occur through the exchange of vorticity between the branes. We then give exact instanton type solutions for sigma models targeted on a general Kaehler manifold, and elaborate in this framework on multi-instantons of the O(3) sigma model. The latter have branes, possibly with vorticities, at the instanton positions, thus generalizing our two-brane solution. (author)
4d-flat compactifications with brane vorticities
International Nuclear Information System (INIS)
Randjbar-Daemi, Seif; Rubakov, Valery
2004-01-01
We present solutions in six-dimensional gravity coupled to a sigma model, in the presence of three-brane sources. The space transverse to the branes is a compact non-singular manifold. The example of O(3) sigma model in the presence of two three-branes is worked out in detail. We show that the four-dimensional flatness is obtained with a single condition involving the brane tensions, which are in general different and may be both positive, and another characteristic of the branes, vorticity. We speculate that the adjustment of the effective four-dimensional cosmological constant may occur through the exchange of vorticity between the branes. We then give exact instanton type solutions for sigma models targeted on a general Kaehler manifold, and elaborate in this framework on multi-instantons of the O(3) sigma model. The latter have branes, possibly with vorticities, at the instanton positions, thus generalizing our two-brane solution. (author)
An ambitwistor Yang-Mills Lagrangian
International Nuclear Information System (INIS)
Mason, L.J.; Skinner, D.
2006-01-01
We introduce a Chern-Simons Lagrangian for Yang-Mills theory as formulated on ambitwistor space via the Ward, Isenberg, Yasskin, Green, Witten construction. The Lagrangian requires the selection of a codimension-2 Cauchy-Riemann submanifold which is naturally picked out by the choice of space-time reality structure and we focus on the choice of Euclidean signature. The action is shown to give rise to a space-time action that is equivalent to the standard one, but has just cubic vertices. We identify the ambitwistor propagators and vertices and work out their corresponding expressions on space-time and momentum space. It is proposed that this formulation of Yang-Mills theory underlies the recursion relations of Britto, Cachazo, Feng and Witten and provides the generating principle for twistor diagrams for gauge theory
Numerical simulation of cavitation surge and vortical flows in a diffuser with swirling flow
Energy Technology Data Exchange (ETDEWEB)
Ji, Bin; Wang, Jiong; Xiao, L. Z.; Long, X. [Wuhan University, Hubei (China); Luo, X. [Tsinghua University, Beijing (China); Miyagawa, K. [Waseda University, Tokyo (Japan); Tsujimoto, Yoshinobu [Osaka University, Osaka (Japan)
2016-06-15
The strong swirling flow at the exit of the runner of a Francis turbine at part load causes flow instabilities and cavitation surges in the draft tube, deteriorating the performance of the hydraulic power system. The unsteady cavitating turbulent flow in the draft tube is simplified and modeled by a diffuser with swirling flow using the Scale-adaptive simulation method. Unsteady characteristics of the vortex rope structure and the underlying mechanisms for the interactions between the cavitation and the vortices are both revealed. The generation and evolution of the vortex rope structures are demonstrated with the help of the iso-surfaces of the vapor volume fraction and the Qcriterion. Analysis based on the vorticity transport equation suggests that the vortex dilatation term is much larger along the cavity interface in the diffuser inlet and modifies the vorticity field in regions with high density and pressure gradients. The present work is validated by comparing two types of cavitation surges observed experimentally in the literature with further interpretations based on simulations.
Continuous control of asymmetric forebody vortices in a bi-stable state
Wang, Qi-te; Cheng, Ke-ming; Gu, Yun-song; Li, Zhuo-qi
2018-02-01
Aiming at the problem of continuous control of asymmetric forebody vortices at a high angle of attack in a bi-stable regime, a dual synthetic jet actuator embedded in an ogive forebody was designed. Alternating unsteady disturbance with varying degree asymmetrical flow fields near the nozzles is generated by adjusting the duty cycle of the drive signal of the actuator, specifically embodying the asymmetric time-averaged pattern of jet velocity, vorticity, and turbulent kinetic energy. Experimental results show that within the range of relatively high angles of attack, including the angle-of-attack region in a bi-stable state, the lateral force of the ogive forebody is continuously controlled by adjusting the duty cycle of the drive signal; the position of the forebody vortices in space, the vorticity magnitude, the total pressure coefficient near the vortex core, and the vortex breakdown location are continuously changed with the duty cycle increased observed from the time-averaged flow field. Instantaneous flow field results indicate that although the forebody vortices are in an unsteady oscillation state, a continuous change in the forebody vortices' oscillation balance position as the duty cycle increases leads to a continuous change in the model's surface pressure distribution and time-averaged lateral force. Different from the traditional control principle, in this study, other different degree asymmetrical states of the forebody vortices except the bi-stable state are obtained using the dual synthetic jet control technology.
