Applications of Lagrangian blending functions for grid generation around airplane geometries
Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.; Smith, Robert E.
1990-01-01
A simple procedure has been developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation has been employed for the grid distributions.
Application of Lagrangian blending functions for grid generation around airplane geometries
Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.
1990-01-01
A simple procedure was developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation was employed for the grid distributions.
The semi-Lagrangian method on curvilinear grids
Hamiaz Adnane
2016-09-01
Full Text Available We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Rieben, R N; White, D A; Wallin, B K; Solberg, J M
2006-06-12
We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.
Caramana, E.J.; Shashkov, M.J. [Los Alamos National Lab., NM (United States)
1997-12-31
The bane of Lagrangian hydrodynamics calculations is premature breakdown of the grid topology that results in severe degradation of accuracy and run termination often long before the assumption of Lagrangian zonal mass ceased to be valid. At short spatial grid scales this is usually referred to by the terms hourglass mode or keystone motion associated in particular with underconstrained grids such as quadrilaterals and hexahedrons in two and three dimensions, respectively. At longer spatial scales relative to the grid spacing there is what is referred to ubiquitously as spurious vorticity, or the long-thin zone problem. In both cases the result is anomalous grid distortion and tangling that has nothing to do with the actual solution, as would be the case for turbulent flow. In this work the authors show how such motions can be eliminated by the proper use of subzonal Lagrangian masses, and associated densities and pressures. These subzonal masses arise in a natural way from the fact that they require the mass associated with the nodal grid point to be constant in time. This is addition to the usual assumption of constant, Lagrangian zonal mass in staggered grid hydrodynamics scheme. The authors show that with proper discretization of subzonal forces resulting from subzonal pressures, hourglass motion and spurious vorticity can be eliminated for a very large range of problems. Finally the authors are presenting results of calculations of many test problems.
Implementation of the Semi-Lagrangian Advection Scheme on a Quasi-Uniform Overset Grid on a Sphere
无
2006-01-01
The semi-Lagrangian advection scheme is implemented on a new quasi-uniform overset (Yin-Yang) grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry with two perpendicularly-oriented latitude-longitude grid components (called Yin and Yang respectively) that overlapp each other, and this effectively avoids the coordinate singularity and the grid convergence near the poles. In this overset grid, the way of transferring data between the Yin and Yang components is the key to maintaining the accuracy and robustness in numerical solutions. A numerical interpolation for boundary data exchange, which maintains the accuracy of the original advection scheme and is computationally efficient, is given in this paper. A standard test of the solid-body advection proposed by Williamson is carried out on the Yin-Yang grid. Numerical results show that the quasi-uniform Yin-Yang grid can get around the problems near the poles, and the numerical accuracy in the original semi-Lagrangian scheme is effectively maintained in the Yin-Yang grid.
Lagrangian Quantum Homology for Lagrangian cobordism
Singer, Berit
2015-01-01
We extend the definition of Lagrangian quantum homology to monotone Lagrangian cobordism and establish its general algebraic properties. In particular we develop a relative version of Lagrangian quantum homology associated to a cobordism relative to a part of its boundary and study relations of this invariant to the ambient quantum homology.
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.
Mimetic Theory for Cell-Centered Lagrangian Finite Volume Formulation on General Unstructured Grids
Sambasivan, Shiv Kumar [Los Alamos National Laboratory; Shashkov, Mikhail J. [Los Alamos National Laboratory; Burton, Donald E. [Los Alamos National Laboratory; Christon, Mark A. [Los Alamos National Laboratory
2012-07-19
A finite volume cell-centered Lagrangian scheme for solving large deformation problems is constructed based on the hypo-elastic model and using the mimetic theory. Rigorous analysis in the context of gas and solid dynamics, and arbitrary polygonal meshes, is presented to demonstrate the ability of cell-centered schemes in mimicking the continuum properties and principles at the discrete level. A new mimetic formulation based gradient evaluation technique and physics-based, frame independent and symmetry preserving slope limiters are proposed. Furthermore, a physically consistent dissipation model is employed which is both robust and inexpensive to implement. The cell-centered scheme along with these additional new features are applied to solve solids undergoing elasto-plastic deformation.
Sitaraman, Hariswaran [National Renewable Energy Lab. (NREL), Golden, CO (United States); Grout, Ray [National Renewable Energy Lab. (NREL), Golden, CO (United States)
2015-10-30
The load balancing strategies for hybrid solvers that involve grid based partial differential equation solution coupled with particle tracking are presented in this paper. A typical Message Passing Interface (MPI) based parallelization of grid based solves are done using a spatial domain decomposition while particle tracking is primarily done using either of the two techniques. One of the techniques is to distribute the particles to MPI ranks to whose grid they belong to while the other is to share the particles equally among all ranks, irrespective of their spatial location. The former technique provides spatial locality for field interpolation but cannot assure load balance in terms of number of particles, which is achieved by the latter. The two techniques are compared for a case of particle tracking in a homogeneous isotropic turbulence box as well as a turbulent jet case. We performed a strong scaling study for more than 32,000 cores, which results in particle densities representative of anticipated exascale machines. The use of alternative implementations of MPI collectives and efficient load equalization strategies are studied to reduce data communication overheads.
Hassen, Y.J.; Koren, B.
2008-01-01
In this paper, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed Cartesian grid. The essence of the present method is that specific
MONOTONIZATION IN GLOBAL OPTIMIZATION
WU ZHIYOU; BAI FUSHENG; ZHANG LIANSHENG
2005-01-01
A general monotonization method is proposed for converting a constrained programming problem with non-monotone objective function and monotone constraint functions into a monotone programming problem. An equivalent monotone programming problem with only inequality constraints is obtained via this monotonization method. Then the existingconvexification and concavefication methods can be used to convert the monotone programming problem into an equivalent better-structured optimization problem.
Richard Liska; Mikhail Shashkov; Burton Wendroff
2011-01-01
We give a brief discussion of some of the contributions of Peter Lax to Computational Fluid Dynamics.These include the Lax-Friedrichs and Lax-Wendroff numerical schemes.We also mention his collaboration in the 1983 HLL Riemann solver. We develop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids.We apply a composite scheme that uses a LaxFriedrichs time step as a dissipative filter after several Lax-Wendroff time steps.Numerical results for Noh's infinite strength shock problem,the Sedov blast wave problem,and the Saltzman piston problem are presented.
Cohen Stuart, D.C.; Kleijn, C.R.; Kenjeres, S.
2010-01-01
In this paper we report on a newly developed particle tracking scheme for fluid flow simulations on 3D unstructured grids, aiming to provide detailed insights in the particle behaviour in complex geometries. A possible field of applications is the Magnetic Drug Targeting (MDT) technique, on which th
Monotone Boolean approximation
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.
Korshunov, A D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
2003-10-31
Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published. However, until now there has been no sufficiently complete monograph or survey of results of investigations concerning monotone Boolean functions. The object of this survey is to present the main results on monotone Boolean functions obtained during the last 50 years.
Nucci, M. C.; Leach, P. G. L.
2007-01-01
Searching for a Lagrangian may seem either a trivial endeavour or an impossible task. In this paper we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H Goldstein, {\\it Classical Mechanics}, 2nd edition (Addison-Wesley, Reading, 1980)] and the damped harmonic ...
Nucci, M. C.; Leach, P. G. L.
2007-12-01
Searching for a Lagrangian may seem either a trivial endeavor or an impossible task. In this paper, we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H. Goldstein, Classical Mechanics, 2nd edition (Addison-Wesley, Reading, MA, 1980)], and the damped harmonic oscillator. This is the first paper in a series dedicated to this subject.
Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs
X. X. HUANG; K. L. TEO; X. Q. YANG
2006-01-01
In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.
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 ...
Guionnet, A
2012-01-01
By solving a free analog of the Monge-Amp\\`ere equation, we prove a non-commutative analog of Brenier's monotone transport theorem: if an $n$-tuple of self-adjoint non-commutative random variables $Z_{1},...,Z_{n}$ satisfies a regularity condition (its conjugate variables $\\xi_{1},...,\\xi_{n}$ should be analytic in $Z_{1},...,Z_{n}$ and $\\xi_{j}$ should be close to $Z_{j}$ in a certain analytic norm), then there exist invertible non-commutative functions $F_{j}$ of an $n$-tuple of semicircular variables $S_{1},...,S_{n}$, so that $Z_{j}=F_{j}(S_{1},...,S_{n})$. Moreover, $F_{j}$ can be chosen to be monotone, in the sense that $F_{j}=\\mathscr{D}_{j}g$ and $g$ is a non-commutative function with a positive definite Hessian. In particular, we can deduce that $C^{*}(Z_{1},...,Z_{n})\\cong C^{*}(S_{1},...,S_{n})$ and $W^{*}(Z_{1},...,Z_{n})\\cong L(\\mathbb{F}(n))$. Thus our condition is a useful way to recognize when an $n$-tuple of operators generate a free group factor. We obtain as a consequence that the q-deforme...
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2002-10-19
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2004-01-28
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
Monotone partitions and almost partitions
Bonanzinga, M.; Cammaroto, F.; van Mill, J.; Pansera, B.A.
2014-01-01
In this paper we are interested in monotone versions of partitionability of topological spaces and weak versions thereof. We identify several classes of spaces with these properties by constructing trees of open sets with various properties.
Swinbank, Richard; Purser, James
2006-01-01
Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges). One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as "Fibonacci grids". They can be thought of as mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples (to give two of the many botanical examples). These grids possess virtually uniform and highly isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of these grids in shallow water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional semi-implicit and semi-Lagrangian weather prediction or climate models.
Euler-Lagrangian computation for estuarine hydrodynamics
Cheng, Ralph T.
1983-01-01
The transport of conservative and suspended matter in fluid flows is a phenomenon of Lagrangian nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an Eulerian formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an Eulerian reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the Eulerian and Lagrangian computational techniques.
Why Monotonous Repetition is Unsatisfying
Salingaros, Nikos A
2011-01-01
Human beings prefer ordered complexity and not randomness in their environment, a result of our perceptual system evolving to interpret natural forms. We also recognize monotonously repeating forms as unnatural. Although widespread in today's built environment, such forms generate reactions ranging from boredom to unease. Christopher Alexander has introduced rules for generating forms adapted to natural geometries, which show structured variation with multiple symmetries in a hierarchy of scales. It turns out to be impossible to generate monotonously repeating forms by following those rules. As it is highly probable that traditional artifacts, buildings, and cities were created instinctively using a version of the same rules, this is the reason we never find monotonously repeating forms in traditional cultures.
Lagrangian Methods Of Cosmic Web Classification
Fisher, J D; Johnson, M S T
2015-01-01
The cosmic web defines the large scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. (2012) is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or halos) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian nature admits a straight forward inclusion of the Hubble flow negating the necessity of a visually defined thresh...
Monotonicity of social welfare optima
Hougaard, Jens Leth; Østerdal, Lars Peter Raahave
2010-01-01
This paper considers the problem of maximizing social welfare subject to participation constraints. It is shown that for an income allocation method that maximizes a social welfare function there is a monotonic relationship between the incomes allocated to individual agents in a given coalition...... (with at least three members) and its participation constraint if and only if the aggregate income to that coalition is always maximized. An impossibility result demonstrates that there is no welfare maximizing allocation method in which agents' individual incomes monotonically increase in society......'s income. Thus, for any such allocation method, there are situations where some agents have incentives to prevent society in becoming richer....
Block-structured adaptive meshes and reduced grids for atmospheric general circulation models.
Jablonowski, Christiane; Oehmke, Robert C; Stout, Quentin F
2009-11-28
Adaptive mesh refinement techniques offer a flexible framework for future variable-resolution climate and weather models since they can focus their computational mesh on certain geographical areas or atmospheric events. Adaptive meshes can also be used to coarsen a latitude-longitude grid in polar regions. This allows for the so-called reduced grid setups. A spherical, block-structured adaptive grid technique is applied to the Lin-Rood finite-volume dynamical core for weather and climate research. This hydrostatic dynamics package is based on a conservative and monotonic finite-volume discretization in flux form with vertically floating Lagrangian layers. The adaptive dynamical core is built upon a flexible latitude-longitude computational grid and tested in two- and three-dimensional model configurations. The discussion is focused on static mesh adaptations and reduced grids. The two-dimensional shallow water setup serves as an ideal testbed and allows the use of shallow water test cases like the advection of a cosine bell, moving vortices, a steady-state flow, the Rossby-Haurwitz wave or cross-polar flows. It is shown that reduced grid configurations are viable candidates for pure advection applications but should be used moderately in nonlinear simulations. In addition, static grid adaptations can be successfully used to resolve three-dimensional baroclinic waves in the storm-track region.
On Attracting Lagrangian Coherent Structures
Karrasch, Daniel
2013-01-01
In this note, we show that in the autonomous, two-dimensional incompressible saddle flow, contrary to common intuition, also attracting Lagrangian Coherent Structures (LCSs) can show up as ridges of the forward finite-time Lyapunov exponent (FTLE) field. This raises the issue of characterization of attracting LCSs from forward time FTLE analysis. First, we extend recent results of Haller & Sapsis (2011) [11] on the relation between forward and backward maximal and minimal stretching rates to the whole finite-time Lyapunov spectrum and to stretching directions by considering the singular value decomposition (SVD) of the deformation gradient. We show two significant advantages of the SVD compared to the usual eigendecomposition of the Cauchy-Green strain tensor: (1) one gains theoretical insight into local deformation under a finite-time dynamical system, and (2) one obtains both complete forward and backward strain information from a single grid advection. Furthermore, we give a short and direct proof of t...
A Characterization of Generalized Monotone Normed Cones
S.ROMAGUERA; E.A.S(A)NCHEZ-P(E)REZ; O.VALERO
2007-01-01
Let C be a cone and consider a quasi-norm p defined on it. We study the structure of the couple (C, p) as a topological space in the case where the function p is also monotone. We characterize when the topology of a quasi-normed cone can be defined by means of a monotone norm. We also define and study the dual cone of a monotone normed cone and the monotone quotient of a general cone.We provide a decomposition theorem which allows us to write a cone as a direct sum of a monotone subcone that is isomorphic to the monotone quotient and other particular subcone.
Testing Monotonicity of Pricing Kernels
Timofeev, Roman
2007-01-01
In this master thesis a mechanism to test mononicity of empirical pricing kernels (EPK) is presented. By testing monotonicity of pricing kernel we can determine whether utility function is concave or not. Strictly decreasing pricing kernel corresponds to concave utility function while non-decreasing EPK means that utility function contains some non-concave regions. Risk averse behavior is usually described by concave utility function and considered to be a cornerstone of classical behavioral ...
Monotonicity of chi-square test statistics
Ryu, Keunkwan
2003-01-01
This paper establishes monotonicity of the chi-square test statistic. As the more efficient parameter estimator is plugged into the test statistic, the degrees of freedom of the resulting chi-square test statistic monotonically increase.
Some Generalizations of Monotonicity Condition and Applications
虞旦盛; 周颂平
2006-01-01
@@ O Introduction It is well known that there are a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc..
Nielson, Hanne Riis; Nielson, Flemming
2009-01-01
The calculus of communicating systems, CCS, was introduced by Robin Milner as a calculus for modelling concurrent systems. Subsequently several techniques have been developed for analysing such models in order to get further insight into their dynamic behaviour. In this paper we present a static...... analysis for approximating the control structure embedded within the models. We formulate the analysis as an instance of a monotone framework and thus draw on techniques that often are associated with the efficient implementation of classical imperative programming languages. We show how to construct...
Lagrangian methods of cosmic web classification
Fisher, J. D.; Faltenbacher, A.; Johnson, M. S. T.
2016-05-01
The cosmic web defines the large-scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid-based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or haloes) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian nature admits a straightforward inclusion of the Hubble flow negating the necessity of a visually defined threshold value which is commonly employed by grid-based classification methods.
A hybrid Eulerian-Lagrangian flow solver
Palha, Artur; Ferreira, Carlos Simao; van Bussel, Gerard
2015-01-01
Currently, Eulerian flow solvers are very efficient in accurately resolving flow structures near solid boundaries. On the other hand, they tend to be diffusive and to dampen high-intensity vortical structures after a short distance away from solid boundaries. The use of high order methods and fine grids, although alleviating this problem, gives rise to large systems of equations that are expensive to solve. Lagrangian solvers, as the regularized vortex particle method, have shown to eliminate (in practice) the diffusion in the wake. As a drawback, the modelling of solid boundaries is less accurate, more complex and costly than with Eulerian solvers (due to the isotropy of its computational elements). Given the drawbacks and advantages of both Eulerian and Lagrangian solvers the combination of both methods, giving rise to a hybrid solver, is advantageous. The main idea behind the hybrid solver presented is the following. In a region close to solid boundaries the flow is solved with an Eulerian solver, where th...
Sepe, D.
2013-01-01
The obstruction to construct a Lagrangian bundle over a fixed integral affine manifold was constructed by Dazord and Delzant (J Differ Geom 26:223–251, 1987) and shown to be given by ‘twisted’ cup products in Sepe (Differ GeomAppl 29(6): 787–800, 2011). This paper uses the topology of universal Lagr
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Symmetries in Lagrangian Field Theory
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
On the sample monotonization problem
Takhanov, R. S.
2010-07-01
The problem of finding a maximal subsample in a training sample consisting of the pairs “object-answer” that does not violate monotonicity constraints is considered. It is proved that this problem is NP-hard and that it is equivalent to the problem of finding a maximum independent set in special directed graphs. Practically important cases in which a partial order specified on the set of answers is a complete order or has dimension two are considered in detail. It is shown that the second case is reduced to the maximization of a quadratic convex function on a convex set. For this case, an approximate polynomial algorithm based on linear programming theory is proposed.
Symplectic Applicability of Lagrangian Surfaces
Lorenzo Nicolodi
2009-06-01
Full Text Available We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equations. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.
Renormalization and effective lagrangians
Polchinski, Joseph
1984-01-01
There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional λø 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed.
Gravity, Time, and Lagrangians
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
Gravity, Time, and Lagrangians
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
2010-09-30
the vertical interpolation adjustment given by Equation 8 (SL OMT ), NOGAPS SL/SI with non-interpolation in the vertical (SL NIV), and the non semi...interpolation scheme (SL OMT ), the non-interpolating scheme in the vertical (SL NIV) and the non semi-Lagrangian NOGAPS (EULER). Figures 4 and...2009 comparing the control NOGAPS SL/SI with the adjusted vertical interpolation scheme (SL OMT ), the non-interpolating scheme in the vertical (SL NIV
Monotonic Allocation Schemes in Clan Games
Voorneveld, M.; Tijs, S.H.; Grahn, S.
2000-01-01
Total clan games are characterized using monotonicity, veto power of the clan members, and a concavity condition reflecting the decreasing marginal contribution of non-clan members to growing coalitions.This decreasing marginal contribution is incorporated in the notion of a bi-monotonic allocation
Monotone models for prediction in data mining
Velikova, M.V.
2006-01-01
This dissertation studies the incorporation of monotonicity constraints as a type of domain knowledge into a data mining process. Monotonicity constraints are enforced at two stages¿data preparation and data modeling. The main contributions of the research are a novel procedure to test the degree of
Monotonic Stable Solutions for Minimum Coloring Games
Hamers, H.J.M.; Miquel, S.; Norde, H.W.
2011-01-01
For the class of minimum coloring games (introduced by Deng et al. (1999)) we investigate the existence of population monotonic allocation schemes (introduced by Sprumont (1990)). We show that a minimum coloring game on a graph G has a population monotonic allocation scheme if and only if G is (P4,
Monotonicity-preserving linear multistep methods
Hundsdorfer, W.; Ruuth, S.J.; Spiteri, R.J.
2002-01-01
In this paper we provide an analysis of monotonicity properties for linear multistep methods. These monotonicity properties include positivity and the diminishing of total variation. We also pay particular attention to related boundedness properties such as the total-variation-bounded (TVB) property
Version Spaces and Generalized Monotone Boolean Functions
J.C. Bioch (Cor); T. Ibaraki
2002-01-01
textabstractWe consider generalized monotone functions f: X --> {0,1} defined for an arbitrary binary relation <= on X by the property x <= y implies f(x) <= f(y). These include the standard monotone (or positive) Boolean functions, regular Boolean functions and other interesting functions as speci
Version Spaces and Generalized Monotone Boolean Functions
J.C. Bioch (Cor); T. Ibaraki
2002-01-01
textabstractWe consider generalized monotone functions f: X --> {0,1} defined for an arbitrary binary relation <= on X by the property x <= y implies f(x) <= f(y). These include the standard monotone (or positive) Boolean functions, regular Boolean functions and other interesting functions as
Monotone Hurwitz numbers in genus zero
Goulden, I P; Novak, Jonathan
2012-01-01
Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of the branched covers counted by the Hurwitz numbers, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two results that are reminiscent of those for classical Hurwitz numbers. The first is the monotone join-cut equation, a partial differential equation with initial conditions that characterizes the generating function for monotone Hurwitz numbers in arbitrary genus. The second is our main result, in which we give an explicit formula for monotone Hurwitz numbers in genus zero.
A truly noninterpolating semi-Lagrangian Lax-Wendroff method
Olim, M.
1994-06-01
A truly noninterpolating semi-Lagrangian method has been developed. It is based upon a modification of a standard Lax-Wendroff scheme and is unconditionally stable on a regular rectangular grid. The method is explicit and second-order accurate in both time and space. It is suggested that the computational cost and memory allocation required by this method are the least possible for a semi-Lagrangian algorithm of this order of accuracy. The numerical experiments presented indicate that the algorithm is very accurate indeed.
Generalized Superfield Lagrangian Quantization
Lavrov, P M; Moshin, P Y
2002-01-01
We consider an extension of the gauge-fixing procedure in the framework of the Lagrangian superfield BRST and BRST-antiBRST quantization schemes for arbitrary gauge theories, taking into account the possible ambiguity in the choice of the superfield antibracket. We show that this ambiguity is fixed by the algebraic properties of the antibracket and the form of the BRST and antiBRST transformations, realized in terms of superspace translations. The Ward identities related to the generalized gauge-fixing procedure are obtained.
Lagrangian vector field and Lagrangian formulation of partial differential equations
M.Chen
2005-01-01
Full Text Available In this paper we consider the Lagrangian formulation of a system of second order quasilinear partial differential equations. Specifically we construct a Lagrangian vector field such that the flows of the vector field satisfy the original system of partial differential equations.
Viable harvest of monotone bioeconomic models
De Lara, Michel; Cabrera, Hector Ramirez
2009-01-01
Some monospecies age class models, as well as specific multi-species models (with so-called technical interactions), exhibit useful monotonicity properties. This paper deals with discrete time monotone bioeconomics dynamics in the presence of state and control constraints. In practice, these latter ``acceptable configurations'' represent production and preservation requirements to be satisfied for all time, and they also possess monotonicity properties. A state $\\state$ is said to belong to the viability kernel if there exists a trajectory, of states and controls, starting from $\\state$ and satisfying the constraints. Under monotonicity assumptions, we present upper and lower estimates of the viability kernel. This helps delineating domains where a viable management is possible. Numerical examples, in the context of fisheries management, for the Chilean sea bass (\\emph{Dissostichus eleginoides}) and Alfonsino (\\emph{Beryx splendens}) are given.
Hyperbolic monotonicity in the Hilbert ball
Reich Simeon
2006-01-01
Full Text Available We first characterize -monotone mappings on the Hilbert ball by using their resolvents and then study the asymptotic behavior of compositions and convex combinations of these resolvents.
Topological Classification of Lagrangian Fibrations
Sepe, D
2009-01-01
We define topological invariants of regular Lagrangian fibrations using the integral affine structure on the base space and we show that these coincide with the classes known in the literature. We also classify all symplectic types of Lagrangian fibrations with base $\\rpr$ and fixed monodromy representation, generalising a construction due to Bates.