A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
Li, Wenliang
2018-04-01
We propose a framework for Lorentz-invariant Lagrangian field theories where Ostrogradsky's scalar ghosts could be absent. A key ingredient is the generalized Kronecker delta. The general Lagrangians are reformulated in the language of differential forms. The absence of higher order equations of motion for the scalar modes stems from the basic fact that every exact form is closed. The well-established Lagrangian theories for spin-0, spin-1, p-form, spin-2 fields have natural formulations in this framework. We also propose novel building blocks for Lagrangian field theories. Some of them are novel nonlinear derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar ghosts are absent in these fully nonlinear theories.
Lagrangian-similarity diffusion-deposition model
International Nuclear Information System (INIS)
Horst, T.W.
1979-01-01
A Lagrangian-similarity diffusion model has been incorporated into the surface-depletion deposition model. This model predicts vertical concentration profiles far downwind of the source that agree with those of a one-dimensional gradient-transfer model
A qualitative semi-classical treatment of an isolated semi-polar quantum dot
International Nuclear Information System (INIS)
Young, Toby D
2011-01-01
To qualitatively determine the behaviour of micro-macro properties of a quantum dot grown in a non-polar direction, we propose a simple semi-classical model based on well established ideas. We take into account the following empirical phenomena: (i) The displacement and induced strain at heterojunctions; (ii) The electrostatic potential arising from piezoelectric and spontaneous polarisation; and (iii) The localisation of excitons (particle-hole pairs) arising from quantum confinement. After some algebraic manipulation used to cast the formalism into an arbitrarily rotated frame, a numerical model is developed for the case of a semi-polar wurtzite GaN quantum dot buried in a wurtzite AlN matrix. This scheme is found to provide a satisfying qualitative description of an isolated semi-polar quantum dot in a way that is accessible to further physical interpretation and quantification.
Leading-order classical Lagrangians for the nonminimal standard-model extension
Reis, J. A. A. S.; Schreck, M.
2018-03-01
In this paper, we derive the general leading-order classical Lagrangian covering all fermion operators of the nonminimal standard-model extension (SME). Such a Lagrangian is considered to be the point-particle analog of the effective field theory description of Lorentz violation that is provided by the SME. At leading order in Lorentz violation, the Lagrangian obtained satisfies the set of five nonlinear equations that govern the map from the field theory to the classical description. This result can be of use for phenomenological studies of classical bodies in gravitational fields.
Synthesis and characterization of semi-IPNs based on PVP and PLLA
International Nuclear Information System (INIS)
Camilo, A.P.R.; Mano, V.; Felisberti, M.I.
2010-01-01
The specific interest in the synthesis of semi-IPNs based on PLLA and PVP homopolymers due to the fact these are biodegradable and biocompatible, which allows us to infer applications in the medical field as sutures, implants, matrices for controlled release of drugs etc. The objective was to prepare a multicomponent material amphiphile in the form of semi-interpenetrating polymer networks, based on poly (L-lactide), PLLA, hydrophobic homopolymer, and poly (vinylpyrrolidone), PVP, hydrophilic component. The preparation of semi-IPN combined the polymerization and crosslinking of N-vinylpyrrolidone in the presence of poly (L-lactide). The products were characterized by spectroscopic and thermal methods. (author)
Infrared and visible image fusion based on total variation and augmented Lagrangian.
Guo, Hanqi; Ma, Yong; Mei, Xiaoguang; Ma, Jiayi
2017-11-01
This paper proposes a new algorithm for infrared and visible image fusion based on gradient transfer that achieves fusion by preserving the intensity of the infrared image and then transferring gradients in the corresponding visible one to the result. The gradient transfer suffers from the problems of low dynamic range and detail loss because it ignores the intensity from the visible image. The new algorithm solves these problems by providing additive intensity from the visible image to balance the intensity between the infrared image and the visible one. It formulates the fusion task as an l 1 -l 1 -TV minimization problem and then employs variable splitting and augmented Lagrangian to convert the unconstrained problem to a constrained one that can be solved in the framework of alternating the multiplier direction method. Experiments demonstrate that the new algorithm achieves better fusion results with a high computation efficiency in both qualitative and quantitative tests than gradient transfer and most state-of-the-art methods.
Gopi, Varun P; Palanisamy, P; Wahid, Khan A; Babyn, Paul; Cooper, David
2013-01-01
Micro-computed tomography (micro-CT) plays an important role in pre-clinical imaging. The radiation from micro-CT can result in excess radiation exposure to the specimen under test, hence the reduction of radiation from micro-CT is essential. The proposed research focused on analyzing and testing an alternating direction augmented Lagrangian (ADAL) algorithm to recover images from random projections using total variation (TV) regularization. The use of TV regularization in compressed sensing problems makes the recovered image quality sharper by preserving the edges or boundaries more accurately. In this work TV regularization problem is addressed by ADAL which is a variant of the classic augmented Lagrangian method for structured optimization. The per-iteration computational complexity of the algorithm is two fast Fourier transforms, two matrix vector multiplications and a linear time shrinkage operation. Comparison of experimental results indicate that the proposed algorithm is stable, efficient and competitive with the existing algorithms for solving TV regularization problems. Copyright © 2013 Elsevier Ltd. All rights reserved.