Monotone Rank and Separations in Computational Complexity
Li, Yang D
2011-01-01
In the paper, we introduce the concept of monotone rank, and using it as a powerful tool, we obtain several important and strong separation results in computational complexity. We show a super-exponential separation between monotone and non-monotone computation in the non-commutative model, and thus give the answer to a longstanding open problem posed by Nisan \\cite{Nis1991} in algebraic complexity. More specifically, we exhibit a homogeneous algebraic function $f$ of degree $d$ ($d$ even) on $n$ variables with the monotone algebraic branching program (ABP) complexity $\\Omega(n^{d/2})$ and the non-monotone ABP complexity $O(d^2)$. We propose a relaxed version of the famous Bell's theorem\\cite{Bel1964}\\cite{CHSH1969}. Bell's theorem basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics, and therefore is an impossibility result. Bell's theorem heavily relies on the diversity of the measurements. We prove that even if we fix the measurement, infinite amo...
Parallel algorithms for semi-lagrangian advection
Malevsky, A. V.; Thomas, S. J.
1997-08-01
Numerical time step limitations associated with the explicit treatment of advection-dominated problems in computational fluid dynamics are often relaxed by employing Eulerian-Lagrangian methods. These are also known as semi-Lagrangian methods in the atmospheric sciences. Such methods involve backward time integration of a characteristic equation to find the departure point of a fluid particle arriving at a Eulerian grid point. The value of the advected field at the departure point is obtained by interpolation. Both the trajectory integration and repeated interpolation influence accuracy. We compare the accuracy and performance of interpolation schemes based on piecewise cubic polynomials and cubic B-splines in the context of a distributed memory, parallel computing environment. The computational cost and interprocessor communication requirements for both methods are reported. Spline interpolation has better conservation properties but requires the solution of a global linear system, initially appearing to hinder a distributed memory implementation. The proposed parallel algorithm for multidimensional spline interpolation has almost the same communication overhead as local piecewise polynomial interpolation. We also compare various techniques for tracking trajectories given different values for the Courant number. Large Courant numbers require a high-order ODE solver involving multiple interpolations of the velocity field.
Lagrangian-Only Quantum Theory
Wharton, K B
2013-01-01
Despite the importance of the path integral, there have been relatively few attempts to look to the Lagrangian for a more realistic framework that might underlie quantum theory. While such realism is not available for the standard path integral or quantum field theory, a promising alternative is to only consider field histories for which the Lagrangian density is always zero. With this change, it appears possible to replace amplitudes with equally-weighted probabilities. This paper demonstrates a proof-of-principle for this approach, using a toy Lagrangian that corresponds to an arbitrary spin state. In this restricted framework one can derive both the Born rule and its limits of applicability. The fact that the Lagrangian obeys future boundary constraints also results in the first continuous, spacetime-based, hidden-variable description of a Bell-inequality-violating system.
Lagrangian Modeling of the Atmosphere
Schultz, Colin
2013-08-01
Like watching a balloon borne by the breeze, a Lagrangian model tracks a parcel of air as it flows through the atmosphere. Whether running forward or backward in time, Lagrangian models offer a powerful tool for tracking and understanding the fates, or origins, of atmospheric flows. In the AGU monograph Lagrangian Modeling of the Atmosphere, editors John Lin, Dominik Brunner, Christoph Gerbig, Andreas Stohl, Ashok Luhar, and Peter Webley explore the nuances of the modeling technique. In this interview Eos talks to Lin about the growing importance of Lagrangian modeling as the world settles on climate change mitigation strategies, the societal value of operational modeling, and how recent advances are making it possible to run these complex calculations at home.
The Lagrangian in Quantum Mechanics
Dirac, P. A. M.
Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue, as a result of which the whole of the classical Hamiltonian theory, which is just a structure built up on this notion, could be taken over in all its details into quantum mechanics. Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. In the first place the Lagrangian method allows one to collect together all the equations of motion and express them as the stationary property of a certain action function. (This action function is just the time-integral of the Lagrangian.) There is no corresponding action principle in terms of the coordinates and momenta of the Hamiltonian theory. Secondly the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially non-relativistic in form, since it marks out a particular time variable as the canonical conjugate of the Hamiltonian function. For these reasons it would seem desirable to take up the question of what corresponds in the quantum theory to the Lagrangian method of the classical theory. A little consideration shows, however, that one cannot expect to be able to take over the classical Lagrangian equations in any very direct way. These equations involve partial derivatives of the Lagrangian with respect to the coordinates and velocities and no meaning can be given to such derivatives in quantum mechanics. The only differentiation process that can be carried out with respect to the dynamical variables of
The monotonic and fatigue behavior of CFCCs
Miriyala, N.; Liaw, P.K.; McHargue, C.J. [Univ. of Tennessee, Knoxville, TN (United States); Snead, L.L. [Oak Ridge National Laboratory, TN (United States)
1996-04-01
Flexure tests were performed to study the fabric orientation effects on the monotonic and fatigue behavior of two commercially available continuous fiber reinforced ceramic composites (CFCCs), namely (i) Nicalon fiber fabric reinforced alumina (Al{sub 2}O{sub 3}) matrix composite fabricated by a direct molten metal oxidation (DIMOX) process and, (ii) Nicalon fiber fabric reinforced silicon carbide (SiC) matrix composite fabricated by an isothermal chemical vapor infiltration (ICVI) process. The fabric orientation effects on the monotonic and fatigue behavior were strong in the Nicalon/Al{sub 2}O{sub 3} composite, while they were relatively weak in the Nicalon/SiC composite.
Weighted monotonicity inequalities for unbounded operators
Hoa, Dinh Trung
2011-01-01
Let $\\tau$ be a faithful normal semifinite trace on a von Neumann algebra $\\mathcal{M}$. For a continuous nonnegative convex monotone nondecreasing function $f$ on convex subset $\\Omega$ of $\\mathbb{R}$ and weight nonnegative Borel function $w$ we consider weighted monotonicity inequalities of the form {equation*} \\tau(w(A)^{1/2}f(A)w(A)^{1/2}) \\le \\tau (w(A)^{1/2}f(B)w(A)^{1/2}), {equation*} where $A$ and $B$ are unbounded operators affiliated with respect to algebra $\\mathcal{M}$.
Lagrangian description of nonlinear chromatography
LIANG Heng; LIU Xiaolong
2004-01-01
Under the framework of non-equilibrium thermodynamic separation theory (NTST), Local Lagrangian approach (LLA) was proposed to deal with the essential issues of the convection and diffusion (shock waves) phenomena in nonlinear chromatography with recursion equations based on the three basic theorems, Lagrangian description, continuity axiom and local equilibrium assumption (LEA). This approach remarkably distinguished from the system of contemporary chromatographic theories (Eulerian description-partial differential equations), and can felicitously match modern cybernetics.
Chang, E. C.; Yoshimura, K.
2016-12-01
The non-iteration dimensional-split semi-Lagrangian (NDSL) advection scheme is applied to the Experimental Climate Prediction Center (ECPC) regional spectral model (RSM) in order to alleviate the Gibbs phenomenon. The Gibbs problem is solved by replacing the spectral prognostic vapor and radioactive tracer calculations with the NDSL method, which considers advection of tracers on grid system without spectral space transformations. The NDSL scheme in the RSM successfully solved the Gibbs problem of the radioactive tracers for the Fukushima nuclear power plant accident case. In this study, analyses are focused on the improvement of the simulated precipitation from the RSM by applying the NDSL scheme for hydrometeors. It is shown that the NDSL improves location and intensity of the precipitation for the case of the Changma front over Korea. Furthermore, a mass-conserving NDSL scheme is also tested with the monotonic NDSL scheme for the Changma case. The mass-conserving scheme shows advantages in the simulated humidity fields and rainfall intensity.
Presymplectic structures and intrinsic Lagrangians
Grigoriev, Maxim
2016-01-01
It is well-known that a Lagrangian induces a compatible presymplectic form on the equation manifold (stationary surface, understood as a submanifold of the respective jet-space). Given an equation manifold and a compatible presymplectic form therein, we define the first-order Lagrangian system which is formulated in terms of the intrinsic geometry of the equation manifold. It has a structure of a presymplectic AKSZ sigma model for which the equation manifold, equipped with the presymplectic form and the horizontal differential, serves as the target space. For a wide class of systems (but not all) we show that if the presymplectic structure originates from a given Lagrangian, the proposed first-order Lagrangian is equivalent to the initial one and hence the Lagrangian per se can be entirely encoded in terms of the intrinsic geometry of its stationary surface. If the compatible presymplectic structure is generic, the proposed Lagrangian is only a partial one in the sense that its stationary surface contains the...
Monotone Comparative Statics for the Industry Composition
Laugesen, Anders Rosenstand
2015-01-01
We let heterogeneous firms face decisions on a number of complementary activities in a monopolistically-competitive industry. The endogenous level of competition and selection regarding entry and exit of firms introduces a wedge between monotone comparative statics (MCS) at the firm level and MCS...
On a Monotone Ill-posed Problem
Nguyen BUONG
2005-01-01
A class of a posteriori parameter choice strategies for the operator version of Tikhonovregularization (including variants of Morozov's and Arcangeli's methods) is proposed and used in investigating the rate of convergence of the regularized solution for ill-posed nonlinear equation involving a monotone operator in Banach space.
Population Monotonic Path Schemes for Simple Games
Ciftci, B.B.; Borm, P.E.M.; Hamers, H.J.M.
2006-01-01
A path scheme for a simple game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path.A path scheme is called population monotonic if a player's payoff does not decrease as the pa
Monotone method for nonlinear nonlocal hyperbolic problems
Azmy S. Ackleh
2003-02-01
Full Text Available We present recent results concerning the application of the monotone method for studying existence and uniqueness of solutions to general first-order nonlinear nonlocal hyperbolic problems. The limitations of comparison principles for such nonlocal problems are discussed. To overcome these limitations, we introduce new definitions for upper and lower solutions.
Limit points of the monotonic schemes
Salomon, J
2005-01-01
Many numerical simulations in quantum (bilinear) control use the monotonically convergent algorithms of Krotov (introduced by Tannor), Zhu & Rabitz or the general form of Maday & Turinici. This paper presents an analysis of the limit set of controls provided by these algorithms and a proof of convergence in a particular case.
REGULAR RELATIONS AND MONOTONE NORMAL ORDERED SPACES
XU XIAOQUAN; LIU YINGMING
2004-01-01
In this paper the classical theorem of Zareckii about regular relations is generalized and an intrinsic characterization of regularity is obtained. Based on the generalized Zareckii theorem and the intrinsic characterization of regularity, the authors give a characterization of monotone normality of ordered spaces. A new proof of the UrysohnNachbin lemma is presented which is quite different from the classical one.
Monotonicity and bounds on Bessel functions
Larry Landau
2000-07-01
Full Text Available survey my recent results on monotonicity with respect to order of general Bessel functions, which follow from a new identity and lead to best possible uniform bounds. Application may be made to the "spreading of the wave packet" for a free quantum particle on a lattice and to estimates for perturbative expansions.
Strong monotonicity for analytic ordinary differential equations
Sebastian Walcher
2009-09-01
Full Text Available We present a necessary and sufficient criterion for the flow of an analytic ordinary differential equation to be strongly monotone; equivalently, strongly order-preserving. The criterion is given in terms of the reducibility set of the derivative of the right-hand side. Some applications to systems relevant in biology and ecology, including nonlinear compartmental systems, are discussed.
A monotonic archive for pareto-coevolution.
de Jong, Edwin D
2007-01-01
Coevolution has already produced promising results, but its dynamic evaluation can lead to a variety of problems that prevent most algorithms from progressing monotonically. An important open question therefore is how progress towards a chosen solution concept can be achieved. A general solution concept for coevolution is obtained by viewing opponents or tests as objectives. In this setup known as Pareto-coevolution, the desired solution is the Pareto-optimal set. We present an archive that guarantees monotonicity for this solution concept. The algorithm is called the Incremental Pareto-Coevolution Archive (IPCA), and is based on Evolutionary Multi-Objective Optimization (EMOO). By virtue of its monotonicity, IPCA avoids regress even when combined with a highly explorative generator. This capacity is demonstrated on a challenging test problem requiring both exploration and reliability. IPCA maintains a highly specific selection of tests, but the size of the test archive nonetheless grows unboundedly. We therefore furthermore investigate how archive sizes may be limited while still providing approximate reliability. The LAyered Pareto-Coevolution Archive (LAPCA) maintains a limited number of layers of candidate solutions and tests, and thereby permits a trade-off between archive size and reliability. The algorithm is compared in experiments, and found to be more efficient than IPCA. The work demonstrates how the approximation of a monotonic algorithm can lead to algorithms that are sufficiently reliable in practice while offering better efficiency.
Limit properties of monotone matrix functions
Behrndt, Jussi; Hassi, Seppo; de Snoo, Henk; Wietsma, Rudi
2012-01-01
The basic objects in this paper are monotonically nondecreasing n x n matrix functions D(center dot) defined on some open interval l = (a, b) of R and their limit values D(a) and D(b) at the endpoints a and b which are, in general, selfadjoint relations in C-n. Certain space decompositions induced b
Concerns on Monotonic Imbalance Bounding Matching Methods
Yatracos, Yannis G.
2013-01-01
Concerns are expressed for the Monotonic Imbalance Bounding (MIB) property (Iacus et al. 2011) and for MIB matching because i) the definition of the MIB property leads to inconsistencies and the nature of the imbalance measure is not clearly defined, ii) MIB property does not generalize Equal Percent Bias Reducing (EPBR) property, iii) MIB matching does not provide statistical information available with EPBR matching.
Nonparametric confidence intervals for monotone functions
Groeneboom, P.; Jongbloed, G.
2015-01-01
We study nonparametric isotonic confidence intervals for monotone functions. In [Ann. Statist. 29 (2001) 1699–1731], pointwise confidence intervals, based on likelihood ratio tests using the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the trea
Competitive learning of monotone Boolean functions
2014-01-01
We apply competitive analysis onto the problem of minimizing the number of queries to an oracle to completely reconstruct a given monotone Boolean function. Besides lower and upper bounds on the competitivity we determine optimal deterministic online algorithms for the smallest problem instances.
Nonparametric confidence intervals for monotone functions
Groeneboom, P.; Jongbloed, G.
2015-01-01
We study nonparametric isotonic confidence intervals for monotone functions. In [Ann. Statist. 29 (2001) 1699–1731], pointwise confidence intervals, based on likelihood ratio tests using the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the
Edit Distance to Monotonicity in Sliding Windows
Chan, Ho-Leung; Lam, Tak-Wah; Lee, Lap Kei
2011-01-01
of a data stream is becoming well-understood over the past few years. Motivated by applications on network quality monitoring, we extend the study to estimating the edit distance to monotonicity of a sliding window covering the w most recent items in the stream for any w ≥ 1. We give a deterministic...
New concurrent iterative methods with monotonic convergence
Yao, Qingchuan [Michigan State Univ., East Lansing, MI (United States)
1996-12-31
This paper proposes the new concurrent iterative methods without using any derivatives for finding all zeros of polynomials simultaneously. The new methods are of monotonic convergence for both simple and multiple real-zeros of polynomials and are quadratically convergent. The corresponding accelerated concurrent iterative methods are obtained too. The new methods are good candidates for the application in solving symmetric eigenproblems.
Classification Trees for Problems with Monotonicity Constraints
R. Potharst (Rob); A.J. Feelders
2002-01-01
textabstractFor classification problems with ordinal attributes very often the class attribute should increase with each or some of the explaining attributes. These are called classification problems with monotonicity constraints. Classical decision tree algorithms such as CART or C4.5 generally do
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).
About non standard Lagrangians in cosmology
Dimitrijevic, Dragoljub D.; Milosevic, Milan [Department of Physics, Faculty of Science and Mathematics, University of Nis, Visegradska 33, P.O. Box 224, 18000 Nis (Serbia)
2012-08-17
A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.
Monotone operators and "bigger conjugate" functions
Bauschke, Heinz H; Wang, Xianfu; Yao, Liangjin
2011-01-01
We study a question posed by Stephen Simons in his 2008 monograph involving "bigger conjugate" (BC) functions and the partial infimal convolution. As Simons demonstrated in his monograph, these function have been crucial to the understanding and advancement of the state-of-the-art of harder problems in monotone operator theory, especially the sum problem. In this paper, we provide some tools for further analysis of BC--functions which allow us to answer Simons' problem in the negative. We are also able to refute a similar but much harder conjecture which would have generalized a classical result of Br\\'ezis, Crandall and Pazy. Our work also reinforces the importance of understanding unbounded skew linear relations to construct monotone operators with unexpected properties.
Convex functions, monotone operators and differentiability
Phelps, Robert R
1993-01-01
The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space. The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions. The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler. The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational princ...
Complexity of Non-Monotonic Logics
Thomas, Michael
2010-01-01
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been considered, e.g., extension with default rules, extension with modal belief operators, or modification of the semantics. In this survey we consider a logical formalism from each of the above possibilities, namely Reiter's default logic, Moore's autoepistemic logic and McCarthy's circumscription. Additionally, we consider abduction, where one is not interested in inferences from a given knowledge base but in computing possible explanations for an observation with respect to a given knowledge base. Complexity results for different reasoning tasks for propositional variants of these logics have been studied already in the nineties. In recent years, however, a renewed interest in complexity issues can be observed. One current focal approach is to consider parameterized problems and ...
Linear Inviscid Damping for Monotone Shear Flows
Zillinger, Christian
2014-01-01
In this article we prove linear stability, inviscid damping and scattering of the 2D Euler equations around regular, strictly monotone shear flows $(U(y),0)$ in a periodic channel under Sobolev perturbations. We treat the settings of an infinite channel, $\\mathbb{T} \\times \\mathbb{R}$, as well as a finite channel, $\\mathbb{T} \\times [0,1]$, with impermeable boundary. We first prove inviscid damping with optimal algebraic rates for strictly monotone shear flows under the assumption of controlling the regularity of the scattered vorticity. Subsequently, we establish linear stability of the scattering equation in Sobolev spaces under perturbations which are of not too large wave-length with respect to $x$, depending on $U''$.
Lagrangian continuum dynamics in ALEGRA.
Wong, Michael K. W.; Love, Edward
2007-12-01
Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.
Improved selection in totally monotone arrays
Mansour, Y. (Harvard Univ., Cambridge, MA (United States). Aiken Computation Lab.); Park, J.K. (Sandia National Labs., Albuquerque, NM (United States)); Schieber, B. (International Business Machines Corp., Yorktown Heights, NY (United States). Thomas J. Watson Research Center); Sen, S. (AT and T Bell Labs., Murray Hill, NJ (United States))
1991-01-01
This paper's main result is an O(({radical}{bar m}lgm)(n lg n) + mlg n)-time algorithm for computing the kth smallest entry in each row of an m {times} n totally monotone array. (A two-dimensional A = a(i,j) is totally monotone if for all i{sub 1} < i{sub 2} and j{sub 1} < j{sup 2}, < a(i{sub 1},j{sub 2}) implies a(i{sub 2},j{sub 1})). For large values of k (in particular, for k=(n/2)), this algorithm is significantly faster than the O(k(m+n))-time algorithm for the same problem due to Kravets and Park. An immediate consequence of this result is an O(n{sup 3/2} lg{sup 2}n)-time algorithm for computing the kth nearest neighbor of each vertex of a convex n-gon. In addition to the main result, we also give an O(n lg m)-time algorithm for computing an approximate median in each row of an m {times} n totally monotone array; this approximate median is an entry whose rank in its row lies between (n/4) and (3n/4) {minus} 1. 20 refs., 3 figs.
Edit Distance to Monotonicity in Sliding Windows
Chan, Ho-Leung; Lee, Lap-Kei; Pan, Jiangwei; Ting, Hing-Fung; Zhang, Qin
2011-01-01
Given a stream of items each associated with a numerical value, its edit distance to monotonicity is the minimum number of items to remove so that the remaining items are non-decreasing with respect to the numerical value. The space complexity of estimating the edit distance to monotonicity of a data stream is becoming well-understood over the past few years. Motivated by applications on network quality monitoring, we extend the study to estimating the edit distance to monotonicity of a sliding window covering the $w$ most recent items in the stream for any $w \\ge 1$. We give a deterministic algorithm which can return an estimate within a factor of $(4+\\eps)$ using $O(\\frac{1}{\\eps^2} \\log^2(\\eps w))$ space. We also extend the study in two directions. First, we consider a stream where each item is associated with a value from a partial ordered set. We give a randomized $(4+\\epsilon)$-approximate algorithm using $O(\\frac{1}{\\epsilon^2} \\log \\epsilon^2 w \\log w)$ space. Second, we consider an out-of-order strea...
A Discrete Approach to Meshless Lagrangian Solid Modeling
Matthew Marko
2017-07-01
Full Text Available The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles apply stresses expected with Hooke’s law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke’s law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with smoothed particle hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for fluid–solid interactions.
Weak monotonicity inequality and partial regularity for harmonic maps
沈尧天; 严树森
1999-01-01
The notion of locally weak monotonicity inequality for weakly harmonic maps is introduced and various results on this class of maps are obtained. For example, the locally weak monotonicity inequality is nearly equivalent to the ε-regularity.
Monotonic Loading of Circular Surface Footings on Clay
Ibsen, Lars Bo; Barari, Amin
2011-01-01
Appropriate modeling of offshore foundations under monotonic loading is a significant challenge in geotechnical engineering. This paper reports experimental and numerical analyses, specifically investigating the response of circular surface footings during monotonic loading and elastoplastic beha...
A Student's Guide to Lagrangians and Hamiltonians
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Lagrangian multi-particle statistics
Lüthi, Beat; Berg, Jacob; Ott, Søren
2007-01-01
Combined measurements of the Lagrangian evolution of particle constellations and the coarse-grained velocity derivative tensor. partial derivative(u) over tilde (i) /partial derivative x(j) are presented. The data are obtained from three-dimensional particle tracking measurements in a quasi isotr...
Galilean invariance in Lagrangian mechanics
Mohallem, J. R.
2015-10-01
The troublesome topic of Galilean invariance in Lagrangian mechanics is discussed in two situations: (i) A particular case involving a rheonomic constraint in uniform motion and (ii) the general translation of an entire system and the constants of motion involved. A widespread impropriety in most textbooks is corrected, concerning a condition for the equality h = E to hold.
Tsunami intrusion in wide meandering channels: a Lagrangian numerical experiment
Couston, L. A.; Alam, M. R.
2015-12-01
Among the many difficulties of tsunami forecast, wave runup on sloped beaches remains a major obstacle in numerical simulations. Traditional Eulerian models must adjust the fluid flow domain continuously due to the moving shorelines, which can significantly affect the computational cost and results accuracy. An efficient though uncommon alternative for accurate runup predictions still exists, consisting in using a Lagrangian model as recently shown by e.g. Couston et al. (2015) who studied the runup of landslide tsunamis in lakes with a non-dispersive Lagrangian model. Here we introduce a fully-nonlinear Boussinesq-type model derived in the Lagrangian framework to investigate various cases of long-wave runup on curved beaches and meandering channels. The governing equations are expressed in terms of curvilinear Lagrangian coordinates, making the model suitable for accurate runup computations at shorelines of arbitrary geometry while retaining the inherent simplicity of a physical model discretized on a fixed and structured grid. We implement an elliptic grid generation algorithm to map the physical space to the computational space, and a high-order finite-difference scheme for time integration. The numerical model has a linear complexity in the number of unknowns when neglecting dispersive effects. We show that the formation of edge waves due to the sloped banks of a wide channel has a significant influence on the capability of a meander or constriction in reflecting the intruding tsunami, and we investigate the effect of dispersion. Reference: Couston, L.-A., Mei, C. C., & Alam, M.-R. (2015). Landslide tsunamis in lakes. Journal of Fluid Mechanics, 772, 784-804.
A-monotonicity and applications to nonlinear variational inclusion problems
Ram U. Verma
2004-01-01
Full Text Available A new notion of the A-monotonicity is introduced, which generalizes the H-monotonicity. Since the A-monotonicity originates from hemivariational inequalities, and hemivariational inequalities are connected with nonconvex energy functions, it turns out to be a useful tool proving the existence of solutions of nonconvex constrained problems as well.