Dimensional reduction of 10d heterotic string effective lagrangian with higher derivative terms
International Nuclear Information System (INIS)
Lalak, Z.; Pawelczyk, J.
1989-11-01
Dimensional reduction of the 10d Supergravity-Yang-Mills theories containing up to four derivatives is described. Unexpected nondiagonal corrections to 4d gauge kinetic function and negative contributions to scalar potential are found. We analyzed the general structure of the resulting lagrangian and discuss the possible phenomenological consequences. (author)
Lagrangian descriptors of driven chemical reaction manifolds.
Craven, Galen T; Junginger, Andrej; Hernandez, Rigoberto
2017-08-01
The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.
International Nuclear Information System (INIS)
Fujimoto, Kazuya; Tsubota, Makoto
2011-01-01
We consider a trapped atomic Bose-Einstein condensate penetrated by a repulsive Gaussian potential and theoretically investigate the dynamics induced by oscillating the Gaussian potential. Our study is based on the numerical calculation of the two-dimensional Gross-Pitaevskii equation. Our calculation reveals the dependence of the characteristic behavior of the condensate on the amplitude and frequency of the oscillating potential. These dynamics are deeply related to the nucleation and dynamics of quantized vortices and solitons. When the potential oscillates with a large amplitude, it nucleates many vortex pairs that move away from the potential. When the amplitude of the oscillation is small, it nucleates solitons through an annihilation of vortex pairs. We discuss three issues concerning the nucleation of vortices. The first is the phase diagram for the nucleation of vortices and solitons near the oscillating potential. The second is the mechanism and critical velocity of the nucleation. The critical velocity of the nucleation is an important issue in quantum fluids, and we propose an expression for the velocity containing both the coherence length and the size of the potential. The third is the divergence of the nucleation time, which is the time it takes for the potential to nucleate vortices, near the critical parameters for vortex nucleation.
Effects of sharp vorticity gradients in two-dimensional hydrodynamic turbulence
DEFF Research Database (Denmark)
Kuznetsov, E.A.; Naulin, Volker; Nielsen, Anders Henry
2007-01-01
The appearance of sharp vorticity gradients in two-dimensional hydrodynamic turbulence and their influence on the turbulent spectra are considered. We have developed the analog of the vortex line representation as a transformation to the curvilinear system of coordinates moving together with the ......The appearance of sharp vorticity gradients in two-dimensional hydrodynamic turbulence and their influence on the turbulent spectra are considered. We have developed the analog of the vortex line representation as a transformation to the curvilinear system of coordinates moving together...... with the divorticity lines. Compressibility of this mapping can be considered as the main reason for the formation of the sharp vorticity gradients at high Reynolds numbers. For two-dimensional turbulence in the case of strong anisotropy the sharp vorticity gradients can generate spectra which fall off as k−3 at large...
Liu, Xiao; Shi, Jun; Zhou, Shichong; Lu, Minhua
2014-01-01
The dimensionality reduction is an important step in ultrasound image based computer-aided diagnosis (CAD) for breast cancer. A newly proposed l2,1 regularized correntropy algorithm for robust feature selection (CRFS) has achieved good performance for noise corrupted data. Therefore, it has the potential to reduce the dimensions of ultrasound image features. However, in clinical practice, the collection of labeled instances is usually expensive and time costing, while it is relatively easy to acquire the unlabeled or undetermined instances. Therefore, the semi-supervised learning is very suitable for clinical CAD. The iterated Laplacian regularization (Iter-LR) is a new regularization method, which has been proved to outperform the traditional graph Laplacian regularization in semi-supervised classification and ranking. In this study, to augment the classification accuracy of the breast ultrasound CAD based on texture feature, we propose an Iter-LR-based semi-supervised CRFS (Iter-LR-CRFS) algorithm, and then apply it to reduce the feature dimensions of ultrasound images for breast CAD. We compared the Iter-LR-CRFS with LR-CRFS, original supervised CRFS, and principal component analysis. The experimental results indicate that the proposed Iter-LR-CRFS significantly outperforms all other algorithms.
Dynamics of two-dimensional solitary vortices in a low-β plasma with convective motion
International Nuclear Information System (INIS)
Makino, Mitsuhiro; Kamimura, Tetsuo; Taniuti, Tosiya.
1980-12-01
Numerical studies of the Hasegawa-Mima equation, derived in the context of drift waves but equivalent to the quasigeostrophic vortex potential equation for Rossby waves, show the stable properties of solitary vortices which are two dimensional, localized, steady and translating solutions of this same equation. A solitary vortex can propagate only in the direction (x-direction) perpendicular to the density gradient. When this solitary vortex solution is inclined at some angle with respect to the x-axis, its propagation direction oscillates in the x and y plane. In two dimensional collisions, i.e. head-on collision and overtaking, solitary vortices interact two-dimensionally and recover their initial shapes at the end of both types of collisions. (author)
Böckmann, Marcus; Doltsinis, Nikos L; Marx, Dominik
2015-06-09
An extended Lagrangian formalism that allows for a smooth transition between two different descriptions of interactions during a molecular dynamics simulation is presented. This time-adaptive method is particularly useful in the context of multiscale simulation as it provides a sound recipe to switch on demand between different hierarchical levels of theory, for instance between ab initio ("QM") and force field ("MM") descriptions of a given (sub)system in the course of a molecular dynamics simulation. The equations of motion can be integrated straightforwardly using the usual propagators, such as the Verlet algorithm. First test cases include a bath of harmonic oscillators, of which a subset is switched to a different force constant and/or equilibrium position, as well as an all-MM to QM/MM transition in a hydrogen-bonded water dimer. The method is then applied to a smectic 8AB8 liquid crystal and is shown to be able to switch dynamically a preselected 8AB8 molecule from an all-MM to a QM/MM description which involves partition boundaries through covalent bonds. These examples show that the extended Lagrangian approach is not only easy to implement into existing code but that it is also efficient and robust. The technique moreover provides easy access to a conserved energy quantity, also in cases when Nosé-Hoover chain thermostatting is used throughout dynamical switching. A simple quadratic driving potential proves to be sufficient to guarantee a smooth transition whose time scale can be easily tuned by varying the fictitious mass parameter associated with the auxiliary variable used to extend the Lagrangian. The method is general and can be applied to time-adaptive switching on demand between two different levels of theory within the framework of hybrid scale-bridging simulations.
International Nuclear Information System (INIS)
Zhu, Zhaohuan; Stone, James M.
2014-01-01
We study particle trapping at the edge of a gap opened by a planet in a protoplanetary disk. In particular, we explore the effects of turbulence driven by the magnetorotational instability on particle trapping, using global three-dimensional magnetohydrodynamic (MHD) simulations including Lagrangian dust particles. We study disks either in the ideal MHD limit or dominated by ambipolar diffusion (AD) which plays an essential role at the outer regions of a protoplanetary disk. With ideal MHD, strong turbulence (the equivalent viscosity parameter α ∼ 10 –2 ) in disks prevents vortex formation at the edge of the gap opened by a 9 M J planet, and most particles (except the particles that drift fastest) pile up at the outer gap edge almost axisymmetrically. When AD is considered, turbulence is significantly suppressed (α ≲ 10 –3 ), and a large vortex forms at the edge of the planet induced gap, which survives ∼1000 orbits. The vortex can efficiently trap dust particles that span 3 orders of magnitude in size within 100 planetary orbits. We have also carried out two-dimensional hydrodynamical (HD) simulations using viscosity as an approximation to MHD turbulence. These HD simulations can reproduce vortex generation at the gap edge as seen in MHD simulations. Finally, we use our simulation results to generate synthetic images for ALMA dust continuum observations on Oph IRS 48 and HD 142527, which show good agreement with existing observations. Predictions for future ALMA cycle 2 observations have been made. We conclude that the asymmetry in ALMA observations can be explained by dust trapping vortices and the existence of vortices could be the evidence that the outer protoplanetary disks are dominated by AD with α < 10 –3 at the disk midplane.
Integration over families of Lagrangian submanifolds in BV formalism
Mikhailov, Andrei
2018-03-01
Gauge fixing is interpreted in BV formalism as a choice of Lagrangian submanifold in an odd symplectic manifold (the BV phase space). A natural construction defines an integration procedure on families of Lagrangian submanifolds. In string perturbation theory, the moduli space integrals of higher genus amplitudes can be interpreted in this way. We discuss the role of gauge symmetries in this construction. We derive the conditions which should be imposed on gauge symmetries for the consistency of our integration procedure. We explain how these conditions behave under the deformations of the worldsheet theory. In particular, we show that integrated vertex operator is actually an inhomogeneous differential form on the space of Lagrangian submanifolds.
El-Nabulsi, Rami Ahmad
2018-03-01
Recently, the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations. Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties. One interesting form related to the inverse variational problem is the logarithmic Lagrangian, which has a number of motivating features related to the Liénard-type and Emden nonlinear differential equations. Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians. In this communication, we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians. One interesting consequence concerns the emergence of an extra pressure term, which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field. The case of the stellar halo of the Milky Way is considered.
Late-Stage Vortical Structures and Eddy Motions in a Transitional Boundary Layer
International Nuclear Information System (INIS)
Xiao-Bing, Liu; Zheng-Qing, Chen; Chao-Qun, Liu
2010-01-01
A high-order direct numerical simulation of flow transition over a flat-plate at a free stream Mach number 0.5 is carried out. Formation and development of three-dimensional vortical structures, typically shown as A-vortices, hairpin vortices and ring-like vortices, are observed. Numerical results show that there is a strong downdraft motion of fluid excited by every ring-like vortex in the late-stage of the transition process. At two sides of the vortical structure centerline, the downdraft motions induced by the ring-like vortex and the rotating legs superimpose. This is responsible for the appearance of a high-speed streak associated with the positive spike observed in a previous investigation and the appearance of a high-shear layer in the near wall region. (fundamental areas of phenomenology(including applications))
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation
Directory of Open Access Journals (Sweden)
Yuncheng You
2008-12-01
Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.