On the strong monotonicity of the CABARET scheme
Ostapenko, V. V.
2012-03-01
The strong monotonicity of the CABARET scheme with single flux correction is analyzed as applied to the linear advection equation. It is shown that the scheme is strongly monotone (has the NED property) at Courant numbers r ∈ (0,0,5), for which it is monotone. Test computations illustrating this property of the CABARET scheme are presented.
Testing Manifest Monotonicity Using Order-Constrained Statistical Inference
Tijmstra, Jesper; Hessen, David J.; van der Heijden, Peter G. M.; Sijtsma, Klaas
2013-01-01
Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores,…
Data Assimilation With Regional Lagrangian Models
1999-09-30
Journal of Marine Systems . RESULTS We are able to fit the inviscid Lagrangian model with synthetic Lagrangian data for short periods of time (1-2 days...Mead and A.F. Bennett, 1999. Towards regional assimilation of data: The Lagrangian form of the reduced gravity model and its inverse, (submitted), Journal of Marine Systems .
Wehrl entropy, Lieb conjecture and entanglement monotones
Mintert, F; Mintert, Florian; Zyczkowski, Karol
2004-01-01
We propose to quantify the entanglement of pure states of $N \\times N$ bipartite quantum system by defining its Husimi distribution with respect to $SU(N)\\times SU(N)$ coherent states. The Wehrl entropy is minimal if and only if the pure state analyzed is separable. The excess of the Wehrl entropy is shown to be equal to the subentropy of the mixed state obtained by partial trace of the bipartite pure state. This quantity, as well as the generalized (R{\\'e}nyi) subentropies, are proved to be Schur--convex, so they are entanglement monotones and may be used as alternative measures of entanglement.
Topological recursion and a quantum curve for monotone Hurwitz numbers
Do, Norman; Dyer, Alastair; Mathews, Daniel V.
2017-10-01
Classical Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data. Monotone Hurwitz numbers restrict the enumeration by imposing a further monotonicity condition on such factorisations. In this paper, we prove that monotone Hurwitz numbers arise from the topological recursion of Eynard and Orantin applied to a particular spectral curve. We furthermore derive a quantum curve for monotone Hurwitz numbers. These results extend the collection of enumerative problems known to be governed by the paradigm of topological recursion and quantum curves, as well as the list of analogues between monotone Hurwitz numbers and their classical counterparts.
Anchored Lagrangian submanifolds and their Floer theory
Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru
2009-01-01
We introduce the notion of (graded) anchored Lagrangian submanifolds and use it to study the filtration of Floer' s chain complex. We then obtain an anchored version of Lagrangian Floer homology and its (higher) product structures. They are somewhat different from the more standard non-anchored version. The anchored version discussed in this paper is more naturally related to the variational picture of Lagrangian Floer theory and so to the likes of spectral invariants. We also discuss rationality of Lagrangian submanifold and reduction of the coefficient ring of Lagrangian Floer cohomology of thereof.
The Monotonicity Puzzle: An Experimental Investigation of Incentive Structures
Jeannette Brosig
2010-05-01
Full Text Available Non-monotone incentive structures, which - according to theory - are able to induce optimal behavior, are often regarded as empirically less relevant for labor relationships. We compare the performance of a theoretically optimal non-monotone contract with a monotone one under controlled laboratory conditions. Implementing some features relevant to real-world employment relationships, our paper demonstrates that, in fact, the frequency of income-maximizing decisions made by agents is higher under the monotone contract. Although this observed behavior does not change the superiority of the non-monotone contract for principals, they do not choose this contract type in a significant way. This is what we call the monotonicity puzzle. Detailed investigations of decisions provide a clue for solving the puzzle and a possible explanation for the popularity of monotone contracts.
Effective Lagrangian for Nonrelativistic Systems
Haruki Watanabe
2014-09-01
Full Text Available The effective Lagrangian for Nambu-Goldstone bosons (NGBs in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing 1 dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in 1+1 dimensions.
Complex Lagrangians and phantom cosmology
Andrianov, A A; Kamenshchik, A Yu
2006-01-01
Motivated by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with PT symmetry, we show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. The model is based on a classical complex Lagrangian of a scalar field. Specific symmetry properties analogous to PT in non-Hermitian quantum mechanics lead to purely real equation of motion.
Lagrangian Hydrocode Simulations of Tsunamigenic, Subaerial Landslides
Schwaiger, H. F.; Parsons, J.; Higman, B.
2006-12-01
The interaction of debris flows, both subaqueous and subaerial, with bodies of water can produce tsunamis with a locally devastating impact. When debris flows begin above the water surface, the impact can produce a large air cavity, significantly increasing the effective volume of water displaced and complicating efforts to model the resulting tsunami. Because grid-based, Eulerian numerical methods have an inherent difficulty tracking material boundaries, we have implemented a particle-based, Lagrangian model (Smoothed Particle Hydrodynamics). The use of a particle model removes the common numerical difficulties associated with large deformation, multi-phase flows such as the numerical diffusion of material boundaries. We treat the debris flow as an incompressible, viscous fluid and the body of water as inviscid. Other rheologies of the debris flow (Mohr-Coulomb or Bingham plastic) can be included through the use of a non-linear viscosity. We apply this model to study the 1958 Lituya Bay landslide and resulting tsunami. Our simulation results compare favorably with field observations as well as a scaled laboratory experiment and a numerical study using an AMR Eulerian compressible fluid model.
Convex functions, monotone operators and differentiability
Phelps, Robert R
1989-01-01
These notes start with an introduction to the differentiability of convex functions on Banach spaces, leading to the study of Asplund spaces and their intriguing relationship to monotone operators (and more general set-values maps) and Banach spaces with the Radon-Nikodym property. While much of this is classical, some of it is presented using streamlined proofs which were not available until recently. Considerable attention is paid to contemporary results on variational principles and perturbed optimization in Banach spaces, exhibiting their close connections with Asplund spaces. An introductory course in functional analysis is adequate background for reading these notes which can serve as the basis for a seminar of a one-term graduate course. There are numerous excercises, many of which form an integral part of the exposition.
Generalized convexity, generalized monotonicity recent results
Martinez-Legaz, Juan-Enrique; Volle, Michel
1998-01-01
A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized conve...
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
Felici, Helene Marie
1992-06-01
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.
Stability of dynamical systems on the role of monotonic and non-monotonic Lyapunov functions
Michel, Anthony N; Liu, Derong
2015-01-01
The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems. For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonicLyapunov functions.Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks. The authors cover the following four general topics: - Representation and modeling of dynamical systems of the types described above - Presentation of Lyapunov and Lagrange stability theory for dynamical sy...
Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods
Hundsdorfer, W.
2011-04-29
In this paper nonlinear monotonicity and boundedness properties are analyzed for linear multistep methods. We focus on methods which satisfy a weaker boundedness condition than strict monotonicity for arbitrary starting values. In this way, many linear multistep methods of practical interest are included in the theory. Moreover, it will be shown that for such methods monotonicity can still be valid with suitable Runge-Kutta starting procedures. Restrictions on the stepsizes are derived that are not only sufficient but also necessary for these boundedness and monotonicity properties. © 2011 Springer Science+Business Media, LLC.
On the monotonicity of multidimensional finite difference schemes
Kovyrkina, O.; Ostapenko, V.
2016-10-01
The classical concept of monotonicity, introduced by Godunov for linear one-dimensional difference schemes, is extended to multidimensional case. Necessary and sufficient conditions of monotonicity are obtained for linear multidimensional difference schemes of first order. The constraints on the numerical viscosity are given that ensure the monotonicity of a difference scheme in the multidimensional case. It is proposed a modification of the second order multidimensional CABARET scheme that preserves the monotonicity of one-dimensional discrete solutions and, as a result, ensures higher smoothness in the computation of multidimensional discontinuous solutions. The results of two-dimensional test computations illustrating the advantages of the modified CABARET scheme are presented.
Alternative expression for the electromagnetic Lagrangian
Saldanha, Pablo L
2015-01-01
We propose an alternative expression for the Lagrangian density that governs the interaction of a charged particle with external electromagnetic fields. The proposed Lagrangian is written in terms of the local superposition of the particle fields with the applied electromagnetic fields, not in terms of the particle charge and of the electromagnetic potentials as is usual. The total Lagrangian for a set of charged particles assumes a simple elegant form with the alternative formulation, giving an aesthetic support for it. The proposed Lagrangian is equivalent to the traditional one in their domain of validity and provides an interesting description of the Aharonov-Bohm effect.
2016-05-01
A computing grid interconnects resources such as high performancecomputers, scientific databases, and computercontrolledscientific instruments of cooperating organizationseach of which is autonomous. It precedes and is quitedifferent from cloud computing, which provides computingresources by vendors to customers on demand. In this article,we describe the grid computing model and enumerate themajor differences between grid and cloud computing.
Monotone measures of ergodicity for Markov chains
J. Keilson
1998-01-01
Full Text Available The following paper, first written in 1974, was never published other than as part of an internal research series. Its lack of publication is unrelated to the merits of the paper and the paper is of current importance by virtue of its relation to the relaxation time. A systematic discussion is provided of the approach of a finite Markov chain to ergodicity by proving the monotonicity of an important set of norms, each measures of egodicity, whether or not time reversibility is present. The paper is of particular interest because the discussion of the relaxation time of a finite Markov chain [2] has only been clean for time reversible chains, a small subset of the chains of interest. This restriction is not present here. Indeed, a new relaxation time quoted quantifies the relaxation time for all finite ergodic chains (cf. the discussion of Q1(t below Equation (1.7]. This relaxation time was developed by Keilson with A. Roy in his thesis [6], yet to be published.
Remarks on a monotone Markov chain
P. Todorovic
1987-01-01
Full Text Available In applications, considerations on stochastic models often involve a Markov chain {ζn}0∞ with state space in R+, and a transition probability Q. For each x R+ the support of Q(x,. is [0,x]. This implies that ζ0≥ζ1≥…. Under certain regularity assumptions on Q we show that Qn(x,Bu→1 as n→∞ for all u>0 and that 1−Qn(x,Bu≤[1−Q(x,Bu]n where Bu=[0,u. Set τ0=max{k;ζk=ζ0}, τn=max{k;ζk=ζτn−1+1} and write Xn=ζτn−1+1, Tn=τn−τn−1. We investigate some properties of the imbedded Markov chain {Xn}0∞ and of {Tn}0∞. We determine all the marginal distributions of {Tn}0∞ and show that it is asymptotically stationary and that it possesses a monotonicity property. We also prove that under some mild regularity assumptions on β(x=1−Q(x,Bx, ∑1n(Ti−a/bn→dZ∼N(0,1.
Modeling and simulation challenges in Eulerian-Lagrangian computations of multiphase flows
Diggs, Angela; Balachandar, S.
2017-01-01
The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Grid-Based (GB) methods, the volume fraction is first obtained within each cell as an Eulerian quantity and then interpolated to each particle. In Particle-Based (PB) methods, the particle volume fraction is obtained at each particle and then projected onto the Eulerian grid. Traditionally, GB methods are used in multiphase flow, but sub-grid resolution can be obtained through use of PB methods. By evaluating the total error and its components we compare the performance of GB and PB methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities.
Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems
Boglaev Igor
2009-01-01
Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.
Regularization and Iterative Methods for Monotone Variational Inequalities
Xiubin Xu
2010-01-01
Full Text Available We provide a general regularization method for monotone variational inequalities, where the regularizer is a Lipschitz continuous and strongly monotone operator. We also introduce an iterative method as discretization of the regularization method. We prove that both regularization and iterative methods converge in norm.
LIMITED MEMORY BFGS METHOD FOR NONLINEAR MONOTONE EQUATIONS
Weijun Zhou; Donghui Li
2007-01-01
In this paper, we propose an algorithm for solving nonlinear monotone equations by combining the limited memory BFGS method (L-BFGS) with a projection method. We show that the method is globally convergent if the equation involves a Lipschitz continuous monotone function. We also present some preliminary numerical results.
Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface
Xinru Liu
2014-01-01
Full Text Available A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.
An example of special Lagrangian fibration
FU Jixiang
2005-01-01
On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4directions.
Electroweak Chiral Lagrangian for Neutral Higgs Boson
WANG Shun-Zhi; WANG Qing
2008-01-01
A neutral Higgs boson is added into the traditional electroweak chiral Lagrangian by writing down all possible high dimension operators. The matter part of the Lagrangian is investigated in detail. We find that if Higgs field dependence of Yukawa couplings can be factorized out, there will be no flavour changing neutral couplings; neutral Higgs can induce coupling between light and heavy neutrinos.
A functional LMO invariant for Lagrangian cobordisms
Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël
2008-01-01
Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le–Murakami–Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category...
Anomalous effective lagrangians and vector resonance models
Pallante, E.; Petronzio, R.
1993-01-01
Chiral lagrangians including vector resonances have been shown to saturate the finite part of some of the counterterms needed to regularize ordinary one-loop effective lagrangians of pseudoscalar interactions with external currents. The equivalence between different models has been discussed in the
Monotone complete C*-algebras and generic dynamics
Saitô, Kazuyuki
2015-01-01
This monograph is about monotone complete C*-algebras, their properties and the new classification theory. A self-contained introduction to generic dynamics is also included because of its important connections to these algebras. Our knowledge and understanding of monotone complete C*-algebras has been transformed in recent years. This is a very exciting stage in their development, with much discovered but with many mysteries to unravel. This book is intended to encourage graduate students and working mathematicians to attack some of these difficult questions. Each bounded, upward directed net of real numbers has a limit. Monotone complete algebras of operators have a similar property. In particular, every von Neumann algebra is monotone complete but the converse is false. Written by major contributors to this field, Monotone Complete C*-algebras and Generic Dynamics takes readers from the basics to recent advances. The prerequisites are a grounding in functional analysis, some point set topology and an eleme...
Space-Time Transformation in Flux-form Semi-Lagrangian Schemes
Peter C. Chu Chenwu Fan
2010-01-01
Full Text Available With a finite volume approach, a flux-form semi-Lagrangian (TFSL scheme with space-time transformation was developed to provide stable and accurate algorithm in solving the advection-diffusion equation. Different from the existing flux-form semi-Lagrangian schemes, the temporal integration of the flux from the present to the next time step is transformed into a spatial integration of the flux at the side of a grid cell (space for the present time step using the characteristic-line concept. The TFSL scheme not only keeps the good features of the semi-Lagrangian schemes (no Courant number limitation, but also has higher accuracy (of a second order in both time and space. The capability of the TFSL scheme is demonstrated by the simulation of the equatorial Rossby-soliton propagation. Computational stability and high accuracy makes this scheme useful in ocean modeling, computational fluid dynamics, and numerical weather prediction.
A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO
Heisenberg, Lavinia; Bartelmann, Matthias
2010-01-01
Subject of this paper is a careful and detailed analysis of the PINOCCHIO algorithm for studying the relative velocity statistics of merging haloes in Lagrangian perturbation theory. Given a cosmological background model, a power spectrum of fluctuations as well as a Gaussian linear density contrast field $\\delta_{\\rm l}$ is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position $\\bmath{q}$ and each smoothing radius $R$, the collapse time, the velocities and ellipsoidal truncation are computed using Lagrangian Perturbation Theory. The collapsed medium is then fragmented into isolated objects by an algorithm designed to mimic the accretion and merger events of hierarchical collapse. Directly after the fragmentation process the mass function, merger histories of haloes and the statistics of the relative velocities at merging are evaluated. We reimplemented the algorithm in C++ and optimised the construction of halo merging histories. Comparin...
Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows
Innocenti, A; Chibbaro, S
2016-01-01
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves for a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided b...
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.
A Lagrangian approach to classical thermodynamics
Stokes, A.
2017-02-01
The specification of microstates of interacting dynamical systems is different in Lagrangian and Hamiltonian approaches whenever the interaction Lagrangian depends on generalised velocities. In almost all cases of physical interest however, velocity-dependent interaction Lagrangians do not couple velocities belonging to different subsystems. For these cases we define reduced system and bath Lagrangian macrostates, which like the underlying microstates differ from their Hamiltonian counterparts. We then derive exact first and second laws of thermodynamics without any modification of the original system and bath quantities. This approach yields manifestly gauge-invariant definitions of work and free energy, and a gauge-invariant Jarzynski equality is derived. The formalism is applied in deriving the thermodynamic laws for a material system within the radiation reservoir. The Lagrangian partition of the total energy is manifestly gauge-invariant and is in accordance with Poynting's theorem.
Time-Dependent Lagrangian Biomechanics
Ivancevic, Tijana T
2009-01-01
In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. On this extended configuration space we develop time-dependent biomechanical Lagrangian dynamics, using derived jet spaces of velocities and accelerations, as well as the underlying geometric evolution of the mass-inertia matrix. Keywords: Human time-dependent biomechanics, configuration manifold, jet spaces, geometric evolution
Attili, Antonio
2013-09-01
A Lagrangian particle scheme is applied to the solution of soot dynamics in turbulent nonpremixed flames. Soot particulate is described using a method of moments and the resulting set of continuum advection-reaction equations is solved using the Lagrangian particle scheme. The key property of the approach is the independence between advection, described by the movement of Lagrangian notional particles along pathlines, and internal aerosol processes, evolving on each notional particle via source terms. Consequently, the method overcomes the issues in Eulerian grid-based schemes for the advection of moments: errors in the advective fluxes pollute the moments compromising their realizability and the stiffness of source terms weakens the stability of the method. The proposed scheme exhibits superior properties with respect to conventional Eulerian schemes in terms of stability, accuracy, and grid convergence. Taking into account the quality of the solution, the Lagrangian approach can be computationally more economical than commonly used Eulerian schemes as it allows the resolution requirements dictated by the different physical phenomena to be independently optimized. Finally, the scheme posseses excellent scalability on massively parallel computers. © 2013 Elsevier Ltd.
B. Rutherford
2012-12-01
Full Text Available The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation.
Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance.
The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.
The Number of Monotone and Self-Dual Boolean Functions
Haviarova L.
2014-12-01
Full Text Available In the present paper we study properties of pre-complete class of Boolean functions - monotone Boolean functions. We discuss interval graph, the abbreviated d.n.f., a minimal d.n.f. and a shortest d.n.f. of this function. Then we present a d.n.f. with the highest number of conjunctionsand we determinate the exact number of them. We count the number of monotone Boolean functions with some special properties. In the end we estimate the number of Boolean functionthat are monotone and self-dual at the same time.
Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences
Chen, William Y C; Zhou, Elaine L F
2010-01-01
The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P(x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P(x+1), which leads to the log-concavity of P(x+c) for any $c\\geq 1$ due to Llamas and Mart\\'{\\i}nez-Bernal. As a consequence, we obtain the ratio monotonicity of the Boros-Moll polynomials obtained by Chen and Xia without resorting to the recurrence relations of the coefficients.
1974-01-01
One of the 150 lead grids used in the multiwire proportional chamber g-ray detector. The 0.75 mm diameter holes are spaced 1 mm centre to centre. The grids were made by chemical cutting techniques in the Godet Workshop of the SB Physics.
Critical Point Theory for Lagrangian Systems
Mazzucchelli, Marco
2012-01-01
Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange's reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more spec
Lagrangian Space Nonlinear $E$-mode clustering
Yu, Hao-Ran; Zhu, Hong-Ming
2016-01-01
We study the nonlinear $E$-mode clustering in Lagrangian space by using large scale structure (LSS) $N$-body simulations and use the displacement field information in Lagrangian space to recover the primordial linear density field. We find that, compared to Eulerian nonlinear density fields, the $E$-mode displacement fields in Lagrangian space improves the cross-correlation scale $k$ with initial density field by factor of 6 $\\sim$ 7, containing 2 orders of magnitude more primordial information. This illustrates ability of potential density reconstruction algorithms, to improve the baryonic acoustic oscillation (BAO) measurements from current and future large scale structure surveys.
An Augmented Lagrangian Approach for Scheduling Problems
Nishi, Tatsushi; Konishi, Masami
The paper describes an augmented Lagrangian decomposition and coordination approach for solving single machine scheduling problems to minimize the total weighted tardiness. The problem belongs to the class of NP-hard combinatorial optimization problem. We propose an augmented Lagrangian decomposition and coordination approach, which is commonly used for continuous optimization problems, for solving scheduling problems despite the fact that the problem is nonconvex and non-differentiable. The proposed method shows a good convergence to a feasible solution without heuristically constructing a feasible solution. The performance of the proposed method is compared with that of an ordinary Lagrangian relaxation.
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.
Semi-Lagrangian off-lattice Boltzmann method for weakly compressible flows.
Krämer, Andreas; Küllmer, Knut; Reith, Dirk; Joppich, Wolfgang; Foysi, Holger
2017-02-01
The lattice Boltzmann method is a simulation technique in computational fluid dynamics. In its standard formulation, it is restricted to regular computation grids, second-order spatial accuracy, and a unity Courant-Friedrichs-Lewy (CFL) number. This paper advances the standard lattice Boltzmann method by introducing a semi-Lagrangian streaming step. The proposed method allows significantly larger time steps, unstructured grids, and higher-order accurate representations of the solution to be used. The appealing properties of the approach are demonstrated in simulations of a two-dimensional Taylor-Green vortex, doubly periodic shear layers, and a three-dimensional Taylor-Green vortex.
Lagrangian analysis of premixed turbulent combustion in hydrogen-air flames
Darragh, Ryan; Poludnenko, Alexei; Hamlington, Peter
2016-11-01
Lagrangian analysis has long been a tool used to analyze non-reacting turbulent flows, and has recently gained attention in the reacting flow and combustion communities. The approach itself allows one to separate local molecular effects, such as those due to reactions or diffusion, from turbulent advective effects along fluid pathlines, or trajectories. Accurate calculation of these trajectories can, however, be rather difficult due to the chaotic nature of turbulent flows and the added complexity of reactions. In order to determine resolution requirements and verify the numerical algorithm, extensive tests are described in this talk for prescribed steady, unsteady, and chaotic flows, as well as for direct numerical simulations (DNS) of non-reacting homogeneous isotropic turbulence. The Lagrangian analysis is then applied to DNS of premixed hydrogen-air flames at two different turbulence intensities for both single- and multi-step chemical mechanisms. Non-monotonic temperature and fuel-mass fraction evolutions are found to exist along trajectories passing through the flame brush. Such non-monotonicity is shown to be due to molecular diffusion resulting from large spatial gradients created by turbulent advection. This work was supported by the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-14-1-0273, and the Department of Defense (DoD) High Performance Computing Modernization Program (HPCMP) under a Frontier project award.
Lagrangian transported MDF methods for compressible high speed flows
Gerlinger, Peter
2017-06-01
This paper deals with the application of thermochemical Lagrangian MDF (mass density function) methods for compressible sub- and supersonic RANS (Reynolds Averaged Navier-Stokes) simulations. A new approach to treat molecular transport is presented. This technique on the one hand ensures numerical stability of the particle solver in laminar regions of the flow field (e.g. in the viscous sublayer) and on the other hand takes differential diffusion into account. It is shown in a detailed analysis, that the new method correctly predicts first and second-order moments on the basis of conventional modeling approaches. Moreover, a number of challenges for MDF particle methods in high speed flows is discussed, e.g. high cell aspect ratio grids close to solid walls, wall heat transfer, shock resolution, and problems from statistical noise which may cause artificial shock systems in supersonic flows. A Mach 2 supersonic mixing channel with multiple shock reflection and a model rocket combustor simulation demonstrate the eligibility of this technique to practical applications. Both test cases are simulated successfully for the first time with a hybrid finite-volume (FV)/Lagrangian particle solver (PS).
Plubtieng Somyot
2009-01-01
Full Text Available Abstract We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in this paper extend and improve the corresponding results of Kamimura et al. (2004, and Iiduka and Takahashi (2008. Finally, we apply our convergence theorem to the convex minimization problem, the problem of finding a zero point of a maximal monotone operator and the complementary problem.
Somyot Plubtieng
2009-01-01
Full Text Available We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in this paper extend and improve the corresponding results of Kamimura et al. (2004, and Iiduka and Takahashi (2008. Finally, we apply our convergence theorem to the convex minimization problem, the problem of finding a zero point of a maximal monotone operator and the complementary problem.
On the Monotone Iterative Method for Set Valued Equation
无
2000-01-01
This paper deals with the monotone iterative method for set- valued operator equation in ordered normed space. Some results for the case of single valued operator are generalized here, as an application, a discontinuous nonlinear differential equation problem is discussed.
Monotone method for initial value problem for fractional diffusion equation
ZHANG Shuqin
2006-01-01
Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation.
Lagrangian hydrocode simulations of the 1958 Lituya Bay tsunamigenic rockslide
Schwaiger, H. F.; Higman, B.
2007-07-01
The interaction of debris flows, whether subaqueous or subaerial, with bodies of water can produce tsunamis with a locally devastating impact. When debris flows begin above the water surface, the impact can produce a large air cavity, corresponding to a large effective volume of water displaced and complicating efforts to model the resulting tsunami. Because grid-based, Eulerian numerical methods have an inherent difficulty tracking material boundaries, we have implemented a particle-based, Lagrangian model (Smoothed Particle Hydrodynamics). We treat the debris flow as an incompressible, viscous fluid and the body of water as inviscid. We use this model to simulate the 1958 Lituya Bay rockslide and resulting tsunami. Our simulation results compare favorably with field observations as well as a scaled laboratory experiment and numerical studies.
Mimetic Methods for Lagrangian Relaxation of Magnetic Fields
Candelaresi, Simon; Hornig, Gunnar
2014-01-01
We present a new code that performs a relaxation of a magnetic field towards a force-free state (Beltrami field) using a Lagrangian numerical scheme. Beltrami fields are of interest for the dynamics of many technical and astrophysical plasmas as they are the lowest energy states that the magnetic field can reach. The numerical method strictly preserves the magnetic flux and the topology of magnetic field lines. In contrast to other implementations we use mimetic operators for the spatial derivatives in order to improve accuracy for high distortions of the grid. Compared with schemes using direct derivatives we find that the final state of the simulation approximates a force-free state with a significantly higher accuracy. We implement the scheme in a code which runs on graphical processing units (GPU), which leads to an enhanced computing speed compared to previous relaxation codes.
Approximations for Monotone and Non-monotone Submodular Maximization with Knapsack Constraints
Kulik, Ariel; Tamir, Tami
2011-01-01
Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we consider the problem of maximizing any submodular function subject to $d$ knapsack constraints, where $d$ is a fixed constant. We establish a strong relation between the discrete problem and its continuous relaxation, obtained through {\\em extension by expectation} of the submodular function. Formally, we show that, for any non-negative submodular function, an $\\alpha$-approximation algorithm for the continuous relaxation implies a randomized $(\\alpha - \\eps)$-approximation algorithm for the discrete problem. We use this relation to improve the best known approximation ratio for the problem to $1/4- \\eps$, for any $\\eps > 0$, and to obtain a nearly optimal $(1-e^{-1}-\\eps)-$approximation ratio for the monotone case, for any $\\eps>0$. We further show that the probabilistic domain ...
Action-Maslov Homomorphism for Monotone Symplectic Manifolds
Branson, Mark
2009-01-01
We explore conditions under which the action-Maslov homomorphism vanishes on monotone symplectic manifolds. Our strategy involves showing that the units in the quantum homology, and thus the Seidel element, have a very specific form. Then we use induction to show that other relevant Gromov-Witten invariants vanish. We prove that these conditions hold for monotone products of projective spaces and for the Grassmannian of 2-planes in $\\C^4$.
Completely monotonic functions related to logarithmic derivatives of entire functions
Pedersen, Henrik Laurberg
2011-01-01
The logarithmic derivative l(x) of an entire function of genus p and having only non-positive zeros is represented in terms of a Stieltjes function. As a consequence, (-1)p(xml(x))(m+p) is a completely monotonic function for all m ≥ 0. This generalizes earlier results on complete monotonicity...... of functions related to Euler's psi-function. Applications to Barnes' multiple gamma functions are given....
Isotonicity of the projection onto the monotone cone
Németh, A B
2012-01-01
A wedge (i.e., a closed nonempty set in the Euclidean space stable under addition and multiplication with non-negative scalars) induces by a standard way a semi-order (a reflexive and transitive binary relation) in the space. The wedges admitting isotone metric projection with respect to the semi-order induced by them are characterized. The obtained result is used to show that the monotone wedge (called monotone cone in regression theory) admits isotone projection.
Monotonic loading of circular surface footings on clay
Ibsen, Lars Bo; Barari, Amin [Aalborg University, Aalborg (Denmark)
2011-12-15
Appropriate modeling of offshore foundations under monotonic loading is a significant challenge in geotechnical engineering. This paper reports experimental and numerical analyses, specifically investigating the response of circular surface footings during monotonic loading and elastoplastic behavior during reloading. By using the findings presented in this paper, it is possible to extend the model to simulate the vertical-load displacement response of offshore bucket foundations.
Convergence for pseudo monotone semiflows on product ordered topological spaces
Yi, Taishan; Huang, Lihong
In this paper, we consider a class of pseudo monotone semiflows, which only enjoy some weak monotonicity properties and are defined on product-ordered topological spaces. Under certain conditions, several convergence principles are established for each precompact orbit of such a class of semiflows to tend to an equilibrium, which improve and extend some corresponding results already known. Some applications to delay differential equations are presented.
Measuring And Explaining The Supersymmetric Lagrangian
Wang, L
2002-01-01
The issues of measuring the supersymmetric Lagrangian once data is available, and making the connections between the low energy effective Lagrangian and fundamental theory, are considered. After a brief introduction to the fundamentals of supersymmetry and overview of Minimal Supersymmetric Standard Model (MSSM), case studies in ways of measuring different parameters in the low energy MSSM Lagrangian are presented. They include: measuring CP violation phases and LSP masses in gluino decay; Higgs production and detection; flavor and CP violation in b → sγ processes; signature of cold dark matter in the cosmic rays. Potential ambiguities in the process of recovering the high energy effective Lagrangian from low energy data are discussed. A new basis, which is explicitly independent of unphysical parameters, is proposed to write the renormalization group equations. After a brief survey of some basic issues of string theory phenomenology, a string theory motivated Pati-Salam like model is const...
Multi-Lagrangians for Integrable Systems
Nutku, Y
2001-01-01
We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit $N$-fold first order local Hamiltonian structure can be cast into variational form with $2N-1$ Lagrangians which will be local functionals of Clebsch potentials. Furthermore we construct a new Lagrangian for polytropic gas dynamics in 1+1 dimensions which is a {\\it local} functional of the physical field variables, namely density and velocity.
Effective Lagrangians and Light Gravitino Phenomenology
Luty, M A; Luty, Markus A.; Ponton, Eduardo
1998-01-01
We construct the low-energy effective lagrangian for supersymmetry breaking models with a light gravitino. Our effective lagrangian is written in terms of the spin-1/2 Goldstino (the longitudinal component of the gravitino) transforming under a non-linear realization of supersymmetry. The Goldstino is derivatively coupled. We use this lagrangian to place bounds on the supersymmetry breaking scale \\sqrt{F} from Goldstino phenomenology. The most stringent bounds come from the coupling of a single photon to Goldstino pairs. For gauge-mediated models, this coupling arises at one loop in the effective lagrangian, and supernova cooling allows \\sqrt{F} > 610 GeV or \\sqrt{F} 140 GeV for tan\\beta = 2.
Detecting Lagrangian fronts with favourable fishery conditions
Prants, S V; Uleysky, M Yu
2012-01-01
Lagrangian fronts in the ocean delineate boundaries between surface waters with different Lagrangian properties. They can be accurately detected in a given velocity field by computing synoptic maps of the drift of synthetic tracers, their Lyapunov exponents, and other Lagrangian indicators. Using Russian ship's catch and location data for a number of commercial fishing seasons in the region of the northwest Pacific with one of the richest fishery in the world, it is shown that the saury fishing grounds with maximal catches are located mainly along those Lagrangian fronts where productive cold waters of the Oyashio Current, warmer waters of the southern branch of the Soya Current, and waters of warm-core Kuroshio rings converge. Computation of those fronts with the altimetric geostrophic velocity fields both in the years with the First and Second Oyashio Intrusions shows that in spite of different oceanographic conditions in both the cases the front locations may serve good indicators of potential fishing grou...
Layered neural networks with non-monotonic transfer functions
Katayama, Katsuki; Sakata, Yasuo; Horiguchi, Tsuyoshi
2003-01-01
We investigate storage capacity and generalization ability for two types of fully connected layered neural networks with non-monotonic transfer functions; random patterns are embedded into the networks by a Hebbian learning rule. One of them is a layered network in which a non-monotonic transfer function of even layers is different from that of odd layers. The other is a layered network with intra-layer connections, in which the non-monotonic transfer function of inter-layer is different from that of intra-layer, and inter-layered neurons and intra-layered neurons are updated alternately. We derive recursion relations for order parameters for those layered networks by the signal-to-noise ratio method. We clarify that the storage capacity and the generalization ability for those layered networks are enhanced in comparison with those with a conventional monotonic transfer function when non-monotonicity of the transfer functions is selected optimally. We also point out that some chaotic behavior appears in the order parameters for the layered networks when non-monotonicity of the transfer functions increases.
On invariant sets in Lagrangian graphs
无
2010-01-01
In this exposition, we show that the Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are sufficiently smooth. We also provide some counterexamples to show that if the Hamiltonian function is not smooth enough, then it may be non-constant on a compact invariant connected subset which lies in a Lagrangian graph.
Lagrangian Formulation of Todorov-Komar Model
Gomis, J.; Kamimura, K.; Pons, J. M.
1984-05-01
The multi-temporal Hamiltonian model of relativistic particle interaction (Todorov-Komar model) is studied from the viewpoint of the Lagrangian formalism. The action is constructed and the gauge structure is clarified.The mathematical coordinates used to describe the Lagrangian are not gauge invariant and are disqualified as the physical coordinates of the interacting particles. The position of the particles is defined as the function of the canonical variables so that the world lines are invariant under the gauge transformations.
A Vertical Grid Module for Baroclinic Models of the Atmosphere
Drake, John B [ORNL
2008-04-01
The vertical grid of an atmospheric model assigns dynamic and thermo- dynamic variables to grid locations. The vertical coordinate is typically not height but one of a class of meteorological variables that vary with atmo- spheric conditions. The grid system is chosen to further numerical approx- imations of the boundary conditions so that the system is terrain following at the surface. Lagrangian vertical coordinates are useful in reducing the numerical errors from advection processes. That the choices will effect the numercial properties and accuracy is explored in this report. A MATLAB class for Lorentz vertical grids is described and applied to the vertical struc- ture equation and baroclinic atmospheric circulation. A generalized meteo- rolgoical coordinate system is developed which can support σ, isentropic θ vertical coordinate, or Lagrangian vertical coordinates. The vertical atmo- spheric column is a MATLAB class that includes the kinematic and ther- modynamic variables along with methods for computing geopoentials and terms relevant to a 3D baroclinc atmospheric model.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding
Krause, Katharina; Klopper, Wim, E-mail: klopper@kit.edu [Karlsruhe Institute of Technology (KIT), Institute of Physical Chemistry, Theoretical Chemistry Group, KIT Campus South, P.O. Box 6980, 76049 Karlsruhe (Germany)
2016-01-28
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.
CERN. Geneva
2004-01-01
The aim of Grid computing is to enable the easy and open sharing of resources between large and highly distributed communities of scientists and institutes across many independent administrative domains. Convincing site security officers and computer centre managers to allow this to happen in view of today's ever-increasing Internet security problems is a major challenge. Convincing users and application developers to take security seriously is equally difficult. This paper will describe the main Grid security issues, both in terms of technology and policy, that have been tackled over recent years in LCG and related Grid projects. Achievements to date will be described and opportunities for future improvements will be addressed.
Popovic, Zorana B.; Kim, Moonil; Rutledge, David B.
1988-01-01
Loading a two-dimensional grid with active devices offers a means of combining the power of solid-state oscillators in the microwave and millimeter-wave range. The grid structure allows a large number of negative resistance devices to be combined. This approach is attractive because the active devices do not require an external locking signal, and the combining is done in free space. In addition, the loaded grid is a planar structure amenable to monolithic integration. Measurements on a 25-MESFET grid at 9.7 GHz show power-combining and frequency-locking without an external locking signal, with an ERP of 37 W. Experimental far-field patterns agree with theoretical results obtained using reciprocity.
Foster, Ian
2001-08-01
The term "Grid Computing" refers to the use, for computational purposes, of emerging distributed Grid infrastructures: that is, network and middleware services designed to provide on-demand and high-performance access to all important computational resources within an organization or community. Grid computing promises to enable both evolutionary and revolutionary changes in the practice of computational science and engineering based on new application modalities such as high-speed distributed analysis of large datasets, collaborative engineering and visualization, desktop access to computation via "science portals," rapid parameter studies and Monte Carlo simulations that use all available resources within an organization, and online analysis of data from scientific instruments. In this article, I examine the status of Grid computing circa 2000, briefly reviewing some relevant history, outlining major current Grid research and development activities, and pointing out likely directions for future work. I also present a number of case studies, selected to illustrate the potential of Grid computing in various areas of science.
Driving performance impairments due to hypovigilance on monotonous roads.
Larue, Grégoire S; Rakotonirainy, Andry; Pettitt, Anthony N
2011-11-01
Drivers' ability to react to unpredictable events deteriorates when exposed to highly predictable and uneventful driving tasks. Highway design reduces the driving task mainly to a lane-keeping manoeuvre. Such a task is monotonous, providing little stimulation and this contributes to crashes due to inattention. Research has shown that driver's hypovigilance can be assessed with EEG measurements and that driving performance is impaired during prolonged monotonous driving tasks. This paper aims to show that two dimensions of monotony - namely road design and road side variability - decrease vigilance and impair driving performance. This is the first study correlating hypovigilance and driver performance in varied monotonous conditions, particularly on a short time scale (a few seconds). We induced vigilance decrement as assessed with an EEG during a monotonous driving simulator experiment. Road monotony was varied through both road design and road side variability. The driver's decrease in vigilance occurred due to both road design and road scenery monotony and almost independently of the driver's sensation seeking level. Such impairment was also correlated to observable measurements from the driver, the car and the environment. During periods of hypovigilance, the driving performance impairment affected lane positioning, time to lane crossing, blink frequency, heart rate variability and non-specific electrodermal response rates. This work lays the foundation for the development of an in-vehicle device preventing hypovigilance crashes on monotonous roads.
Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.
Holm, Darryl D.
2002-06-01
We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.
Geometric Properties of the Monotonic Logical Grid Algorithm for Near Neighbor Calculations.
1986-04-24
ON * THE NEAR MISS PROBABILITY ................ o...................... 9 ANLSI F WPPNG (RANDOMPv MOTION)............................1.0 APPENDE...so near neighbor coming quite "close". It is these rare " near miss " events which’ r determine the required NNT size. Additional information concerning...34 near miss " probability. Such information .provides a criterion for optimizing (or minimizing) the NNT based on the ’cutoff radius" R, for the particular
Estimating monotonic rates from biological data using local linear regression.
Olito, Colin; White, Craig R; Marshall, Dustin J; Barneche, Diego R
2017-03-01
Accessing many fundamental questions in biology begins with empirical estimation of simple monotonic rates of underlying biological processes. Across a variety of disciplines, ranging from physiology to biogeochemistry, these rates are routinely estimated from non-linear and noisy time series data using linear regression and ad hoc manual truncation of non-linearities. Here, we introduce the R package LoLinR, a flexible toolkit to implement local linear regression techniques to objectively and reproducibly estimate monotonic biological rates from non-linear time series data, and demonstrate possible applications using metabolic rate data. LoLinR provides methods to easily and reliably estimate monotonic rates from time series data in a way that is statistically robust, facilitates reproducible research and is applicable to a wide variety of research disciplines in the biological sciences. © 2017. Published by The Company of Biologists Ltd.
Monotone traveling wavefronts of the KPP-Fisher delayed equation
Gomez, Adrian
2010-01-01
In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-Piskunov-Fisher equation. Since then, this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction-diffusion equations. In this paper, we give a complete solution to the problem of existence and uniqueness of monotone waves in the KPP-Fisher equation. We show that each monotone traveling wave can be found via an iteration procedure. The proposed approach is based on the use of special monotone integral operators (which are different from the usual Wu-Zou operator) and appropriate upper and lower solutions associated to them. The analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach.
Saiz, P.; Andreeva, J.; Cirstoiu, C.; Gaidioz, B.; Herrala, J.; Maguire, E. J.; Maier, G.; Rocha, R.
2008-07-01
Thanks to the Grid, users have access to computing resources distributed all over the world. The Grid hides the complexity and the differences of its heterogeneous components. In such a distributed system, it is clearly very important that errors are detected as soon as possible, and that the procedure to solve them is well established. We focused on two of its main elements: the workload and the data management systems. We developed an application to investigate the efficiency of the different centres. Furthermore, our system can be used to categorize the most common error messages, and control their time evolution.
Monotone data visualization using rational trigonometric spline interpolation.
Ibraheem, Farheen; Hussain, Maria; Hussain, Malik Zawwar
2014-01-01
Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically.
Monotone Data Visualization Using Rational Trigonometric Spline Interpolation
Farheen Ibraheem
2014-01-01
Full Text Available Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically.
Ultimate generalization to monotonicity for uniform convergence of trigonometric series
无
2010-01-01
Chaundy and Jolliffe proved that if {a n } is a non-increasing (monotonic) real sequence with lim n →∞ a n = 0, then a necessary and sufficient condition for the uniform convergence of the series ∑∞ n=1 a n sin nx is lim n →∞ na n = 0. We generalize (or weaken) the monotonic condition on the coefficient sequence {a n } in this classical result to the so-called mean value bounded variation condition and prove that the generalized condition cannot be weakened further. We also establish an analogue to the generalized Chaundy-Jolliffe theorem in the complex space.
Vector optimization and monotone operators via convex duality recent advances
Grad, Sorin-Mihai
2014-01-01
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
A hybrid Lagrangian-Eulerian numerical model for sea-ice dynamics
无
2007-01-01
A hybrid Lagrangian-Eulerian (HLE) method is developed for sea ice dynamics, which combines the high computational efficiency of finite difference method (FDM) with the high numerical accuracy of smoothed particle hydrodynamics (SPH). In this HLE model, the sea ice cover is represented by a group of Lagrangian ice particles with their own thicknesses and concentrations. These ice variables are interpolated to the Eularian gird nodes using the Gaussian interpolation function. The FDM is used to determine the ice velocities at Eulerian grid nodes, and the velocities of Lagrangian ice particles are interpolated from these grid velocities with the Gaussian function also. The thicknesses and concentrations of ice particles are determined based on their new locations. With the HLE numerical model, the ice ridging process in a rectangular basin is simulated, and the simulated results are validated with the analytical solution. This method is also applied to the simulation of sea ice dynamics in a vortex wind field. At last, this HLE model is applied to the Bohai Sea, and the simulated concentration, thickness and velocity match the satellite images and the field observed data well.
Forecasting for a Lagrangian aircraft campaign
A. Stohl
2004-01-01
Full Text Available A forecast system has been developed in preparation for an upcoming aircraft measurement campaign, where the same air parcels polluted by emissions over North America shall be sampled repeatedly as they leave the continent, during transport over the Atlantic, and upon their arrival over Europe. This paper describes the model system in advance of the campaign, in order to make the flight planners familiar with the novel model output. The aim of a Lagrangian strategy is to infer changes in the chemical composition and aerosol distribution occurring en route by measured upwind/downwind differences. However, guiding aircraft repeatedly into the same polluted air parcels requires careful forecasting, for which no suitable model system exists to date. This paper describes a procedure using both Eulerian-type (i.e. concentration fields and Lagrangian-type (i.e. trajectories model output from the Lagrangian particle dispersion model FLEXPART to predict the best opportunities for a Lagrangian experiment. The best opportunities are defined as being highly polluted air parcels which receive little or no emission input after the first measurement, which experience relatively little mixing, and which are reachable by as many aircraft as possible. For validation the system was applied to the period of the NARE 97 campaign where approximately the same air masses were sampled on different flights. Measured upwind/downwind differences in carbon monoxide (CO and ozone (O3 decreased significantly as the threshold values used for accepting cases as Lagrangian were tightened. This proves that the model system can successfully identify Lagrangian opportunities.
Forecasting for a Lagrangian aircraft campaign
A. Stohl
2004-05-01
Full Text Available A forecast system has been developed in preparation for an upcoming aircraft measurement campaign, where the same air parcels polluted by emissions over North America shall be sampled repeatedly as they leave the continent, during transport over the Atlantic, and upon their arrival over Europe. This paper describes the model system in advance of the campaign, in order to make the flight planners familiar with the novel model output. The aim of a Lagrangian strategy is to infer changes in the chemical composition and aerosol distribution occurring en route by measured upwind/downwind differences. However, guiding aircraft repeatedly into the same polluted air parcels requires careful forecasting, for which no suitable model system exists to date. This paper describes a procedure using both Eulerian-type (i.e. concentration fields and Lagrangian-type (i.e. trajectories model output from the Lagrangian particle dispersion model FLEXPART to predict the best opportunities for a Lagrangian experiment. The best opportunities are defined as being highly polluted air parcels which receive little or no emission input after the first measurement, which experience relatively little mixing, and which are reachable by as many aircraft as possible. For validation the system was applied to the period of the NARE 97 campaign where approximately the same air masses were sampled on different flights. Measured upwind/downwind differences in carbon monoxide (CO and ozone (O_{3} decreased significantly as the threshold values used for accepting cases as Lagrangian were tightened. This proves that the model system can successfully identify Lagrangian opportunities.
Lagrangians for the W-Algebra Models
Gaite, J C
1994-01-01
The field algebra of the minimal models of W-algebras is amenable to a very simple description as a polynomial algebra generated by few elementary fields, corresponding to order parameters. Using this description, the complete Landau-Ginzburg lagrangians for these models are obtained. Perturbing these lagrangians we can explore their phase diagrams, which correspond to multicritical points with $D_n$ symmetry. In particular, it is shown that there is a perturbation for which the phase structure coincides with that of the IRF models of Jimbo et al.
Effective Lagrangian in de Sitter Spacetime
Kitamoto, Hiroyuki
2016-01-01
Scale invariant fluctuations of metric are universal feature of quantum gravity in de Sitter spacetime. We construct an effective Lagrangian which summarizes their implications on local physics by integrating super-horizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective Lagrangian as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.
Maxwell-like Lagrangians for higher spins
Campoleoni, Andrea
2012-01-01
We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless fields produce single-particle actions, while whenever trace constraints can be dispensed with the resulting Lagrangians display the same reducible, multi-particle spectra as those emerging from the tensionless limit of free open-string field theory. For all explored options the corresponding kinetic operators take essentially the same form as in the spin-one, Maxwell case.
The Mather problem for lower semicontinuous Lagrangians
Gomes, Diogo A.
2013-08-01
In this paper we develop the Aubry-Mather theory for Lagrangians in which the potential energy can be discontinuous. Namely we assume that the Lagrangian is lower semicontinuous in the state variable, piecewise smooth with a (smooth) discontinuity surface, as well as coercive and convex in the velocity. We establish existence of Mather measures, various approximation results, partial regularity of viscosity solutions away from the singularity, invariance by the Euler-Lagrange flow away from the singular set, and further jump conditions that correspond to conservation of energy and tangential momentum across the discontinuity. © 2013 Springer Basel.
Learn the Lagrangian: A Vector-Valued RKHS Approach to Identifying Lagrangian Systems.