Longitudinal vortices in a transitioning boundary layer
International Nuclear Information System (INIS)
Anders, J.B.; Backwelder, R.F.
1980-01-01
Naturally occurring spanwise variations of the streamwise velocity component, characteristic of longitudinal vortices embedded in a transitioning boundary layer were explored using hot-wire anemometers. A vibrating ribbon introduced stable or unstable Tollmien-Schlichting waves into the laminar boundary layer. These damped or growing disturbances always developed a strong three-dimensional pattern even though no spanwise perturbations were artificially induced. Changing the radius of the leading edge and other modifications to the flat plate, wind tunnel and boundary layer did not alter the spanwise wavelength of the vortices. (orig.)
Scaling properties of Wilson loops pierced by P-vortices
DEFF Research Database (Denmark)
Dunn, Patrick; Greensite, Jeffrey Paul
2012-01-01
P-vortices, in an SU(N) lattice gauge theory, are excitations on the center-projected Z(N) lattice. We study the ratio of expectation values of SU(2) Wilson loops, on the unprojected lattice, linked to a single P-vortex, to that of Wilson loops which are not linked to any P-vortices. When...
Imparting small vorticity to a Bianchi type-VIh empty spacetime
Batakis, Nikos A.
1981-04-01
We present and briefly discuss a Bianchi type-VIh empty spacetime. The field equations have been solved after being linearized with respect to a parameter which imparts vorticity to the model. The limit of zero vorticity is an already known solution.
Internal and vorticity waves in decaying stratified flows
Matulka, A.; Cano, D.
2009-04-01
Most predictive models fail when forcing at the Rossby deformation Radius is important and a large range of scales have to be taken into account. When mixing of reactants or pollutants has to be accounted, the range of scales spans from hundreds of Kilometers to the Bachelor or Kolmogorov sub milimiter scales. We present some theoretical arguments to describe the flow in terms of the three dimensional vorticity equations, using a lengthscale related to the vorticity (or enstrophy ) transport. Effect of intermittent eddies and non-homogeneity of diffusion are also key issues in the environment because both stratification and rotation body forces are important and cause anisotropy/non-homogeneity. These problems need further theoretical, numerical and observational work and one approach is to try to maximize the relevant geometrical information in order to understand and therefore predict these complex environmental dispersive flows. The importance of the study of turbulence structure and its relevance in diffusion of contaminants in environmental flows is clear when we see the effect of environmental disasters such as the Prestige oil spill or the Chernobil radioactive cloud spread in the atmosphere. A series of Experiments have been performed on a strongly stratified two layer fluid consisting of Brine in the bottom and freshwater above in a 1 square meter tank. The evolution of the vortices after the passage of a grid is video recorded and Particle tracking is applied on small pliolite particles floating at the interface. The combination of internal waves and vertical vorticity produces two separate time scales that may produce resonances. The vorticity is seen to oscilate in a complex way, where the frecuency decreases with time.
On the dynamics of second-order Lagrangian systems
Directory of Open Access Journals (Sweden)
Ronald Adams
2017-04-01
Full Text Available In this article we are concerned with improving the twist condition for second-order Lagrangian systems. We characterize a local Twist property and demonstrate how results on the existence of simple closed characteristics can be extended in the case of the Swift-Hohenberg / extended Fisher-Kolmogorov Lagrangian. Finally, we describe explicit evolution equations for broken geodesic curves that could be used to investigate more general systems or closed characteristics.
Ma, Chi; Varghese, Tomy
2012-04-01
Accurate cardiac deformation analysis for cardiac displacement and strain imaging over time requires Lagrangian description of deformation of myocardial tissue structures. Failure to couple the estimated displacement and strain information with the correct myocardial tissue structures will lead to erroneous result in the displacement and strain distribution over time. Lagrangian based tracking in this paper divides the tissue structure into a fixed number of pixels whose deformation is tracked over the cardiac cycle. An algorithm that utilizes a polar-grid generated between the estimated endocardial and epicardial contours for cardiac short axis images is proposed to ensure Lagrangian description of the pixels. Displacement estimates from consecutive radiofrequency frames were then mapped onto the polar grid to obtain a distribution of the actual displacement that is mapped to the polar grid over time. A finite element based canine heart model coupled with an ultrasound simulation program was used to verify this approach. Segmental analysis of the accumulated displacement and strain over a cardiac cycle demonstrate excellent agreement between the ideal result obtained directly from the finite element model and our Lagrangian approach to strain estimation. Traditional Eulerian based estimation results, on the other hand, show significant deviation from the ideal result. An in vivo comparison of the displacement and strain estimated using parasternal short axis views is also presented. Lagrangian displacement tracking using a polar grid provides accurate tracking of myocardial deformation demonstrated using both finite element and in vivo radiofrequency data acquired on a volunteer. In addition to the cardiac application, this approach can also be utilized for transverse scans of arteries, where a polar grid can be generated between the contours delineating the outer and inner wall of the vessels from the blood flowing though the vessel.