Cheng, Ching-An; Huang, Han-Pang
2016-12-01
We study the modeling of Lagrangian systems with multiple degrees of freedom. Based on system dynamics, canonical parametric models require ad hoc derivations and sometimes simplification for a computable solution; on the other hand, due to the lack of prior knowledge in the system's structure, modern nonparametric models in machine learning face the curse of dimensionality, especially in learning large systems. In this paper, we bridge this gap by unifying the theories of Lagrangian systems and vector-valued reproducing kernel Hilbert space. We reformulate Lagrangian systems with kernels that embed the governing Euler-Lagrange equation-the Lagrangian kernels-and show that these kernels span a subspace capturing the Lagrangian's projection as inverse dynamics. By such property, our model uses only inputs and outputs as in machine learning and inherits the structured form as in system dynamics, thereby removing the need for the mundane derivations for new systems as well as the generalization problem in learning from scratches. In effect, it learns the system's Lagrangian, a simpler task than directly learning the dynamics. To demonstrate, we applied the proposed kernel to identify the robot inverse dynamics in simulations and experiments. Our results present a competitive novel approach to identifying Lagrangian systems, despite using only inputs and outputs.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
Ku, S. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Hager, R. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Chang, C. S. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Kwon, J. M. [National Fusion Research Institute, Republic of Korea; Parker, S. E. [University of Colorado Boulder, USA
2016-06-01
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
Ku, S., E-mail: sku@pppl.gov [Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States); Hager, R.; Chang, C.S. [Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States); Kwon, J.M. [National Fusion Research Institute (Korea, Republic of); Parker, S.E. [University of Colorado Boulder (United States)
2016-06-15
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.
A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma
Ku, S.; Hager, R.; Chang, C. S.; Kwon, J. M.; Parker, S. E.
2016-06-01
In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation - e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others - can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function - driven by ionization, charge exchange and wall loss - is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.
MONOTONE ITERATION FOR ELLIPTIC PDEs WITH DISCONTINUOUS NONLINEAR TERMS
Zou Qingsong
2005-01-01
In this paper, we use monotone iterative techniques to show the existence of maximal or minimal solutions of some elliptic PDEs with nonlinear discontinuous terms. As the numerical analysis of this PDEs is concerned, we prove the convergence of discrete extremal solutions.
Modeling non-monotone risk aversion using SAHARA utility functions
A. Chen; A. Pelsser; M. Vellekoop
2011-01-01
We develop a new class of utility functions, SAHARA utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk averse for very low values of wealth. The class contains the well-known exponential and
On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions
Ciepliński Krzysztof
2009-01-01
Full Text Available We investigate the existence and uniqueness of solutions of the functional equation , , where are closed intervals, and , are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result.
L^p solutions of reflected BSDEs under monotonicity condition
Rozkosz, Andrzej
2012-01-01
We prove existence and uniqueness of L^p solutions of reflected backward stochastic differential equations with p-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by the penalization method. Our results are new even in the classical case p=2.
A monotonic method for solving nonlinear optimal control problems
Salomon, Julien
2009-01-01
Initially introduced in the framework of quantum control, the so-called monotonic algorithms have shown excellent numerical results when dealing with various bilinear optimal control problems. This paper aims at presenting a unified formulation of such procedures and the intrinsic assumptions they require. In this framework, we prove the feasibility of the general algorithm. Finally, we explain how these assumptions can be relaxed.
On Some Conjectures on the Monotonicity of Some Arithmetical Sequences
2012-01-01
THE MONOTONICITY OF SOME ARITHMETICAL SEQUENCES ∗ Florian Luca † Centro de Ciencias Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089...visit of P. S. to the Centro de Ciencias Matemáticas de la UNAM in Morelia in August 2012. During the preparation of this paper, F. L. was supported in
Interval Routing and Minor-Monotone Graph Parameters
Bakker, E.M.; Bodlaender, H.L.; Tan, R.B.; Leeuwen, J. van
2006-01-01
We survey a number of minor-monotone graph parameters and their relationship to the complexity of routing on graphs. In particular we compare the interval routing parameters κslir(G) and κsir(G) with Colin de Verdi`ere’s graph invariant μ(G) and its variants λ(G) and κ(G). We show that for all the k
Multivariate Regression with Monotone Missing Observation of the Dependent Variables
Raats, V.M.; van der Genugten, B.B.; Moors, J.J.A.
2002-01-01
Multivariate regression is discussed, where the observations of the dependent variables are (monotone) missing completely at random; the explanatory variables are assumed to be completely observed.We discuss OLS-, GLS- and a certain form of E(stimated) GLS-estimation.It turns out that
Minimum Cost Spanning Tree Games and Population Monotonic Allocation Schemes
Norde, H.W.; Moretti, S.; Tijs, S.H.
2001-01-01
In this paper we present the Subtraction Algorithm that computes for every classical minimum cost spanning tree game a population monotonic allocation scheme.As a basis for this algorithm serves a decomposition theorem that shows that every minimum cost spanning tree game can be written as nonnegati
Size monotonicity and stability of the core in hedonic games
Dimitrov, Dinko; Sung, Shao Chin
2011-01-01
We show that the core of each strongly size monotonic hedonic game is not empty and is externally stable. This is in sharp contrast to other sufficient conditions for core non-emptiness which do not even guarantee the existence of a stable set in such games.
Monotone missing data and repeated controls of fallible authors
Raats, V.M.
2004-01-01
Chapters 2 and 3 focus on repeated audit controls with categorical variables. Chapter 4 and 5 introduce and analyse a very general multivariate regression model for (monotone) missing data. In the final Chapter 6 the previous chapters are combined into a more realistic model for repeated audit contr
A POTENTIAL REDUCTION ALGORITHM FOR MONOTONE VARIATIONAL INEQUALITY PROBLEMS
无
2000-01-01
A potential reduction algorithm is proposed for the solution of monotone variational inequality problems. At each step of the algorithm, a system of linear equations is solved to get the search direction and the Armijo's rule is used to determine the stepsize.It is proved that the algorithm is globally convergent. Computational results are reported.
Relaxing monotonicity in the identification of local average treatment effects
Huber, Martin; Mellace, Giovanni
In heterogeneous treatment effect models with endogeneity, the identification of the local average treatment effect (LATE) typically relies on an instrument that satisfies two conditions: (i) joint independence of the potential post-instrument variables and the instrument and (ii) monotonicity...
Incorporating "Unconscious Reanalysis" into an Incremental, Monotonic Parser
Sturt, P
1995-01-01
This paper describes an implementation based on a recent model in the psycholinguistic literature. We define a parsing operation which allows the reanalysis of dependencies within an incremental and monotonic processing architecture, and discuss search strategies for its application in a head-initial language (English) and a head-final language (Japanese).
Interval Routing and Minor-Monotone Graph Parameters
Bakker, E.M.; Bodlaender, H.L.; Tan, R.B.; Leeuwen, J. van
2006-01-01
We survey a number of minor-monotone graph parameters and their relationship to the complexity of routing on graphs. In particular we compare the interval routing parameters κslir(G) and κsir(G) with Colin de Verdi`ere’s graph invariant μ(G) and its variants λ(G) and κ(G). We show that for all the
Reasoning Biases, Non-Monotonic Logics, and Belief Revision
Dutilh Novaes, Catarina; Veluwenkamp, Herman
2017-01-01
A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science etc.: various logics (epistemic logics; non-monotonic logics), probabilistic systems (most notably, but not exclusi
The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows
Lufkin, Eric A.; Hawley, John F.
1993-01-01
We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.
A new Lagrangian method for three-dimensional steady supersonic flows
Loh, Ching-Yuen; Liou, Meng-Sing
1993-01-01
In this report, the new Lagrangian method introduced by Loh and Hui is extended for three-dimensional, steady supersonic flow computation. The derivation of the conservation form and the solution of the local Riemann solver using the Godunov and the high-resolution TVD (total variation diminished) scheme is presented. This new approach is accurate and robust, capable of handling complicated geometry and interactions between discontinuous waves. Test problems show that the extended Lagrangian method retains all the advantages of the two-dimensional method (e.g., crisp resolution of a slip-surface (contact discontinuity) and automatic grid generation). In this report, we also suggest a novel three dimensional Riemann problem in which interesting and intricate flow features are present.
GYSELA, a full-f global gyrokinetic Semi-Lagrangian code for ITG turbulence simulations
Grandgirard, V.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Crouseilles, N.; Latu, G.; Sonnendrücker, E.; Besse, N.; Bertrand, P.
2006-11-01
This work addresses non-linear global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence with the GYSELA code. The particularity of GYSELA code is to use a fixed grid with a Semi-Lagrangian (SL) scheme and this for the entire distribution function. The 4D non-linear drift-kinetic version of the code already showns the interest of such a SL method which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been upgrated to run 5D simulations of toroidal ITG turbulence. Linear benchmarks and non-linear first results prove that semi-lagrangian codes can be a credible alternative for gyrokinetic simulations.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Solution of the Euler Equations
Anderson, R W; Elliott, N S; Pember, R B
2003-02-14
A new method that combines staggered grid arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the methods are driven by the need to reconcile traditional AMR techniques with the staggered variables and moving, deforming meshes associated with Lagrange based ALE schemes. We develop interlevel solution transfer operators and interlevel boundary conditions first in the case of purely Lagrangian hydrodynamics, and then extend these ideas into an ALE method by developing adaptive extensions of elliptic mesh relaxation techniques. Conservation properties of the method are analyzed, and a series of test problem calculations are presented which demonstrate the utility and efficiency of the method.
Baoshan Zhu; Kyoji Kamemoto
2005-01-01
In this study, an advanced Lagrangian vortexboundary element method is applied to simulate the unsteady impeller-diffuser interactions in a diffuser pump not only for design but also for off-design considerations. In velocity calculations based on the Biot-Savart law we do not have to grid large portions of the flow field and the calculation points are concentrated in the regions where vorticity is present.Lagrangian representation of the evolving vorticity field is well suited to moving boundaries. An integral pressure equation shows that the pressure distribution can be estimated directly from the instantaneous velocity and vorticity field.The numerical results are compared with the experimental data and the comparisons show that the method used in this study can provide us insight into the complicated unsteady impeller-diffuser interaction phenomena in a diffuser pump.
Eulerian and modified Lagrangian approaches to multi-dimensional condensation and coagulation
Li, Xiang-Yu; Haugen, N E L; Svensson, G
2016-01-01
Turbulence is believed to play a crucial role in cloud droplet growth. It makes the collision process of inertial particles strongly nonlinear, which motivates the study of two rather different numerical schemes. Here, an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and coagulation. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow, or just gravitational acceleration without gas flow. Discrepancies between different schemes are most strongly exposed when condensation and coagulation are studied separately, while their combined effects tend to result in smaller discrepancies. In the Eulerian approach, the late growth of the mean particle radius slows down for finer mass bins, especially for collisions caused by different particle sizes. In the Lagrangian approach it is nearly independent of grid resolution at early times and weak...
Lagrangian theoretical framework of dynamics of nonholonomic systems
无
2007-01-01
@@ By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.
Lagrangian theoretical framework of dynamics of nonholonomic systems
LIANG; LiFu
2007-01-01
By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right. ……
On Stability of the Mechanical Lagrangian Systems
Valer Niminet
2011-12-01
Full Text Available
We consider MLS (mechanical Lagrangian systems with
external forces. We give some conditions of stability and dissipativity and show that the energy of the system decreases on the integral curves.
Key words: LMS, stability, dissipative system.
Lagrangian tetragons and instabilities in Hamiltonian dynamics
Entov, Michael; Polterovich, Leonid
2017-01-01
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.
Experimental design for drifting buoy Lagrangian test
Saunders, P. M.
1975-01-01
A test of instrumentation fabricated to measure the performance of a free drifting buoy as a (Lagrangian) current meter is described. Specifically it is proposed to distinguish between the trajectory of a drogued buoy and the trajectory of the water at the level of the drogue by measuring the flow relative to the drogue.
Towards effective Lagrangians for adelic strings
Dragovich, Branko
2009-01-01
p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By this way, one can consider adelic strings as a very useful instrument in the further investigation of modern string theory. It is remarkable that for some scalar p-adic strings exist effective Lagrangians, which are based on real instead of p-adic numbers and describe not only four-point scattering amplitudes but also all higher ones at the tree level. In this work, starting from p-adic Lagrangians, we consider some approaches to construction of effective field Lagrangians for p-adic sector of adelic strings. It yields Lagrangians for nonlinear and nonlocal scalar field theory, where spacetime nonlocality is determined by an infinite number of derivatives contained in the operator-valued Riemann zeta function. Owing to the Riemann zeta function in the dynamics of these sca...
A new semi-Lagrangian difference scheme
季仲贞; 陈嘉滨
2001-01-01
A new completely energy-conserving semi-Lagrangian scheme is constructed. The numerical solution of shallow water equation shows that this conservative scheme preserves the total energy in twelve significant digits, while the traditional scheme does only in five significant digits.
Lagrangian duality and cone convexlike functions
J.B.G. Frenk (Hans); G. Kassay
2005-01-01
textabstractIn this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation s
Lagrangian duality and cone convexlike functions
J.B.G. Frenk (Hans); G. Kassay
2005-01-01
textabstractIn this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation
Target Lagrangian kinematic simulation for particle-laden flows
Murray, S.; Lightstone, M. F.; Tullis, S.
2016-09-01
The target Lagrangian kinematic simulation method was motivated as a stochastic Lagrangian particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target Lagrangian integral timescale. In addition to recovering the expected Lagrangian properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark.
National Aeronautics and Space Administration — Structured multiblock grid of HIRENASD wing with medium grid density, about 10 mill grid points, 9.5 mill cells. Starting from coarse AIAA AEPW structured grid,...
Classification of Lagrangian Fibrations over a Klein Bottle
Sepe, D
2009-01-01
This paper completes the classification of regular Lagrangian fibratiopns over compact surfaces. \\cite{misha} classifies regular Lagrangian fibrations over $\\mathbb{T}^2$. The main theorem in \\cite{hirsch} is used in order to classify integral affine structures on the Klein bottle $K^2$ and, hence, regular Lagrangian fibrations over this space.
Lagrangian multiplier and massive Yang-Mills fields
Li, Z.P.
1982-09-01
If we give appropriate constraint to the gauge invariant Lagrangian, the variation principle of the action convert to the variational problems with subsidiary condition. The effective Lagrangian which contains Lagrangian multiplier may have the mass term of the mesons. In that case we obtain naturally the massive Yang-Mills fields which was discussed by Nakanishi.
Saiz, P; Rocha, R; Andreeva, J
2007-01-01
We are offering a system to track the efficiency of different components of the GRID. We can study the performance of both the WMS and the data transfers At the moment, we have set different parts of the system for ALICE, ATLAS, CMS and LHCb. None of the components that we have developed are VO specific, therefore it would be very easy to deploy them for any other VO. Our main goal is basically to improve the reliability of the GRID. The main idea is to discover as soon as possible the different problems that have happened, and inform the responsible. Since we study the jobs and transfers issued by real users, we see the same problems that users see. As a matter of fact, we see even more problems than the end user does, since we are also interested in following up the errors that GRID components can overcome by themselves (like for instance, in case of a job failure, resubmitting the job to a different site). This kind of information is very useful to site and VO administrators. They can find out the efficien...
Lagrangian statistics in turbulent channel flow: implications for Lagrangian stochastic models
Stelzenmuller, Nickolas; Polanco, Juan Igancio; Vinkovic, Ivana; Mordant, Nicolas
2016-11-01
Lagrangian acceleration and velocity correlations in statistically one-dimesional turbulence are presented in the context of the development of Lagrangian stochastic models of inhomogeneous turbulent flows. These correlations are measured experimentally by 3D PTV in a high aspect ratio water channel at Reτ = 1450 , and numerically from DNS performed at the same Reynolds number. Lagrangian timescales, key components of Lagrangian stochastic models, are extracted from acceleration and velocity autocorrelations. The evolution of these timescales as a function of distance to the wall is presented, and compared to similar quantities measured in homogeneous isotropic turbulence. A strong dependance of all Lagrangian timescales on wall distance is present across the width of the channel. Significant cross-correlations are observed between the streamwise and wall-normal components of both acceleration and velocity. Lagrangian stochastic models of this flow must therefore retain dependance on the wall-normal coordinate and the components of acceleration and velocity, resulting in significantly more complex models than those used for homogeneous isotropic turbulence. We gratefully acknowledge funding from the Agence Nationale de la Recherche, LabEx Tec 21, and CONICYT Becas Chile.
Non-monotonic effect of confinement on the glass transition
Varnik, Fathollah; Franosch, Thomas
2016-04-01
The relaxation dynamics of glass forming liquids and their structure are influenced in the vicinity of confining walls. This effect has mostly been observed to be a monotonic function of the slit width. Recently, a qualitatively new behaviour has been uncovered by Mittal and coworkers, who reported that the single particle dynamics in a hard-sphere fluid confined in a planar slit varies in a non-monotonic way as the slit width is decreased from five to roughly two particle diametres (Mittal et al 2008 Phys. Rev. Lett. 100 145901). In view of the great potential of this effect for applications in those fields of science and industry, where liquids occur under strong confinement (e.g. nano-technology), the number of researchers studying various aspects and consequences of this non-monotonic behaviour has been rapidly growing. This review aims at providing an overview of the research activity in this newly emerging field. We first briefly discuss how competing mechanisms such as packing effects and short-range attraction may lead to a non-monotonic glass transition scenario in the bulk. We then analyse confinement effects on the dynamics of fluids using a thermodynamic route which relates the single particle dynamics to the excess entropy. Moreover, relating the diffusive dynamics to the Widom’s insertion probability, the oscillations of the local dynamics with density at moderate densities are fairly well described. At high densities belonging to the supercooled regime, however, this approach breaks down signaling the onset of strongly collective effects. Indeed, confinement introduces a new length scale which in the limit of high densities and small pore sizes competes with the short-range local order of the fluid. This gives rise to a non-monotonic dependence of the packing structure on confinement, with a corresponding effect on the dynamics of structural relaxation. This non-monotonic effect occurs also in the case of a cone-plate type channel, where the degree
Classification of Flat Lagrangian Surfaces in Complex Lorentzian Plane
Bang-Yen CHEN; Johan FASTENAKELS
2007-01-01
One of the most fundamental problems in the study of Lagrangian submanifolds fromRiemannian geometric point of view is to classify Lagrangian immersions of real space forms intocomplex space forms. The main purpose of this paper is thus to classify flat Lagrangian surfaces inthe Lorentzian complex plane C12. Our main result states that there are thirty-eight families of flatLagrangian surfaces in C12. Conversely, every flat Lagrangian surface in C12 is locally congruent to oneof the thirty-eight families.
A Hybrid Approach to Proving Memory Reference Monotonicity
Oancea, Cosmin E.
2013-01-01
Array references indexed by non-linear expressions or subscript arrays represent a major obstacle to compiler analysis and to automatic parallelization. Most previous proposed solutions either enhance the static analysis repertoire to recognize more patterns, to infer array-value properties, and to refine the mathematical support, or apply expensive run time analysis of memory reference traces to disambiguate these accesses. This paper presents an automated solution based on static construction of access summaries, in which the reference non-linearity problem can be solved for a large number of reference patterns by extracting arbitrarily-shaped predicates that can (in)validate the reference monotonicity property and thus (dis)prove loop independence. Experiments on six benchmarks show that our general technique for dynamic validation of the monotonicity property can cover a large class of codes, incurs minimal run-time overhead and obtains good speedups. © 2013 Springer-Verlag.
Measurement of non-monotonic Casimir forces between silicon nanostructures
Tang, L.; Wang, M.; Ng, C. Y.; Nikolic, M.; Chan, C. T.; Rodriguez, A. W.; Chan, H. B.
2017-01-01
Casimir forces are of fundamental interest because they originate from quantum fluctuations of the electromagnetic field. Apart from controlling this force via the optical properties of materials, a number of novel geometries have been proposed to generate repulsive and/or non-monotonic Casimir forces between bodies separated by vacuum gaps. Experimental realization of these geometries, however, is hindered by the difficulties in alignment when the bodies are brought into close proximity. Here, using an on-chip platform with integrated force sensors and actuators, we circumvent the alignment problem and measure the Casimir force between two surfaces with nanoscale protrusions. We demonstrate that the force depends non-monotonically on the displacement. At some displacements, the Casimir force leads to an effective stiffening of the nanomechanical spring. Our findings pave the way for exploiting the Casimir force in nanomechanical systems using structures of complex and non-conventional shapes.
A Monotonic Precise Current DAC for Sensor Applications
P. Horsky
2008-12-01
Full Text Available In this paper a 17 bit monotonic precise current DAC for sensor applications is described. It is working in a harsh automotive environment in a wide temperature range with high output voltage swing and low current consumption. To guarantee monotonicity current division and segmentation techniques are used. To improve the output impedance, the accuracy and the voltage compliance of the DAC, two active cascoding loops and one follower loop are used. The resolution of the DAC is further increased by applying pulse width modulation to one fine LSB current. To achieve low power consumption unused coarse current sources are switched off. Several second order technological effects influencing final performance and circuits dealing with them are discussed.
Computation of Optimal Monotonicity Preserving General Linear Methods
Ketcheson, David I.
2009-07-01
Monotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal methods even among classes involving very high order accuracy and that use many steps and/or stages. The optimality of some recently proposed methods is verified, and many more efficient methods are found. We use similar algorithms to find optimal strong stability preserving linear multistep methods of both explicit and implicit type, including methods for hyperbolic PDEs that use downwind-biased operators.
Rational functions with maximal radius of absolute monotonicity
Loczi, Lajos
2014-05-19
We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions arise in the application of implicit s-stage, order p Runge-Kutta methods for initial value problems and the radius of absolute monotonicity governs the numerical preservation of properties like positivity and maximum-norm contractivity. We construct a function with p=2 and R>2s, disproving a conjecture of van de Griend and Kraaijevanger. We determine the maximum attainable radius for functions in several one-parameter families of rational functions. Moreover, we prove earlier conjectured optimal radii in some families with 2 or 3 parameters via uniqueness arguments for systems of polynomial inequalities. Our results also prove the optimality of some strong stability preserving implicit and singly diagonally implicit Runge-Kutta methods. Whereas previous results in this area were primarily numerical, we give all constants as exact algebraic numbers.
Computing 3-D steady supersonic flow via a new Lagrangian approach
Loh, C. Y.; Liou, M.-S.
1993-01-01
The new Lagrangian method introduced by Loh and Hui (1990) is extended for 3-D steady supersonic flow computation. Details of the conservation form, the implementation of the local Riemann solver, and the Godunov and the high resolution TVD schemes are presented. The new approach is robust yet accurate, capable of handling complicated geometry and reactions between discontinuous waves. It keeps all the advantages claimed in the 2-D method of Loh and Hui, e.g., crisp resolution for a slip surface (contact discontinuity) and automatic grid generation along the stream.
ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code
Noble, Charles R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Anderson, Andrew T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Barton, Nathan R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Bramwell, Jamie A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Capps, Arlie [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Chang, Michael H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Chou, Jin J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Dawson, David M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Diana, Emily R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Dunn, Timothy A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Faux, Douglas R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Fisher, Aaron C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Greene, Patrick T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Heinz, Ines [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kanarska, Yuliya [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Khairallah, Saad A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Liu, Benjamin T. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Margraf, Jon D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nichols, Albert L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nourgaliev, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Puso, Michael A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Reus, James F. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Robinson, Peter B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Shestakov, Alek I. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Solberg, Jerome M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Taller, Daniel [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Tsuji, Paul H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); White, Christopher A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); White, Jeremy L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-05-23
ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian- Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid finite element and finite volume formulation to model fluid and elastic-plastic response of materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates many physical phenomena.
On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions
Krzysztof Ciepliński
2009-01-01
Full Text Available We investigate the existence and uniqueness of solutions φ:I→J of the functional equation φ(f(x=F(φ(x, x∈I, where I,J are closed intervals, and f:I→I, F:J→J are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result.