Dynamics of vortices in complex wakes: Modeling, analysis, and experiments
Basu, Saikat
The thesis develops singly-periodic mathematical models for complex laminar wakes which are formed behind vortex-shedding bluff bodies. These wake structures exhibit a variety of patterns as the bodies oscillate or are in close proximity of one another. The most well-known formation comprises two counter-rotating vortices in each shedding cycle and is popularly known as the von Karman vortex street. Of the more complex configurations, as a specific example, this thesis investigates one of the most commonly occurring wake arrangements, which consists of two pairs of vortices in each shedding period. The paired vortices are, in general, counter-rotating and belong to a more general definition of the 2P mode, which involves periodic release of four vortices into the flow. The 2P arrangement can, primarily, be sub-classed into two types: one with a symmetric orientation of the two vortex pairs about the streamwise direction in a periodic domain and the other in which the two vortex pairs per period are placed in a staggered geometry about the wake centerline. The thesis explores the governing dynamics of such wakes and characterizes the corresponding relative vortex motion. In general, for both the symmetric as well as the staggered four vortex periodic arrangements, the thesis develops two-dimensional potential flow models (consisting of an integrable Hamiltonian system of point vortices) that consider spatially periodic arrays of four vortices with their strengths being +/-Gamma1 and +/-Gamma2. Vortex formations observed in the experiments inspire the assumed spatial symmetry. The models demonstrate a number of dynamic modes that are classified using a bifurcation analysis of the phase space topology, consisting of level curves of the Hamiltonian. Despite the vortex strengths in each pair being unequal in magnitude, some initial conditions lead to relative equilibrium when the vortex configuration moves with invariant size and shape. The scaled comparisons of the
Jacobitz, Frank G; Schneider, Kai; Bos, Wouter J T; Farge, Marie
2016-01-01
The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar dependence on the rotation to shear ratio. The variance and flatness of both accelerations are analyzed and the extreme values of the Eulerian acceleration are observed to be above those of the Lagrangian acceleration. For strong rotation it is observed that flatness yields values close to three, corresponding to Gaussian-like behavior, and for moderate and vanishing rotation the flatness increases. Furthermore, the Lagrangian and Eulerian accelerations are shown to be strongly correlated for strong rotation due to a reduced nonlinear term in this case. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian acceleration is even more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. Moreover, the dynamics of a passive scalar with gradient production in the direction of the mean velocity gradient is analyzed and the influence of the rotation to shear ratio is studied. Concerning the concentration of a passive scalar spread by the flow, the pdf of its Eulerian time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the Eulerian time rate of change of scalar concentration is mainly due to advection, while its Lagrangian counterpart is only due to gradient production and viscous dissipation.
The influence of trailed vorticity on flutter speed estimations
International Nuclear Information System (INIS)
Pirrung, Georg R; Madsen, Helge Aa; Kim, Taeseong
2014-01-01
This paper briefly describes the implementation of a coupled near and far wake model for wind turbine rotor induction in the aeroelastic code HAWC2 and its application for flutter analysis of the NREL 5 MW wind turbine. The model consists of a far wake part based on Blade Element Momentum (BEM) theory, which is coupled with Beddoes' near wake model for trailed vorticity. The first part of this work outlines the implementation in HAWC2, with a focus on the interaction of the induction from the blade based near wake model with the induction from the polar grid based BEM model in HAWC2. The influence of the near wake model on the aeroelastic stability of the blades of the NREL 5 MW turbine in overspeed conditions is investigated in the second part of the paper. The analysis is based on a runaway case in which the turbine is free to speed up without generator torque and vibrations start building up at a critical rotor speed. Blades with modified torsional and flapwise stiffness are also investigated. A flutter analysis is often part of the stability investigations for new blades but is normally carried out with engineering models that do not include the influence of unsteady trailed vorticity. Including this influence results in a slightly increased safety margin against classical flutter in all simulated cases
Constraint theory, singular lagrangians and multitemporal dynamics
International Nuclear Information System (INIS)
Lusanna, L.
1988-01-01
Singular Lagrangians and constraint theory permeate theoretical physics, as shown by the relevance of gauge theories, string models and general relativity. Their study used finite---dimensional models as a guide to develop the theory, but their main use was in classical field theory, due to the necessity of understanding their quantization. The covariant quantization of singular Lagrangians led to the BRST approach and to the theory of the effective action. On the other hand their phase---space formulation, culminated with the BFV approach for first class, second class and reducible constraints. It, in turn, gave new insights in the theory of singular Lagrangians and constraints and in their cohomological aspects. However the Hamiltonian approach to field theory is highly nontrivial, is open to criticism due to its problems with locality, geometry and manifest covariance and its canonical quantization has still to be developed, because there is no proof of the renormalizability of the Schroedinger representation of field theory. This paper discusses how, notwithstanding these developments, there is still a big amount of ambiguity at every level of the theory
Acoustic streaming: an arbitrary Lagrangian-Eulerian perspective.
Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco
2017-08-25
We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.
Lagrangian intersection Floer theory anomaly and obstruction, part II
Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru
2009-01-01
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A_\\infty-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A_\\infty algebras and A_\\infty bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-co...
Lagrangian intersection Floer theory anomaly and obstruction, part I
Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru
2009-01-01
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A_\\infty-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A_\\infty algebras and A_\\infty bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-co...
Lagrangian formulation of classical BMT-theory
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Pupasov-Maksimov, Andrey; Deriglazov, Alexei; Guzman, Walberto
2013-01-01
Full text: The most popular classical theory of electron has been formulated by Bargmann, Michel and Telegdi (BMT) in 1959. The BMT equations give classical relativistic description of a charged particle with spin and anomalous magnetic momentum moving in homogeneous electro-magnetic field. This allows to study spin dynamics of polarized beams in uniform fields. In particular, first experimental measurements of muon anomalous magnetic momentum were done using changing of helicity predicted by BMT equations. Surprisingly enough, a systematic formulation and the analysis of the BMT theory are absent in literature. In the present work we particularly fill this gap by deducing Lagrangian formulation (variational problem) for BMT equations. Various equivalent forms of Lagrangian will be discussed in details. An advantage of the obtained classical model is that the Lagrangian action describes a relativistic spinning particle without Grassmann variables, for both free and interacting cases. This implies also the possibility of canonical quantization. In the interacting case, an arbitrary electromagnetic background may be considered, which generalizes the BMT theory formulated to the case of homogeneous fields. The classical model has two local symmetries, which gives an interesting example of constrained classical dynamics. It is surprising, that the case of vanishing anomalous part of the magnetic momentum is naturally highlighted in our construction. (author)
Jeong, Peter Inuk
Synthetic jet (SJ) control of a low-Reynolds number, unsteady, compressible, viscous flow over a NACA 65-(1)412 airfoil, typical for unmanned air vehicles and gas turbines, has been investigated computationally. A particular focus was placed in the development and control of Lagrangian Coherent Structures (LCS) and the associated Finite-Time Lyapunov Exponent (FTLE) fields. The FTLE fields quantitatively measure of the repulsion rate in forward-time and the attraction rate in backward-time, and provide a unique perspective on effective flow control. A Discontinuous-Galerkin (DG) methods, high-fidelity Navier-Stokes solver performs direct numerical simulation (DNS) of the airfoil flow. Three SJ control strategies have been investigated: immediately downstream of flow separation, normal to the separated shear layer; near the leading edge, normal to the airfoil suction side; near the trailing edge, normal to the airfoil pressure side. A finite difference algorithm computes the FTLE from DNS velocity data. A baseline flow without SJ control is compared to SJ actuated flows. The baseline flow forms a regular, time-periodic, asymmetric von Karman vortex street in the wake. The SJ downstream of flow separation increases recirculation region vorticity and reduces the effective angle of attack. This decreases the time-averaged lift by 2:98% and increases the time-averaged drag by 5:21%. The leading edge SJ produces small vortices that deflect the shear layer downwards, and decreases the effective angle of attack. This reduces the time-averaged lift by 1:80%, and the time-averaged drag by 1:84%. The trailing edge SJ produces perturbations that add to pressure side vortices without affecting global flow characteristics. The time-averaged lift decreases by 0:47%, and the time-averaged drag increases by 0:20%. For all SJ cases, the aerodynamic performance is much more dependent on changes to the pressure distribution than changes to the skin friction distribution. No proposed
VISUALIZATION METHODS OF VORTICAL FLOWS IN COMPUTATIONAL FLUID DYNAMICS AND THEIR APPLICATIONS
Directory of Open Access Journals (Sweden)
K. N. Volkov
2014-05-01
Full Text Available The paper deals with conceptions and methods for visual representation of research numerical results in the problems of fluid mechanics and gas. The three-dimensional nature of unsteady flow being simulated creates significant difficulties for the visual representation of results. It complicates control and understanding of numerical data, and exchange and processing of obtained information about the flow field. Approaches to vortical flows visualization with the usage of gradients of primary and secondary scalar and vector fields are discussed. An overview of visualization techniques for vortical flows using different definitions of the vortex and its identification criteria is given. Visualization examples for some solutions of gas dynamics problems related to calculations of jets and cavity flows are presented. Ideas of the vortical structure of the free non-isothermal jet and the formation of coherent vortex structures in the mixing layer are developed. Analysis of formation patterns for spatial flows inside large-scale vortical structures within the enclosed space of the cubic lid-driven cavity is performed. The singular points of the vortex flow in a cubic lid-driven cavity are found based on the results of numerical simulation; their type and location are identified depending on the Reynolds number. Calculations are performed with fine meshes and modern approaches to the simulation of vortical flows (direct numerical simulation and large-eddy simulation. Paradigm of graphical programming and COVISE virtual environment are used for the visual representation of computational results. Application that implements the visualization of the problem is represented as a network which links are modules and each of them is designed to solve a case-specific problem. Interaction between modules is carried out by the input and output ports (data receipt and data transfer giving the possibility to use various input and output devices.