Block Monotone Iterative Algorithms for Variational Inequalities with Nonlinear Operators
Ming-hui Ren; Jin-ping Zeng
2008-01-01
Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established.Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.
Monotonic Property in Field Algebra of G-Spin Model
蒋立宁
2003-01-01
Let F be the field algebra of G-spin model, D(G) the double algebra of a finite group G and D(H) the sub-Hopf algerba of D(G) determined by the subgroup H of G. The paper builds a correspondence between D(H) and the D(H)-invariant sub-C*-algebra AH in F, and proves that the correspondence is strictly monotonic.
Modeling argumentation based semantics using non-monotonic reasoning
2005-01-01
Argumentation theory is an alternative style of formalizing non-monotonic reasoning. It seems, argumentation theory is a suitable framework for practical and uncertain reasoning, where arguments support conclusions. Dung's approach is an unifying framework which has played an influential role on argumentation research and Artificial Intelligence. Even though the success of the argumentation theory, it seems that argumentation theory is so far from being efficiently implemented like the logic ...
Nonparametric estimation for hazard rate monotonously decreasing system
Han Fengyan; Li Weisong
2005-01-01
Estimation of density and hazard rate is very important to the reliability analysis of a system. In order to estimate the density and hazard rate of a hazard rate monotonously decreasing system, a new nonparametric estimator is put forward. The estimator is based on the kernel function method and optimum algorithm. Numerical experiment shows that the method is accurate enough and can be used in many cases.
Stability and monotonicity of Lotka-Volterra type operators
Mukhamedov, Farrukh
2009-01-01
In the present paper, we study Lotka-Volterra (LV) type operators defined in finite dimensional simplex. We prove that any LV type operator is a surjection of the simplex. After, we introduce a new class of LV-type operators, called $M$LV type. We prove convergence of their trajectories and study certain its properties. Moreover, we show that such kind of operators have totaly different behavior than ${\\mathbf{f}}$-monotone LV type operators.
Monotone traveling wavefronts of the KPP-Fisher delayed equation
Gomez, Adrian; Trofimchuk, Sergei
In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-Piskunov-Fisher equation u(t,x)=Δu(t,x)+u(t,x)(1-u(t-h,x)), u⩾0, x∈R. Since then, this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction-diffusion equations. In this paper, we give a complete solution to the problem of existence and uniqueness of monotone waves in Eq. (*). We show that each monotone traveling wave can be found via an iteration procedure. The proposed approach is based on the use of special monotone integral operators (which are different from the usual Wu-Zou operator) and appropriate upper and lower solutions associated to them. The analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach.
Solving the power flow equations: a monotone operator approach
Dvijotham, Krishnamurthy [California Inst. of Technology (CalTech), Pasadena, CA (United States); Low, Steven [California Inst. of Technology (CalTech), Pasadena, CA (United States); Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-07-21
The AC power flow equations underlie all operational aspects of power systems. They are solved routinely in operational practice using the Newton-Raphson method and its variants. These methods work well given a good initial “guess” for the solution, which is always available in normal system operations. However, with the increase in levels of intermittent generation, the assumption of a good initial guess always being available is no longer valid. In this paper, we solve this problem using the theory of monotone operators. We show that it is possible to compute (using an offline optimization) a “monotonicity domain” in the space of voltage phasors. Given this domain, there is a simple efficient algorithm that will either find a solution in the domain, or provably certify that no solutions exist in it. We validate the approach on several IEEE test cases and demonstrate that the offline optimization can be performed tractably and the computed “monotonicity domain” includes all practically relevant power flow solutions.
Synchronous Lagrangian variational principles in General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in relativistic classical field theory which are either asynchronous or synchronous. The historical Einstein-Hilbert and Palatini variational formulations are found to belong to the first category. Nevertheless, it is shown that an alternative route exists which permits one to cast these principles in terms of equivalent synchronous Lagrangian variational formulations. The advantage is twofold. First, synchronous approaches allow one to overcome the lack of gauge symmetry of the asynchronous principles. Second, the property of manifest covariance of the theory is also restored at all levels, including the symbolic Euler-Lagrange equations, with the variational Lagrangian density being now identified with a $4-$scalar. As an application, a joint synchronous variational principle...
A Lagrangian particle level set method
Hieber, Simone E.; Koumoutsakos, Petros
2005-11-01
We present a novel particle level set method for capturing interfaces. The level set equation is solved in a Lagrangian frame using particles that carry the level set information. A key aspect of the method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field. The Lagrangian description of the level set method is inherently adaptive and exact in the case of solid body motions. The efficiency and accuracy of the method is demonstrated in several benchmark problems in two and three dimensions involving pure advection and curvature induced motion of the interface. The simplicity of the particle description is shown to be well suited for real time simulations of surfaces involving cutting and reconnection as in virtual surgery environments.
Multiloop Information from the QED Effective Lagrangian
Dunne, G V; Dunne, Gerald V.; Schubert, Christian
2006-01-01
We obtain information on the QED photon amplitudes at high orders in perturbation theory starting from known results on the QED effective Lagrangian in a constant electric field. A closed-form all-order result for the weak field limit of the imaginary part of this Lagrangian has been given years ago by Affleck, Alvarez and Manton (for scalar QED) and by Lebedev and Ritus (for spinor QED). We discuss the evidence for its correctness, and conjecture an analogous formula for the case of a self-dual field. From this extension we then obtain, using Borel analysis, the leading asymptotic growth for large N of the maximally helicity violating component of the L - loop N - photon amplitude in the low energy limit. The result leads us to conjecture that the perturbation series converges for the on-shell renormalized QED N - photon amplitudes in the quenched approximation.
Mechanisms underlying temperature extremes in Iberia: a Lagrangian perspective
João A. Santos
2015-04-01
Full Text Available The mechanisms underlying the occurrence of temperature extremes in Iberia are analysed considering a Lagrangian perspective of the atmospheric flow, using 6-hourly ERA-Interim reanalysis data for the years 1979–2012. Daily 2-m minimum temperatures below the 1st percentile and 2-m maximum temperatures above the 99th percentile at each grid point over Iberia are selected separately for winter and summer. Four categories of extremes are analysed using 10-d backward trajectories initialized at the extreme temperature grid points close to the surface: winter cold (WCE and warm extremes (WWE, and summer cold (SCE and warm extremes (SWE. Air masses leading to temperature extremes are first transported from the North Atlantic towards Europe for all categories. While there is a clear relation to large-scale circulation patterns in winter, the Iberian thermal low is important in summer. Along the trajectories, air mass characteristics are significantly modified through adiabatic warming (air parcel descent, upper-air radiative cooling and near-surface warming (surface heat fluxes and radiation. High residence times over continental areas, such as over northern-central Europe for WCE and, to a lesser extent, over Iberia for SWE, significantly enhance these air mass modifications. Near-surface diabatic warming is particularly striking for SWE. WCE and SWE are responsible for the most extreme conditions in a given year. For WWE and SCE, strong temperature advection associated with important meridional air mass transports are the main driving mechanisms, accompanied by comparatively minor changes in the air mass properties. These results permit a better understanding of mechanisms leading to temperature extremes in Iberia.
Lagrangian Vortices in Developing Tropical Cyclones
2015-06-25
cyclones B. Rutherford,a* T. J. Dunkertona and M. T. Montgomeryb aNorthwest Research Associates, Redmond, WA, USA bNaval Postgraduate School, Monterey...article has been contributed to by a US Government employee and his work is in the public domain in the USA. Tracking pre-genesis tropical cyclones is...season. All of the Lagrangian coherent structures that can be identified by this field are shown for developing disturbances and mature cyclones . The
Equivalent Lagrangians: Generalization, Transformation Maps, and Applications
N. Wilson
2012-01-01
Full Text Available Equivalent Lagrangians are used to find, via transformations, solutions and conservation laws of a given differential equation by exploiting the possible existence of an isomorphic algebra of Lie point symmetries and, more particularly, an isomorphic Noether point symmetry algebra. Applications include ordinary differential equations such as the Kummer equation and the combined gravity-inertial-Rossbywave equation and certain classes of partial differential equations related to multidimensional wave equations.
Ocean Model Assessment with Lagrangian Metrics
2016-06-07
Ocean Model Assessment With Lagrangian Metrics” Pearn P. Niiler Scripps Institution of Oceanography 9500 Gilman Drive MC 0213 La Jolla, CA...project are to aid in the development of accurate modeling of upper ocean circulation by using data on circulation observations to test models . These tests...or metrics, will be statistical measures of model and data comparisons. It is believed that having accurate models of upper ocean currents will
Introduction to Focus Issue: Lagrangian Coherent Structures.
Peacock, Thomas; Dabiri, John
2010-03-01
The topic of Lagrangian coherent structures (LCS) has been a rapidly growing area of research in nonlinear dynamics for almost a decade. It provides a means to rigorously define and detect transport barriers in dynamical systems with arbitrary time dependence and has a wealth of applications, particularly to fluid flow problems. Here, we give a short introduction to the topic of LCS and review the new work presented in this Focus Issue.
Lagrangian Observations and Modeling of Marine Larvae
Paris, Claire B.; Irisson, Jean-Olivier
2017-04-01
Just within the past two decades, studies on the early-life history stages of marine organisms have led to new paradigms in population dynamics. Unlike passive plant seeds that are transported by the wind or by animals, marine larvae have motor and sensory capabilities. As a result, marine larvae have a tremendous capacity to actively influence their dispersal. This is continuously revealed as we develop new techniques to observe larvae in their natural environment and begin to understand their ability to detect cues throughout ontogeny, process the information, and use it to ride ocean currents and navigate their way back home, or to a place like home. We present innovative in situ and numerical modeling approaches developed to understand the underlying mechanisms of larval transport in the ocean. We describe a novel concept of a Lagrangian platform, the Drifting In Situ Chamber (DISC), designed to observe and quantify complex larval behaviors and their interactions with the pelagic environment. We give a brief history of larval ecology research with the DISC, showing that swimming is directional in most species, guided by cues as diverse as the position of the sun or the underwater soundscape, and even that (unlike humans!) larvae orient better and swim faster when moving as a group. The observed Lagrangian behavior of individual larvae are directly implemented in the Connectivity Modeling System (CMS), an open source Lagrangian tracking application. Simulations help demonstrate the impact that larval behavior has compared to passive Lagrangian trajectories. These methodologies are already the base of exciting findings and are promising tools for documenting and simulating the behavior of other small pelagic organisms, forecasting their migration in a changing ocean.
Inverse Variational Problem for Nonstandard Lagrangians
Saha, A.; Talukdar, B.
2014-06-01
In the mathematical physics literature the nonstandard Lagrangians (NSLs) were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of the equation of motion and solve the associated inverse problem to obtain some of the existing results for NSLs. In addition, we provide a number of alternative Lagrangian representations. The case studies envisaged by us include (i) the usual modified Emden-type equation, (ii) Emden-type equation with dissipative term quadratic in velocity, (iii) Lotka-Volterra model and (vi) a number of the generic equations for dissipative-like dynamical systems. Our method works for nonstandard Lagrangians corresponding to the usual action integral of mechanical systems but requires modification for those associated with the modified actions like S =∫abe L(x ,x˙ , t) dt and S =∫abL 1 - γ(x ,x˙ , t) dt because in the latter case one cannot construct expressions for the Jacobi integrals.
Lagrangian approach and dissipative magnetic systems
Bose, Thomas, E-mail: thomas.bose@physik.uni-halle.de [Martin-Luther-University, Physics Department, Von-Seckendorff-Platz 1, 06114 Halle (Germany); Trimper, Steffen, E-mail: steffen.trimper@physik.uni-halle.de [Martin-Luther-University, Physics Department, Von-Seckendorff-Platz 1, 06114 Halle (Germany)
2011-06-13
A Lagrangian is introduced which includes the coupling between magnetic moments m and the degrees of freedom σ of a reservoir. In case the system-reservoir coupling breaks the time reversal symmetry the magnetic moments perform a damped precession around an effective field which is self-organized by the mutual interaction of the moments. The resulting evolution equation has the form of the Landau-Lifshitz-Gilbert equation. In case the bath variables are constant vector fields the moments m fulfill the reversible Landau-Lifshitz equation. Applying Noether's theorem we find conserved quantities under rotation in space and within the configuration space of the moments. -- Highlights: → We propose a new approach for describing magnetic systems with dissipation on a mesoscopic scale. → The Lagrangian consists of an active magnetic system and a bath. → The coupling between both subsystems breaks the time reversal symmetry. → The suggested Lagrangian leads to the Landau-Lifshitz equation with damping. → We consider symmetry operations by means of Noether's theorem.
Applications the Lagrangian description in aperiodic flows
Mendoza, Carolina; Mancho, Ana Maria
2012-11-01
We use several recently developed Lagrangian tools for describing transport in general aperiodic flows. In our approach the first step is based in a Lagrangian descriptor (the so called function M). It measures the length of particle trajectories on the ocean surface over a given interval of time. We describe its output over satellite altimetry data on the Kuroshio current. The technique is combined with the direct computation of manifolds of Distinguished Hyperbolic trajectories and a very detailed description of transport is achieved across an eddy and a jet on the Kuroshio current,. A second velocity data set is examined with the M function tool. These are obtained from the HYCOM project on the Gulf of Mexico during the time of the oil-spill. We have identified underlying Lagrangian structures and dynamics. We acknowledge to the hospitality of the university of Delaware and the assistance of Bruce Lipphardt and Helga Huntley in accessing the model data sets. We acknowledge to the grants: UPM-AL12-PAC-09, Becas de Movilidad de Caja Madrid 2011, MTM2011-26696 and ILINK-0145.
A Lagrangian-Lagrangian Model for Two-Phase Bubbly Flow around Circular Cylinder
M. Shademan
2014-06-01
Full Text Available A Lagrangian-Lagrangian model is developed using an in-house code to simulate bubble trajectory in two-phase bubbly flow around circular cylinder. Random Vortex Method (RVM which is a Lagrangian approach is used for solving the liquid phase. The significance of RVM relative to other RANS/LES methods is its capability in directly modelling the turbulence. In RVM, turbulence is modeled by solving the vorticity transport equation and there is no need to use turbulence closure models. Another advantage of RVM relative to other CFD approaches is its independence from mesh generation. For the bubbles trajectory, equation of motion of bubbles which takes into account effect of different forces are coupled with the RVM. Comparison of the results obtained from current model with the experimental data confirms the validity of the model. Effect of different parameters including flow Reynolds number, bubble diameter and injection point on the bubbles' trajectory are investigated. Results show that increase in the Reynolds number reduces the rising velocity of the bubbles. Similar behavior is observed for the bubbles when their diameter was decreased. According to the analysis carried out, present Lagrangian-Lagrangian model solves the issues of mesh generation and turbulence modelling which exist in common two phase flow modelling schemes.
Feng Qi
2014-10-01
Full Text Available The authors find the absolute monotonicity and complete monotonicity of some functions involving trigonometric functions and related to estimates the lower bounds of the first eigenvalue of Laplace operator on Riemannian manifolds.
Non-monotonic reasoning in conceptual modeling and ontology design: A proposal
Casini, G
2013-06-01
Full Text Available and modeling of defeasible information and non-monotonic reasoning services. Here we formalize a possible way of introducing non-monotonic reasoning into ORM2 schemas, enriching the language with special set of new constraints....
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
Mixed Monotonicity of Partial First-In-First-Out Traffic Flow Models
Coogan, Samuel; Arcak, Murat; Kurzhanskiy, Alexander A.
2015-01-01
In vehicle traffic networks, congestion on one outgoing link of a diverging junction often impedes flow to other outgoing links, a phenomenon known as the first-in-first-out (FIFO) property. Simplified traffic models that do not account for the FIFO property result in monotone dynamics for which powerful analysis techniques exist. FIFO models are in general not monotone, but have been shown to be mixed monotone - a generalization of monotonicity that enables similarly powerful analysis techni...
Kuhn, Alexander
2013-12-05
Lagrangian coherent structures (LCSs) have become a widespread and powerful method to describe dynamic motion patterns in time-dependent flow fields. The standard way to extract LCS is to compute height ridges in the finite-time Lyapunov exponent field. In this work, we present an alternative method to approximate Lagrangian features for 2D unsteady flow fields that achieve subgrid accuracy without additional particle sampling. We obtain this by a geometric reconstruction of the flow map using additional material constraints for the available samples. In comparison to the standard method, this allows for a more accurate global approximation of LCS on sparse grids and for long integration intervals. The proposed algorithm works directly on a set of given particle trajectories and without additional flow map derivatives. We demonstrate its application for a set of computational fluid dynamic examples, as well as trajectories acquired by Lagrangian methods, and discuss its benefits and limitations. © 2013 The Authors Computer Graphics Forum © 2013 The Eurographics Association and John Wiley & Sons Ltd.
Hegarty, J. D.; Draxler, R.; Stein, A. F.; Brioude, J.; Eluszkiewicz, J.; Mountain, M.; Nehrkorn, T.; Andrews, A. E.
2012-12-01
The accuracy of greenhouse gas (GHG) fluxes estimated using inverse methods is highly dependent on the fidelity of the atmospheric transport model employed. Lagrangian particle dispersion models (LPDMs) driven by customized meteorological output from mesoscale models have emerged as a powerful tool in inverse GHG estimates at policy-relevant regional and urban scales, for several reasons: 1) Mesoscale meteorology can be available at higher resolution than in most global models, and therefore has the potential to be more realistic, 2) the Lagrangian approach minimizes numerical diffusion present in Eulerian models and is thus better able to represent transport in the near-field of measurement locations, and 3) the Lagrangian approach offers an efficient way to compute the grid-scale adjoint of the transport model ("footprints") by running transport backwards in time. Motivated by these considerations, we intercompare three widely used LPDMs (HYSPLIT, STILT, and FLEXPART) driven by identical meteorological input from the Weather Research and Forecasting (WRF) model against measurements from the controlled tracer release experiments (ready-testbed.arl.noaa.gov/HYSPLIT_datem.php). Our analysis includes statistical assessments of each LPDM in terms of its ability to simulate the observed tracer concentrations, reversibility, and sensitivity to the WRF configuration, particularly with regard to the simulation of the planetary boundary layer.
A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO
Heisenberg, Lavinia; Schäfer, Björn Malte; Bartelmann, Matthias
2011-10-01
Subject of this paper is a detailed analysis of the PINpointing Orbit-Crossing Collapsed HIerarchical Object (PINOCCHIO) algorithm for studying the relative velocity statistics of merging haloes in Lagrangian perturbation theory. Given a cosmological background model, a power spectrum of fluctuations as well as a Gaussian linear density contrast field δl is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position q and each smoothing radius R, the collapse time, the velocities and ellipsoidal truncation are computed using Lagrangian perturbation theory. The collapsed medium is then fragmented into isolated objects by an algorithm designed to mimic the accretion and merger events of hierarchical collapse. Directly after the fragmentation process the mass function, merger histories of haloes and the statistics of the relative velocities at merging are evaluated. We reimplemented the algorithm in C++, recovered the mass function and optimized the construction of halo merging histories. When compared with the output of the Millennium Simulation our results suggest that the PINOCCHIO is well suited for studying relative velocities of merging haloes and is able to reproduce the pairwise velocity distribution.
On the formation of localized peaks and non-monotonic tailing of breakthrough curves
Siirila, Erica R.; Sanchez-Vila, Xavier; Fernàndez-Garcia, Daniel
2014-05-01
While breakthrough curve (BTC) analysis is a traditional tool in hydrogeology to obtain hydraulic parameters, in recent years emphasis has been placed on analyzing the shape of the receding portion of the curve. A number of field and laboratory observations have found a constant BTC slope in log-log space, and thus it has been hypothesized that a power law behavior is representative of real aquifers. Usually, monotonicity of the late-time BTC slope is just assumed, meaning that local peaks in the BTC are not considered, and that a local (in time) increase or decrease of BTC slope is also not considered. We contend that local peaks may exist but are sometimes not reported for a number of reasons. For example, when BTCs are obtained from actual measurements, sub-sampling may mask non-monotonicity, or small peaks may be reported as measurement errors and thus smoothed out or removed. When numerical analyses of synthetic aquifers are performed, the simulation method may yield artificially monotonous curves as a consequence of the methods used. For example, Eulerian methods may suffer from numerical dispersion, where curves tend to become over-smoothed while Lagrangian methods may suffer from artificial BTC oscillations stemming from the reconstruction of concentrations from a limited number of particles. A paradigm shift in terms of the BTC shape must also accompany two major advancements within the hydrogeology field: 1) the increase of high frequency data and progression of data collection techniques that diminish the problems of under-sampling BTCs and 2) advancements in supercomputing and numerical simulation allowing for higher resolution of flow and transport problems. As more information is incorporated into BTCs and/or they are obtained in more spatial locations, it is likely that classical definitions of BTC shapes will no longer be adequate descriptors for future treatment of contaminant transport problems. For example, the presence of localized peaks in BTCs
Grid generation and compressible flow computations about a high-speed civil transport configuration
Abolhassani, J. S.; Stewart, J. E.; Farr, N.; Smith, R. E.; Kerr, P. W.; Everton, E. L.
1991-01-01
Techniques and software are discussed for generating grids about a high-speed civil transport configuration. The configuration is defined by a computer-aided design system in wing, fuselage, tail and engine-nacelle components. Grid topology and the surfaces outlining the blocks of the topology are computed with interactive software. The volume grid is computed using software based on transfinite interpolation and Lagrangian blending functions. Several volume grids for inviscid and viscous flow have been generated using this system of codes. Demonstration flowfields around this vehicle are described.
Monotonicity Formula and Regularity for General Free Discontinuity Problems
Bucur, Dorin; Luckhaus, Stephan
2014-02-01
We give a general monotonicity formula for local minimizers of free discontinuity problems which have a critical deviation from minimality, of order d - 1. This result allows us to prove partial regularity results (that is closure and density estimates for the jump set) for a large class of free discontinuity problems involving general energies associated to the jump set, as for example free boundary problems with Robin conditions. In particular, we give a short proof to the De Giorgi-Carriero-Leaci result for the Mumford-Shah functional.
The Non-Monotonic Effect of Financing Constraints on Investment
Hirth, Stefan; Viswanatha, Marc
We analyze investment timing in a discrete-time framework with two possible investment dates, which is an extension of the model by Lyandres (2007). While Lyandres could only show non-monotonicity of investment in market frictions, we derive an investment threshold that is U-shaped in the firm's ......'s liquid funds, a result similar to the infinite-horizon model by Boyle and Guthrie (2003). However, due to the tractability of our model, we can more clearly explain the relevant trade-offs leading to the U-shape....
Contribution to the ergodic theory of piecewise monotone continuous maps
Faller, Bastien
2008-01-01
This thesis is devoted to the ergodic theory of the piecewise monotone continuous maps of the interval. The coding is a classical approach for these maps. Thanks to the coding, we get a symbolic dynamical system which is almost isomorphic to the initial dynamical system. The principle of the coding is very similar to the one of expansion of real numbers. We first define the coding in a perspective similar to the one of the expansions of real numbers; this perspective was already adopted by Ré...
Stability of generalized monotonicity with respect to their characterizations
An, P T
2002-01-01
We show that known types of generalized monotone maps are not stable with respect to their characterizations (i.e., the characterizations are not maintained during an arbitrary map of this type is disturbed by an element with sufficiently small norm) then introduce s-quasimonotone maps, which are stable with respect to their characterization. For gradient maps, s-quasimonotonicity is related to s-quasiconvexity of the underlying function. A necessary and sufficient condition for a univariate polynomial to be s-quasimonotone is given. Furthermore, some stability properties of a-quasiconvex functions are presented.
Deterministic homogenization of parabolic monotone operators with time dependent coefficients
Gabriel Nguetseng
2004-06-01
Full Text Available We study, beyond the classical periodic setting, the homogenization of linear and nonlinear parabolic differential equations associated with monotone operators. The usual periodicity hypothesis is here substituted by an abstract deterministic assumption characterized by a great relaxation of the time behaviour. Our main tool is the recent theory of homogenization structures by the first author, and our homogenization approach falls under the two-scale convergence method. Various concrete examples are worked out with a view to pointing out the wide scope of our approach and bringing the role of homogenization structures to light.
A High-order Eulerian-Lagrangian Finite Element Method for Coupled Electro-mechanical Systems
Brandstetter, Gerd
The main focus of this work is on the development of a high-order Eulerian-Lagrangian finite element method for the simulation of electro-mechanical systems. The coupled problem is solved by a staggered scheme, where the mechanical motion is discretized by standard Lagrangian finite elements, and the electrical field is solved on a fixed Eulerian grid with embedded boundary conditions. Traditional Lagrangian-Lagrangian or arbitrary Lagrangian-Eulerian (ALE) methods encounter deficiencies, for example, when dealing with mesh distortion due to large deformations, or topology changes due to contacting bodies. The presented Eulerian-Lagrangian approach addresses these issues in a natural way. Within this context we develop a high-order immersed boundary discontinuous-Galerkin (IB-DG) method, which is shown to be necessary for (i) the accurate representation of the electrical gradient along nonlinear boundary features such as singular corners, and (ii) to achieve full convergence during the iterative global solution. We develop an implicit scheme based on the mid-point rule, as well as an explicit scheme based on the centered-difference method, with the incorporation of energy conserving, frictionless contact algorithms for an elastic-to-rigid-surface contact. The performance of the proposed method is assessed for several benchmark tests: the electro-static force vector around a singular corner, the quasi-static pull-in of an electro-mechanically actuated switch, the excitation of a carbon nanotube at resonance, and the cyclic impact simulation of a micro-electro-mechanical resonant-switch. We report improved accuracy for the high-order method as compared to low-order methods, and linear convergence in the iterative solution of the staggered scheme. Additionally, we investigate a Newton-Krylov shooting scheme in order to directly find cyclic steady states of electro-mechanical devices excited at resonance-- as opposed to a naive time-stepping from zero initial
Satoh, Masaki; Damtp
1999-10-01
The meridional distribution of potential vorticity (PV) in the troposphere is examined in terms of the Lagrangian transport by using an idealistic general circulation model. A zonally uniform forcing and uniform boundary conditions are applied to the model to particularly examine the PV structure in the mid-latitudes and the subtropics. Trajectories of air parcels released from each grid point of the model and Lagrangian changes in PV are calculated for a period of 60days. Values of PV of each parcel are changing along the Lagrangian motions due to the diabatic effect, the frictional effect and the mixing effect which has smaller scales than those resolvable in the model. Both diabatic and frictional effects are dominant in the lower layers, and the mixing effect is larger in the other regions. It is found that the zonal mean PV changes have different characteristics between the "Underworld" in which isentropes intersect the ground and the "Middleworld" in which isentropes are above the ground and intersect the tropopause. In the Underworld, the zonal mean PV changes are determined by the equatorial flow in the lower layers. In particular, the PV changes are negative in the lower layers of the low- and the mid-latitudes. (The sign of PV tendency is for the northern hemisphere. The southern hemispheric tendency is opposite as in the followings.) This negative tendency is due to the diabatic effect near the surface. In the Middleworld, there remain positive and negative tendency regions, which are resulted from the isentropic mixing. In general, if a parcel moves poleward in the mid-latitudes, the value of PV increases, whereas the value of PV decreases if a parcel moves equatorward. The sign of the Lagrangian mean change in PV corresponds to whether the Lagrangian mean motions cross the PV contours equatorward or poleward in the meridional plane. In particular, the contour of no change in PV has a similar shape to that of meridional distribution of PV in the mid
Continuous Time Random Walks for the Evolution of Lagrangian Velocities
Dentz, Marco; Comolli, Alessandro; Borgne, Tanguy Le; Lester, Daniel R
2016-01-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have non-stationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and non-stationary conditions. We provide explicit expressions for the Lagrangian velocity statistics, and determine the behaviors of...
Innocenti, Alessio; Marchioli, Cristian; Chibbaro, Sergio
2016-11-01
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study particle-laden turbulent flows, when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGSs) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided by LES and then used to advance the SDEs in time. The model consistency is assessed in the limit of particles with zero inertia, when "duplicate fields" are available from both the Eulerian LES and the Lagrangian tracking. Tests with inertial particles were performed to examine the capability of the model to capture the particle preferential concentration and near-wall segregation. Upon comparison with DNS-based statistics, our results show improved accuracy and considerably reduced errors with respect to the case in which no SGS model is used in the equations of particle motion.
The MammoGrid Project Grids Architecture
McClatchey, R; Manset, D; Hauer, T; Estrella, F; Saiz, P; Rogulin, D; Clatchey, Richard Mc; Buncic, Predrag; Manset, David; Hauer, Tamas; Estrella, Florida; Saiz, Pablo; Rogulin, Dmitri
2003-01-01
The aim of the recently EU-funded MammoGrid project is, in the light of emerging Grid technology, to develop a European-wide database of mammograms that will be used to develop a set of important healthcare applications and investigate the potential of this Grid to support effective co-working between healthcare professionals throughout the EU. The MammoGrid consortium intends to use a Grid model to enable distributed computing that spans national borders. This Grid infrastructure will be used for deploying novel algorithms as software directly developed or enhanced within the project. Using the MammoGrid clinicians will be able to harness the use of massive amounts of medical image data to perform epidemiological studies, advanced image processing, radiographic education and ultimately, tele-diagnosis over communities of medical "virtual organisations". This is achieved through the use of Grid-compliant services [1] for managing (versions of) massively distributed files of mammograms, for handling the distri...
Rotor wake and flow analysis using a coupled Eulerian–Lagrangian method
Yongjie Shi
2016-01-01
Full Text Available A coupled Eulerian–Lagrangian methodology was developed in this paper in order to provide an efficient and accurate tool for rotor wake and flow prediction. A Eulerian-based Reynolds-averaged Navier–Stokes (RANS solver was employed to simulate the grid-covered near-body zone, and a grid-free Lagrangian-based viscous wake method (VWM was implemented to model the complicated rotor-wake dynamics in the off-body wake zone. A carefully designed coupling strategy was developed to pass the flow variables between two solvers. A sample case of a forward flying rotor was performed first in order to show the capabilities of the VWM for wake simulations. Next, the coupled method was applied to rotors in several representative flight conditions. Excellent agreement regarding wake geometry, chordwise pressure distribution and sectional normal force with available experimental data demonstrated the validity of the method. In addition, a comparison with the full computational fluid dynamics (CFD method is presented to illustrate the efficiency and accuracy of the proposed coupled method.
A Lagrangian Study of Southeast Pacific Boundary Layer Clouds
Painter, Gallia
Low clouds lie at the heart of climate feedback uncertainties. The representation of clouds in global climate models relies on parameterization of many sub-grid scale processes that are crucial to understanding cloud responses to climate; low clouds in particular exist as a result of tightly coupled microphysical, mesoscale, and synoptic mechanisms. The influence of anthropogenic aerosols on cloud properties could have important ramifications for our understanding of how clouds respond to a changing climate. The VAMOS Ocean-Cloud-Atmosphere-Land Study Regional Experiment (VOCALS REx) sampled the persistent stratocumulus cloud deck located off the coast of Peru and Chile in the southeastern Pacific ocean. Several cloud features found in the stratocumulus deck during VOCALS exhibit signs of interesting aerosol-cloud interactions, including pockets of open cells (POCs). POCs are regions of open-cellular convection surrounded by closed cell stratocumulus, exhibiting not only a marked transition in mesoscale organization and cloud morphology, but also sharp microphysical gradients (especially in droplet concentration) across the boundary between open-cellular and closed cellular convection. In addition, precipitation is often higher at the POC boundaries, hinting at the importance of precipitation in driving their formation. In order to evaluate the microphysical characteristics of POCs prior cloud breakup, we use Lagrangian trajectories coupled with geostationary satellite imagery and cloud retrievals, as well as observational data from VOCALS REx and model data. In three of our case studies, we found regions of anomalously low droplet concentration 18-24 hours prior to POC formation (coupled with liquid water path similar to or higher than surrounding cloud), supporting a precipitation driven mechanism for POC formation. Another group of features with interesting aerosol-cloud interactions observed during VOCALS were mesoscale hook-like features of high droplet
Lagrangian Coherent Structures in the Trieste Gulf
Besio, G.; Enrile, F.; Magaldi, M. G.; Mantovani, C.; Cosoli, S.; Gerin, R.; Poulain, P. M.
2013-12-01
One serious issue in Environmental Science and Engineering concerns the prediction of the fate of contaminants released in a water body. A possible way to tackle this problem consists in forecasting pollutant trajectories from velocity-field data sets obtained by measurements or numerical simulations. A shortcoming of such a traditional approach is the high sensitivity to initial conditions. Another way to understand transport in complex fluid flows comes from a new mathematical tool: Lagrangian Coherent Structures (LCS). The idea of using Lagrangian Structures rose as a meeting point between non-linear dynamics and fluid mechanics. It provides the means to identify material lines that shape trajectory patterns, dividing the flow field into regions with different dynamical behaviours. The objective of this study is the detection of Lagrangian Coherent Structures in the Gulf of Trieste. LCS are calculated from the 2D surface velocity field measured by the coastal radars of the TOSCA (Tracking Oil Spills & Coastal Awareness network) project. Blobs of simulated particles are subjected to chaotic stirring (transport and stretching) that is in agreement with the detected LCS. In the TOSCA project drifters were deployed, too. Therefore, a simple simulation of some of these drifters was carried out. The trajectory of the simulated drifters diverge from the real one: this result is due to the chaotic transport of passive tracers. However, the separation becomes more evident when velocity fields are less accurate because of lack of measurements, previously filled with nearest neighbourhood interpolation. In the light of such results, the use of LCS could be helpful in understanding the trajectory followed by drifters and passive tracers in general, because they can point out the directions along which transport is likely to develop.
Lagrangian form of Schrödinger equation
Arsenović, D.; Burić, N.; Davidović, D. M.; Prvanović, S.
2014-07-01
Lagrangian formulation of quantum mechanical Schrödinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein-Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schrödinger equation.
Webs of Lagrangian Tori in Projective Symplectic Manifolds
Hwang, Jun-Muk
2012-01-01
For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.
New Terms for Compact Form of Electroweak Chiral Lagrangian
YE Wei; ZHANG Hong-Hao; YANG Hong-Wei; YAN Wen-Bin; CHEN Na; J.K. Parry; LI Xue-Song
2008-01-01
The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add several new chiral invariant terms to it and discuss the contributions of these terms to the original electroweak chiral Lagrangian.
Towards Lagrangian approach to quantum computations
Vlasov, A Yu
2003-01-01
In this work is discussed possibility and actuality of Lagrangian approach to quantum computations. Finite-dimensional Hilbert spaces used in this area provide some challenge for such consideration. The model discussed here can be considered as an analogue of Weyl quantization of field theory via path integral in L. D. Faddeev's approach. Weyl quantization is possible to use also in finite-dimensional case, and some formulas may be simply rewritten with change of integrals to finite sums. On the other hand, there are specific difficulties relevant to finite case. This work has some allusions with phase space models of quantum computations developed last time by different authors.
Hamiltonian and Lagrangian theory of viscoelasticity
Hanyga, A.; Seredyńska, M.
2008-03-01
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
Trivial Lagrangians in the Causal Approach
Grigore, Dan-Radu
2015-01-01
We prove the non-uniqueness theorem for the chronological products of a gauge model. We use a cohomological language where the cochains are chronological products, gauge invariance means a cocycle restriction and coboundaries are expressions producing zero sandwiched between physical states. Suppose that we have gauge invariance up to order n of the perturbation theory and we modify the first-order chronological products by a coboundary (a trivial Lagrangian). Then the chronological products up to order n get modified by a coboundary also.
A Neurodynamic Model to Solve Nonlinear Pseudo-Monotone Projection Equation and Its Applications.
Eshaghnezhad, Mohammad; Effati, Sohrab; Mansoori, Amin
2016-09-29
In this paper, a neurodynamic model is given to solve nonlinear pseudo-monotone projection equation. Under pseudo-monotonicity condition and Lipschitz continuous condition, the projection neurodynamic model is proved to be stable in the sense of Lyapunov, globally convergent, globally asymptotically stable, and globally exponentially stable. Also, we show that, our new neurodynamic model is effective to solve the nonconvex optimization problems. Moreover, since monotonicity is a special case of pseudo-monotonicity and also since a co-coercive mapping is Lipschitz continuous and monotone, and a strongly pseudo-monotone mapping is pseudo-monotone, the neurodynamic model can be applied to solve a broader classes of constrained optimization problems related to variational inequalities, pseudo-convex optimization problem, linear and nonlinear complementarity problems, and linear and convex quadratic programming problems. Finally, several illustrative examples are stated to demonstrate the effectiveness and efficiency of our new neurodynamic model.
Introduction to grid computing
Magoules, Frederic; Tan, Kiat-An; Kumar, Abhinit
2009-01-01
A Thorough Overview of the Next Generation in ComputingPoised to follow in the footsteps of the Internet, grid computing is on the verge of becoming more robust and accessible to the public in the near future. Focusing on this novel, yet already powerful, technology, Introduction to Grid Computing explores state-of-the-art grid projects, core grid technologies, and applications of the grid.After comparing the grid with other distributed systems, the book covers two important aspects of a grid system: scheduling of jobs and resource discovery and monitoring in grid. It then discusses existing a
Relativistic Lagrangians for the Lorentz–Dirac equation
Deguchi, Shinichi, E-mail: deguchi@phys.cst.nihon-u.ac.jp [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan); Nakano, Kunihiko [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan); Suzuki, Takafumi [Junior College Funabashi Campus, Nihon University, Narashinodai, Funabashi, Chiba 274-8501 (Japan)
2015-09-15
We present two types of relativistic Lagrangians for the Lorentz–Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz–Dirac equation with a source-like term.
Lagrangian Transport Through Surfaces in Volume-Preserving Flows
Karrasch, Daniel
2015-01-01
Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The recent development of highly accurate semi-Lagrangian methods for solving scalar conservation laws and of Lagrangian approaches to coherent structures in turbulent (geophysical) fluid flows necessitate a new approach to transport from the (Lagrangian) material perspective. We present a Lagrangian framework for calculating transport of conserved quantities through a given surface in $n$-dimensional, fully aperiodic, volume-preserving flows. Our approach does not involve any dynamical assumptions on the surface or its boundary.
The Dirac Conjecture and the Non-uniqueness of Lagrangian
Wang, Yong-Long; Jiang, Hua; Lu, Wei-Tao; Pan, Hong-Zhe
2013-01-01
We prove the validity of the Dirac conjecture generally by adding the total time derivatives of all constraints to the Lagrangian step by step. It is worthy to state that the total time derivatives added to the original Lagrangian can turn up some constraints, and discover the symmetries hidden in the original Lagrangian. For a constrained system, the extended Hamiltonian $H_E$ contains more constraints, and shows more symmetries. We discuss the Cawley's counterexample, and prove it not a real one to the Dirac conjecture. And we offer an example, its extended Hamiltonian is better that its total Hamiltonian for its Lagrangian.
Testing monotonicity of a hazard: asymptotic distribution theory
Groeneboom, Piet
2011-01-01
Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates, which use the monotonicity constraint, and either the empirical distribution function or the empirical cumulative hazard. They measure the excursions of the empirical estimates with respect to the isotonic estimates, due to local non-monotonicity. Asymptotic normality of the test statistics, if the hazard is strictly increasing on [0,a], is established under mild conditions. This is done by first approximating the global empirical distance by an distance with respect to the underlying distribution function. The resulting integral is treated as sum of increasingly many local integrals to which a CLT can be applied. The behavior of the local integrals is determined by a canonical process: the difference between the stochastic process x -> W(x)+x^2 where W is standard two-sid...
DATA PREORDERING IN GENERALIZED PAV ALGORITHM FOR MONOTONIC REGRESSION
Oleg Burdakov; Anders Grimvall; Oleg Sysoev
2006-01-01
Monotonic regression (MR) is a least distance problem with monotonicity constraints induced by a partially ordered data set of observations. In our recent publication [In Ser.Nonconvex Optimization and Its Applications, Springer-Verlag, (2006) 83, pp. 25-33],the Pool-Adjacent-Violators algorithm (PAV) was generalized from completely to partially ordered data sets (posets). The new algorithm, called GPAV, is characterized by the very low computational complexity, which is of second order in the number of observations.It treats the observations in a consecutive order, and it can follow any arbitrarily chosen topological order of the poset of observations. The GPAV algorithm produces a sufficiently accurate solution to the MR problem, but the accuracy depends on the chosen topological order. Here we prove that there exists a topological order for which the resulted GPAV solution is optimal. Furthermore, we present results of extensive numerical experiments,from which we draw conclusions about the most and the least preferable topological orders.
Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-09-20
The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered-grid
Smart Grid Special; Smart Grid Special
Mokoginta, L. [Energiecooperatie ' Wij Krijgen Kippen' , Amsterdam (Netherlands); Messing, M. [Stichting Energietransitie Nederland, Boxtel (Netherlands); Slootweg, H. [Technische Universiteit Eindhoven TUE, Eindhoven (Netherlands); Van der Steen, L.; Brugman, L. [SquareWise, Amsterdam (Netherlands); Bles, M.; Blom, M. [CE Delft, Delft (Netherlands); Nachtegaal, H.; Hoekstra, R. [Bijl partners in public relations, Rotterdam (Netherlands); Van Zutphen, M. [CapGemini, Utrecht (Netherlands); Bakker, D. [PNO Consultants, Schiphol (Netherlands); Van Leeuwen, M. [Norton Rose, Amsterdam (Netherlands); Van Vlerken, J.; De Leeuw, M.; Wijnants, H.J.; Holwerda, B.; Bosch, N.
2012-06-15
A series of 17 articles is dedicated to various aspects of smart grids: expert opinions, the key role of smart grids in a sustainable energy transition, the role of the energy consumer and the grid operators, an energy transition project in the South of Amsterdam (Netherlands), the need for collaboration (e.g. through the Smart Energy Collective), the establishment of local energy corporations, the question whether smart grids are a hype or a necessity, costs and benefits of smart grids, deployment of intelligent smart grids in business areas (experimental areas), the opportunity of deploying Direct Current (DC) grids for an improved energy balance, the Smart Power City Apeldoorn project (SPCA), the experimental area of CloudPower on the isle of Texel, innovation contracts for smart grids, the increase of local, small-scale electricity production, and smart grid pilot projects on Europe. [Dutch] In 17 artikelen wordt aandacht besteed aan diverse aspecten van 'smart grids': meningen van experts, de sleutelrol van smart grids in een duurzame energietransitie, de rol van de energieconsument en de netbeheerders, een energietransitie-project in Amsterdam-Zuid, de noodzaak tot samenwerking (onder meer d.m.v. het Smart Energy Collective), de oprichting van lokale energiecooperaties, de vraag of smart grids een hype zijn of noodzaak, kosten en baten van smart grids, de toepassing van intelligente energienetwerken op bedrijventerreinen ('proeftuinen'), de mogelijkheid om gelijkspanningsnetten toe te passen voor een betere energiebalans, het project Smart Power City Apeldoorn (SPCA), de proeftuin CloudPower op Texel, innovatiecontracten m.b.t. smart grids, de toename van lokale, kleinschalige elektriciteitsproductie, smart grid demonstratieprojecten in Europa.
Variational Contact Symmetries of Constraint Lagrangians
Terzis, Petros A; Christodoulakis, T; Paliathanasis, A; Tsamparlis, M
2015-01-01
The investigation of contact symmetries of re--parametrization invariant Lagrangians of finite degrees of freedom and quadratic in the velocities is presented. The main concern of the paper is those symmetry generators which depend linearly in the velocities. A natural extension of the symmetry generator along the lapse function $N(t)$, with the appropriate extension of the dependence in $\\dot{N}(t)$ of the gauge function, is assumed; this action yields new results. The central finding is that the integrals of motion are either linear or quadratic in velocities and are generated, respectively by the conformal Killing vector fields and the conformal Killing tensors of the configuration space metric deduced from the kinetic part of the Lagrangian (with appropriate conformal factors). The freedom of re--parametrization allows one to appropriately scale $N(t)$, so that the potential becomes constant; in this case the integrals of motion can be constructed from the Killing fields and Killing tensors of the scaled ...
Sigma decomposition: the CP-odd Lagrangian
Hierro, I. M.; Merlo, L.; Rigolin, S.
2016-04-01
In Alonso et al., JHEP 12 (2014) 034, the CP-even sector of the effective chiral Lagrangian for a generic composite Higgs model with a symmetric coset has been constructed, up to four momenta. In this paper, the CP-odd couplings are studied within the same context. If only the Standard Model bosonic sources of custodial symmetry breaking are considered, then at most six independent operators form a basis. One of them is the weak- θ term linked to non-perturbative sources of CP violation, while the others describe CP-odd perturbative couplings between the Standard Model gauge bosons and an Higgs-like scalar belonging to the Goldstone boson sector. The procedure is then applied to three distinct exemplifying frameworks: the original SU(5)/SO(5) Georgi-Kaplan model, the minimal custodial-preserving SO(5)/SO(4) model and the minimal SU(3)/(SU(2) × U(1)) model, which intrinsically breaks custodial symmetry. Moreover, the projection of the high-energy electroweak effective theory to the low-energy chiral effective Lagrangian for a dynamical Higgs is performed, uncovering strong relations between the operator coefficients and pinpointing the differences with the elementary Higgs scenario.
Generating functionals and Lagrangian partial differential equations
Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin [Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, California 92093-0112 (United States)
2013-08-15
The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.
Baoyan Li
2003-09-01
Full Text Available We study the hp version of three families of Eulerian-Lagrangian mixed discontinuous finite element (MDFE methods for the numerical solution of advection-diffusion problems. These methods are based on a space-time mixed formulation of the advection-diffusion problems. In space, they use discontinuous finite elements, and in time they approximately follow the Lagrangian flow paths (i.e., the hyperbolic part of the problems. Boundary conditions are incorporated in a natural and mass conservative manner. In fact, these methods are locally conservative. The analysis of this paper focuses on advection-diffusion problems in one space dimension. Error estimates are explicitly obtained in the grid size h, the polynomial degree p, and the solution regularity; arbitrary space grids and polynomial degree are allowed. These estimates are asymptotically optimal in both h and p for some of these methods. Numerical results to show convergence rates in h and p of the Eulerian-Lagrangian MDFE methods are presented. They are in a good agreement with the theory.
Hartelius, Karsten; Carstensen, Jens Michael
2003-01-01
A method for locating distorted grid structures in images is presented. The method is based on the theories of template matching and Bayesian image restoration. The grid is modeled as a deformable template. Prior knowledge of the grid is described through a Markov random field (MRF) model which...... nodes and the arc prior models variations in row and column spacing across the grid. Grid matching is done by placing an initial rough grid over the image and applying an ensemble annealing scheme to maximize the posterior distribution of the grid. The method can be applied to noisy images with missing...
The regularized monotonicity method: detecting irregular indefinite inclusions
Garde, Henrik; Staboulis, Stratos
2017-01-01
In inclusion detection in electrical impedance tomography, the support of perturbations (inclusion) from a known background conductivity is typically reconstructed from idealized continuum data modelled by a Neumann-to-Dirichlet map. Only few reconstruction methods apply when detecting indefinite...... of approximative measurement models, including the Complete Electrode Model, hence making the method robust against modelling error and noise. In particular, we demonstrate that for a convergent family of approximative models there exists a sequence of regularization parameters such that the outer shape...... of the inclusions is asymptotically exactly characterized. Finally, a peeling-type reconstruction algorithm is presented and, for the first time in literature, numerical examples of monotonicity reconstructions for indefinite inclusions are presented....
Convex analysis and monotone operator theory in Hilbert spaces
Bauschke, Heinz H
2017-01-01
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...