Adiabatic effective action for vortices in neutral and charged superfluids
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Hatsuda, M.; Sato, M.; Yahikozawa, S.; Hatsuda, T.
1996-01-01
Adiabatic effective action for vortices in neutral and charged superfluids at zero temperature are calculated using the topological Landau-Ginzburg theory recently proposed by Hatsuda, Yahikozawa, Ao and Thouless, and vortex dynamics are examined. The Berry phase term arising in the effective action naturally yields the Magnus force in both neutral and charged superfluids. It is shown that in neutral superfluid there is only one degree of freedom, namely the center of vorticities, and the vortex energy is proportional to the sum of all vorticities so that it is finite only for the vanishing total vorticity of the system. On the other hand the effective mass and the vortex energy for a vortex in charged superfluids are defined individually as expected. The effects of the vortex core on these quantities are also estimated. The possible depinning scenario which is governed by the Magnus force and the inertial mass is also discussed
Ka, Hyun W; Chung, Cheng-Shiu; Ding, Dan; James, Khara; Cooper, Rory
2018-02-01
We developed a 3D vision-based semi-autonomous control interface for assistive robotic manipulators. It was implemented based on one of the most popular commercially available assistive robotic manipulator combined with a low-cost depth-sensing camera mounted on the robot base. To perform a manipulation task with the 3D vision-based semi-autonomous control interface, a user starts operating with a manual control method available to him/her. When detecting objects within a set range, the control interface automatically stops the robot, and provides the user with possible manipulation options through audible text output, based on the detected object characteristics. Then, the system waits until the user states a voice command. Once the user command is given, the control interface drives the robot autonomously until the given command is completed. In the empirical evaluations conducted with human subjects from two different groups, it was shown that the semi-autonomous control can be used as an alternative control method to enable individuals with impaired motor control to more efficiently operate the robot arms by facilitating their fine motion control. The advantage of semi-autonomous control was not so obvious for the simple tasks. But, for the relatively complex real-life tasks, the 3D vision-based semi-autonomous control showed significantly faster performance. Implications for Rehabilitation A 3D vision-based semi-autonomous control interface will improve clinical practice by providing an alternative control method that is less demanding physically as well cognitively. A 3D vision-based semi-autonomous control provides the user with task specific intelligent semiautonomous manipulation assistances. A 3D vision-based semi-autonomous control gives the user the feeling that he or she is still in control at any moment. A 3D vision-based semi-autonomous control is compatible with different types of new and existing manual control methods for ARMs.
Directory of Open Access Journals (Sweden)
Brent Knutson
2015-01-01
Full Text Available We present a study of three-dimensional Lagrangian coherent structures (LCS near the Hong Kong International Airport and relate to previous developments of two-dimensional (2D LCS analyses. The LCS are contrasted among three independent models and against 2D coherent Doppler light detection and ranging (LIDAR data. Addition of the velocity information perpendicular to the LIDAR scanning cone helps solidify flow structures inferred from previous studies; contrast among models reveals the intramodel variability; and comparison with flight data evaluates the performance among models in terms of Lagrangian analyses. We find that, while the three models and the LIDAR do recover similar features of the windshear experienced by a landing aircraft (along the landing trajectory, their Lagrangian signatures over the entire domain are quite different—a portion of each numerical model captures certain features resembling those LCS extracted from independent 2D LIDAR analyses based on observations.
International Nuclear Information System (INIS)
Barber, R.W.; Fonty, A.
2003-01-01
This paper describes a novel vortex element method for simulating incompressible laminar flow over a two-dimensional backward-facing step. The model employs an operator-splitting technique to compute the evolution of the vorticity field downstream of abrupt changes in flow geometry. During the advective stage of the computation, a semi-Lagrangian scheme is used to update the positions of the vortex elements, whilst an analytical diffusion algorithm employing Oseen vortices is implemented during the diffusive time step. Redistributing the vorticity analytically instead of using the more traditional random-walk method enables the numerical model to simulate steady flows directly and avoids the need to filter the results to remove the oscillations created by the random-walk procedure. Model validation has been achieved by comparing the length of the recirculating eddy behind a confined backward-facing step against data from experimental and alternative numerical investigations. In addition, results from the vortex element method are compared against predictions obtained using the commercial finite-volume computational fluid dynamics code, CFD-ACE+. The results show that the vortex element scheme marginally overpredicts the length of the downstream recirculating eddy, implying that the method may be associated with an artificial reduction in the vorticity diffusion rate. Nevertheless the results demonstrate that the proposed vortex redistribution scheme provides a practical alternative to traditional random-walk discrete vortex algorithms. (author)