Monotonic childhoods: representations of otherness in research writing
Denise Marcos Bussoletti
2011-12-01
Full Text Available This paper is part of a doctoral thesis entitled “Monotonic childhoods – a rhapsody of hope”. It follows the perspective of a critical psychosocial and cultural study, and aims at discussing the other’s representation in research writing, electing childhood as an allegorical and refl ective place. It takes into consideration, by means of analysis, the drawings and poems of children from the Terezin ghetto during the Second World War. The work is mostly based on Serge Moscovici’s Social Representation Theory, but it is also in constant dialogue with other theories and knowledge fi elds, especially Walter Benjamin’s and Mikhail Bakhtin’s contributions. At the end, the paper supports the thesis that conceives poetics as one of the translation axes of childhood cultures.
PPA BASED PREDICTION-CORRECTION METHODS FOR MONOTONE VARIATIONAL INEQUALITIES
He Bingsheng; Jiang Jianlin; Qian Maijian; Xu Ya
2005-01-01
In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The predictors are produced by inexact PPA steps. The new iterates are then updated by a correction using the PPA formula. We present two profit functions which serve two purposes: First we show that the profit functions are tight lower bounds of the improvements obtained in each iteration. Based on this conclusion we obtain the convergence inexactness restrictions for the prediction step. Second we show that the profit functions are quadratically dependent upon the step lengths, thus the optimal step lengths are obtained in the correction step. In the last part of the paper we compare the strengths of different methods based on their inexactness restrictions.
Strong convergence theorems for maximal monotone mappings in Banach spaces
Zegeye, Habtu
2008-07-01
Let E be a uniformly convex and 2-uniformly smooth real Banach space with dual E*. Let be a Lipschitz continuous monotone mapping with A-1(0)[not equal to][empty set]. For given u,x1[set membership, variant]E, let {xn} be generated by the algorithm xn+1:=[beta]nu+(1-[beta]n)(xn-[alpha]nAJxn), n[greater-or-equal, slanted]1, where J is the normalized duality mapping from E into E* and {[lambda]n} and {[theta]n} are real sequences in (0,1) satisfying certain conditions. Then it is proved that, under some mild conditions, {xn} converges strongly to x*[set membership, variant]E where Jx*[set membership, variant]A-1(0). Finally, we apply our convergence theorems to the convex minimization problems.
Convergence of the natural approximations of piecewise monotone interval maps.
Haydn, Nicolai
2004-06-01
We consider piecewise monotone interval mappings which are topologically mixing and satisfy the Markov property. It has previously been shown that the invariant densities of the natural approximations converge exponentially fast in uniform pointwise topology to the invariant density of the given map provided its derivative is piecewise Lipshitz continuous. We provide an example of a map which is Lipshitz continuous and for which the densities converge in the bounded variation norm at a logarithmic rate. This shows that in general one cannot expect exponential convergence in the bounded variation norm. Here we prove that if the derivative of the interval map is Holder continuous and its variation is well approximable (gamma-uniform variation for gamma>0), then the densities converge exponentially fast in the norm.
A COMPARISON OF DIFFERENT CONTRACTION METHODS FOR MONOTONE VARIATIONAL INEQUALITIES
Bingsheng He; Xiang Wang; Junfeng Yang
2009-01-01
It is interesting to compare the efficiency of two methods when their computational loads in each iteration are equal. In this paper, two classes of contraction methods for monotone variational inequalities are studied in a unified framework. The methods of both classes can be viewed as prediction-correction methods, which generate the same test vector in the prediction step and adopt the same step-size rule in the correction step. The only difference is that they use different search directions. The computational loads of each iteration of the different classes are equal. Our analysis explains theoretically why one class of the contraction methods usually outperforms the other class. It is demonstrated that many known methods belong to these two classes of methods. Finally, the presented numerical results demonstrate the validity of our analysis.
A new non-monotone fitness scaling for genetic algorithm
无
2001-01-01
The properties of selection operators in the genetic algorithm (GA) are studied in detail. It is indicated that the selection of operations is significant for both improving the general fitness of a population and leading to the schema deceptiveness. The stochastic searching characteristics of GA are compared with those of heuristic methods. The influence of selection operators on the GA' s exploration and exploitation is discussed, and the performance of selection operators is evaluated with the premature convergence of the GA taken as an example based on One-Max function. In order to overcome the schema deceptiveness of the GA, a new type of fitness scaling, non monotone scaling, is advanced to enhance the evolutionary ability of a population. The effectiveness of the new scaling method is tested by a trap function and a needle-in-haystack (NiH) function.
MINLIP for the Identification of Monotone Wiener Systems
Pelckmans, Kristiaan
2010-01-01
This paper studies the MINLIP estimator for the identification of Wiener systems consisting of a sequence of a linear FIR dynamical model, and a monotonically increasing (or decreasing) static function. Given $T$ observations, this algorithm boils down to solving a convex quadratic program with $O(T)$ variables and inequality constraints, implementing an inference technique which is based entirely on model complexity control. The resulting estimates of the linear submodel are found to be almost consistent when no noise is present in the data, under a condition of smoothness of the true nonlinearity and local Persistency of Excitation (local PE) of the data. This result is novel as it does not rely on classical tools as a 'linearization' using a Taylor decomposition, nor exploits stochastic properties of the data. It is indicated how to extend the method to cope with noisy data, and empirical evidence contrasts performance of the estimator against other recently proposed techniques.
A new approximate proximal point algorithm for maximal monotone operator
HE; Bingsheng(何炳生); LIAO; Lizhi(廖立志); YANG; Zhenhua(杨振华)
2003-01-01
The problem concerned in this paper is the set-valued equation 0 ∈ T(z) where T is a maximal monotone operator. For given xk and βk ＞ 0, some existing approximate proximal point algorithms take xk+1 = xk such that xk +ek∈ xk + βkT(xk) and||ek|| ≤ηk||xk - xk||, where {ηk} is a non-negative summable sequence. Instead of xk+1 = xk, the new iterate of the proposing method is given by xk+1 = PΩ[xk - ek], where Ω is the domain of T and PΩ(@) denotes the projection on Ω. The convergence is proved under a significantly relaxed restriction supk＞0 ηk ＜ 1.
Evaluation of the Lagrangian Marker Method in CTH: Taylor Impact
2015-03-01
ARL-TR-7235•MAR 2015 US Army Research Laboratory Evaluation of the Lagrangian Marker Method in CTH: Taylor Impact by Stephen Schraml Approved for...Research Laboratory Evaluation of the Lagrangian Marker Method in CTH: Taylor Impact by Stephen Schraml Weapons and Materials Research Directorate, ARL...
Deformations of log-Lagrangian submanifolds of Poisson manifolds
2013-01-01
We consider Lagrangian-like submanifolds in certain even-dimensional 'symplectic-like' Poisson manifolds. We show, under suitable transversality hypotheses, that the pair consisting of the ambient Poisson manifold and the submanifold has unobstructed deformations and that the deformations automatically preserve the Lagrangian-like property.
Parallel Lagrangian models for turbulent transport and chemistry
Crone, Gilia Cornelia
1997-01-01
In this thesis we give an overview of recent stochastic Lagrangian models and present a new particle model for turbulent dispersion and chemical reactions. Our purpose is to investigate and assess the feasibility of the Lagrangian approach for modelling the turbulent dispersion and chemistry
Flux form Semi-Lagrangian methods for parabolic problems
Bonaventura, Luca
2015-01-01
A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and convergence analysis are proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection--diffusion and nonlinear parabolic problems.
Lagrangian supersymmetries depending on derivatives. Global analysis and cohomology
Giachetta, G; Sardanashvily, G
2004-01-01
Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed. In particular, the first variational formula and conservation laws for Lagrangian systems on graded manifolds using contact supersymmetries are obtained.
Geometric Lagrangians for massive higher-spin fields
Francia, D
2007-01-01
Lagrangians for massive, unconstrained, higher-spin bosons and fermions are proposed. The idea is to modify the geometric, gauge invariant Lagrangians describing the corresponding massless theories by the addition of suitable quadratic polynomials. These polynomials provide generalisations of the Fierz-Pauli mass term containing all possible traces of the basic field. No auxiliary fields are needed.
Payoff-monotonic game dynamics and the maximum clique problem.
Pelillo, Marcello; Torsello, Andrea
2006-05-01
Evolutionary game-theoretic models and, in particular, the so-called replicator equations have recently proven to be remarkably effective at approximately solving the maximum clique and related problems. The approach is centered around a classic result from graph theory that formulates the maximum clique problem as a standard (continuous) quadratic program and exploits the dynamical properties of these models, which, under a certain symmetry assumption, possess a Lyapunov function. In this letter, we generalize previous work along these lines in several respects. We introduce a wide family of game-dynamic equations known as payoff-monotonic dynamics, of which replicator dynamics are a special instance, and show that they enjoy precisely the same dynamical properties as standard replicator equations. These properties make any member of this family a potential heuristic for solving standard quadratic programs and, in particular, the maximum clique problem. Extensive simulations, performed on random as well as DIMACS benchmark graphs, show that this class contains dynamics that are considerably faster than and at least as accurate as replicator equations. One problem associated with these models, however, relates to their inability to escape from poor local solutions. To overcome this drawback, we focus on a particular subclass of payoff-monotonic dynamics used to model the evolution of behavior via imitation processes and study the stability of their equilibria when a regularization parameter is allowed to take on negative values. A detailed analysis of these properties suggests a whole class of annealed imitation heuristics for the maximum clique problem, which are based on the idea of varying the parameter during the imitation optimization process in a principled way, so as to avoid unwanted inefficient solutions. Experiments show that the proposed annealing procedure does help to avoid poor local optima by initially driving the dynamics toward promising regions in
Numerical methods for Eulerian and Lagrangian conservation laws
Després, Bruno
2017-01-01
This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.
Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics
Miron, Radu
2012-01-01
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or evolution equations) of these Mechanics are derived from the variational calculus applied to the integral of action and these can be studied by using the methods of Lagrangian or Hamiltonian geometries. More general, the notions of higher order Lagrange or Hamilton spaces have been introduced and developed by the present author. The applications led to the notions of Lagrangian or Hamiltonian Analytical Mechanics of higher order. For short, in this text we aim to solve some difficult problems: The problem of geometrization of classical non conservative mechanical systems; The foundations of geometrical theory of new mechanics: Finslerian, Lagrangian and Hamiltonian;To determine the evolution equations of the classical mechanical systems for whose external forces depend on the hig...
Multi-Scale Analysis of Lagrangian Properties of Turbulence
Wilczek, Michael; Lalescu, Cristian
2016-11-01
Turbulence is a multi-scale problem in space and time with a broad range of strongly interacting degrees of freedom. Lagrangian tracer particles advected with the flow sample this spatio-temporal complexity. This naturally leads to the question of how Lagrangian properties are affected by the scales of turbulence. We attempt to answer this question numerically and theoretically adopting a coarse-graining approach. In an extensive DNS (direct numerical simulation) study, we track tracer particles advected by spatially coarse-grained velocity fields. This allows to distinguish the impact of large-scale sweeping effects and small-scale intermittency on Lagrangian aspects of turbulence. In this presentation we will present results on Lagrangian particle dispersion and velocity fluctuations for various coarse-graining scales. The results will furthermore be discussed in the context of Eulerian-Lagrangian bridging relations.
Lagrangian and Hamiltonian two-scale reduction
Giannoulis, Johannes; Mielke, Alexander
2008-01-01
Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave...
Lagrangian coherent structures and plasma transport processes
Falessi, M V; Schep, T J
2015-01-01
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\\'e map provides a splitting of the phase space into regions where particles have different kinds of motion: periodic, quasi-periodic or chaotic. The boundaries of these regions are transport barriers; i.e., a trajectory cannot cross such boundaries during the whole evolution of the system. Lagrangian Coherent Structure (LCS) generalize this method to systems with the most general time dependence, splitting the phase space into regions with different qualitative behaviours. This leads to the definition of finite-time transport barriers, i.e. trajectories cannot cross the barrier for a finite amount of time. This methodology can be used to identify fast recirculating regions in the dynamical system and to characterize the transport between them.
Instantons in a Lagrangian model of turbulence
Grigorio, Leonardo S; Pereira, Rodrigo M; Chevillard, Laurent
2016-01-01
The role of instantons is investigated in the Lagrangian model for the velocity gradient evolution known as the Recent Fluid Deformation approximation. After recasting the model into the path-integral formalism, the probability distribution function is computed along with the most probable path in the weak noise limit through the saddle-point approximation. Evaluation of the instanton solution is implemented numerically by means of the iteratively Chernykh-Stepanov method. In the case of the longitudinal velocity gradient statistics, due to symmetry reasons, the number of degrees of freedom can be reduced to one, allowing the pdf to be evaluated analytically as well, thereby enabling a prediction of the scaling of the moments as a function of Reynolds number. It is also shown that the instanton solution lies on the Vieillefosse line concerning the RQ-plane. We illustrate how instantons can be unveiled in the stochastic dynamics performing a conditional statistics.
Holography, chiral Lagrangian and form factor relations
Zuo, Fen
2013-01-01
We perform a detailed study of mesonic properties in a class of holographic models of QCD, which is described by the Yang-Mills plus Chern-Simons action. By decomposing the 5 dimensional gauge field into resonances and integrating out the massive ones, we reproduce the Chiral Perturbative Theory Lagrangian up to ${\\cal O}(p^6)$ and obtain all the relevant low energy constants (LECs). The numerical predictions of the LECs show minor model dependence, and agree reasonably with the determinations from other approaches. Interestingly, various model-independent relations appear among them. Some of these relations are found to be the large-distance limits of universal relations between form factors of the anomalous and even-parity sectors of QCD.
Non-Lagrangian theories from brane junctions
Bao, Ling [Chalmers Univ. of Technology, Goeteborg (Sweden); Mitev, Vladimir [Humboldt Univ., Berlin (Germany). Inst. fuer Mathematik und Inst. fuer Physik; Pomoni, Elli [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany). Theory Group; Taki, Masato [RIKEN Nishina Center, Saitama (Japan). Mathematical Physics Lab.; Yagi, Futoshi [International School of Advanced Studies (SISSA), Trieste (Italy); INFN, Trieste (Italy); Korea Institute for Advanced Study (KIAS), Seoul (Korea, Republic of)
2013-10-15
In this article we use 5-brane junctions to study the 5D T{sub N} SCFTs corresponding to the 5D N=1 uplift of the 4D N=2 strongly coupled gauge theories, which are obtained by compactifying N M5 branes on a sphere with three full punctures. Even though these theories have no Lagrangian description, by using the 5-brane junctions proposed by Benini, Benvenuti and Tachikawa, we are able to derive their Seiberg-Witten curves and Nekrasov partition functions. We cross-check our results with the 5D superconformal index proposed by Kim, Kim and Lee. Through the AGTW correspondence, we discuss the relations between 5D superconformal indices and n-point functions of the q-deformed W{sub N} Toda theories.
A perturbative approach to Lagrangian flow networks
Fujiwara, Naoya; Donges, Jonathan F; Donner, Reik V
2016-01-01
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (a...
Lagrangian Coherent Structures: Introduction and Applications
Haller, George
2008-11-01
Lagrangian Coherent Structures (LCS) are distinguished material surfaces that organize the global mixing and transport of fluid particles. While these surfaces define a skeleton that governs all mixing events even in turbulent flows, LCS remain hidden to traditional coherent structure detecting methods based on vorticity, pressure, streamlines, or other frame-dependent quantities. Here we review the mathematical foundations of LCS and discuss how they can be located in an objective (frame-independent) way in complex flows. We also highlight applications to experimental and numerical flow data analysis. Examples include two-dimensional rotating turbulence, hairpin vortices in three-dimensional numerical simulations, passive ocean pollution control and atmospheric clear-air turbulence detection. Some of these examples will be discussed in more detail in later talks within this minisymposium.
Lagrangian mixing in an axisymmetric hurricane model
B. Rutherford
2009-09-01
Full Text Available This paper discusses the extension of established Lagrangian mixing measures to make them applicable to data extracted from a 2-D axisymmetric hurricane simulation. Because of the non-steady and unbounded characteristics of the simulation, the previous measures are extended to a moving frame approach to create time-dependent mixing rates that are dependent upon the initial time of particle integration, and are computed for nonlocal regions. The global measures of mixing derived from finite-time Lyapunov exponents, relative dispersion, and a measured mixing rate are applied to distinct regions representing different characteristic feautures within the model. It is shown that these time-dependent mixing rates exhibit correlations with maximal tangential winds during a quasi-steady state, establishing a connection between mixing and hurricane intensity.
On Active Current Selection for Lagrangian Profilers
J. Jouffroy
2013-01-01
Full Text Available Autonomous Lagrangian profilers are now widely used as measurement and monitoring platforms, notably in observation programs as Argo. In a typical mode of operation, the profilers drift passively at their parking depthbefore making a vertical profile to go back to the surface. This paperpresents simple and computationally-efficient control strategies to activelyselect and use ocean currents so that a profiler can autonomously reach adesired destination. After briefly presenting a typical profiler andpossible mechanical modifications for a coastal environment, we introducesimple mathematical models for the profiler and the currents it will use. Wethen present simple feedback controllers that, using the direction of thecurrents and taking into account the configuration of the environment(coastal or deep-sea, is able to steer the profiler to any desiredhorizontal location. To illustrate the approach, a few results are presentedusing both simulated currents and real current velocity profiles from theNorth Sea.
Mapping of grid faults and grid codes
Iov, F.; Hansen, Anca Daniela; Sørensen, Poul Ejnar
for such investigations. The grid connection requirements for wind turbines have increased significantly during the last 5-10 years. Especially the requirements for wind turbines to stay connected to the grid during and after voltage sags, imply potential challenges in the design of wind turbines. These requirements pose...... challenges for the design of both the electrical system and the mechanical structure of wind turbines. An overview over the frequency of grid faults and the grid connection requirements in different relevant countries is done in this report. The most relevant study cases for the quantification of the loads......The present report is a part of the research project ''Grid fault and designbasis for wind turbine'' supported by Energinet.dk through the grant PSO F&U 6319. The objective of this project is to investigate into the consequences of the new grid connection requirements for the fatigue and extreme...
Mapping of grid faults and grid codes
Iov, Florin; Hansen, A.D.; Sørensen, P.
The present report is a part of the research project "Grid fault and design basis for wind turbine" supported by Energinet.dk through the grant PSO F&U 6319. The objective of this project is to investigate into the consequences of the new grid connection requirements for the fatigue and extreme...... for such investigations. The grid connection requirements for wind turbines have increased significantly during the last 5-10 years. Especially the requirements for wind turbines to stay connected to the grid during and after voltage sags, imply potential challenges in the design of wind turbines. These requirements pose...... challenges for the design of both the electrical system and the mechanical structure of wind turbines. An overview over the frequency of grid faults and the grid connection requirements in different relevant countries is done in this report. The most relevant study cases for the quantification of the loads...
HybridN-order Lagrangian Interpolation Eulerian-Lagrangian Method for Salinity Calculation
吴炎成; 朱首贤; 周林; 游小宝; 张文静
2016-01-01
The Eulerian−Lagrangian method (ELM) has been used by many ocean models as the solution of the advection equation, but the numerical error caused by interpolation imposes restriction on its accuracy. In the present study, hybrid N-order Lagrangian interpolation ELM (LiELM) is put forward in which theN-order Lagrangian interpolation is used at first, then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower. The calculation results of a step-shaped salinity advection model are analyzed, which show that higher order (N=3−8) LiELM can reduce the mean numerical error of salinity calculation, but the numerical oscillation error is still significant. Even number order LiELM makes larger numerical oscillation error than its adjacent odd number order LiELM. HybridN-order LiELM can remove numerical oscillation, and it significantly reduces the mean numerical error whenN is even and the current is in fixed direction, while it makes less effect on mean numerical error whenNis odd or the current direction changes periodically. Hybrid odd number order LiELM makes less mean numerical error than its adjacent even number order LiELM when the current is in the fixed direction, while the mean numerical error decreases asN increases when the current direction changes periodically, so odd number ofN may be better for application. Among various types of HybridN-order LiELM, the scheme reducingN-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.
Strong Stationary Duality for M\\"obius Monotone Markov Chains: Unreliable Networks
Lorek, Pawel
2011-01-01
For Markov chains with a partially ordered finite state space we show strong stationary duality under the condition of M\\"obius monotonicity of the chain. We show relations of M\\"obius monotonicity to other definitions of monotone chains. We give examples of dual chains in this context which have transitions only upwards. We illustrate general theory by an analysis of nonsymmetric random walks on the cube with an application to networks of queues.
On a correspondence between regular and non-regular operator monotone functions
Gibilisco, P.; Hansen, Frank; Isola, T.
2009-01-01
We prove the existence of a bijection between the regular and the non-regular operator monotone functions satisfying a certain functional equation. As an application we give a new proof of the operator monotonicity of certain functions related to the Wigner-Yanase-Dyson skew information.......We prove the existence of a bijection between the regular and the non-regular operator monotone functions satisfying a certain functional equation. As an application we give a new proof of the operator monotonicity of certain functions related to the Wigner-Yanase-Dyson skew information....
Non-monotonic dynamics and crosstalk in signaling pathways and their implications for pharmacology
van Wijk, Roeland; Tans, Sander J.; Wolde, Pieter Rein Ten; Mashaghi, Alireza
2015-06-01
Currently, drug discovery approaches commonly assume a monotonic dose-response relationship. However, the assumption of monotonicity is increasingly being challenged. Here we show that for two simple interacting linear signaling pathways that carry two different signals with different physiological responses, a non-monotonic input-output relation can arise with simple network topologies including coherent and incoherent feed-forward loops. We show that non-monotonicity of the response functions has severe implications for pharmacological treatment. Fundamental constraints are imposed on the effectiveness and toxicity of any drug independent of its chemical nature and selectivity due to the specific network structure.
Igor Boglaev; Matthew Hardy
2008-01-01
This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type.To solve the nonlinear weighted average finite difference scheme for the partial differential equation,we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition.This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. The rate of convergence of the monotone domain decomposition algorithm is estimated.Numerical experiments are presented.
Wald, Ingo; Ize, Santiago
2015-07-28
Parallel population of a grid with a plurality of objects using a plurality of processors. One example embodiment is a method for parallel population of a grid with a plurality of objects using a plurality of processors. The method includes a first act of dividing a grid into n distinct grid portions, where n is the number of processors available for populating the grid. The method also includes acts of dividing a plurality of objects into n distinct sets of objects, assigning a distinct set of objects to each processor such that each processor determines by which distinct grid portion(s) each object in its distinct set of objects is at least partially bounded, and assigning a distinct grid portion to each processor such that each processor populates its distinct grid portion with any objects that were previously determined to be at least partially bounded by its distinct grid portion.
Goel, Sanjay; Papakonstantinou, Vagelis; Kloza, Dariusz
2015-01-01
This book on smart grid security is meant for a broad audience from managers to technical experts. It highlights security challenges that are faced in the smart grid as we widely deploy it across the landscape. It starts with a brief overview of the smart grid and then discusses some of the reported attacks on the grid. It covers network threats, cyber physical threats, smart metering threats, as well as privacy issues in the smart grid. Along with the threats the book discusses the means to improve smart grid security and the standards that are emerging in the field. The second part of the b
匡翠萍; 黄静; 陈思宇; 刘曙光
2012-01-01
建立了适合河口复杂边界的二维潮流盐度数学模型.其中,网格模块是通过多元最小二乘重构的无结构三角网格；潮流模块基于消除了稳定性条件限制的半隐的欧拉-拉格朗日法,并用干湿判断法实现动边界的处理；盐度输运模块采用有限体积法进行离散,并通过用周围单元平均浓度值重构界面浓度的方法得到与连续性离散方程相协调的二阶对流扩散离散方程.通过纯对流和纯扩散数值测试对模型进行了验证,结果表明模型能够较好地模拟盐度输运的对流扩散问题,且具有较高的精度.最后,将模型应用于长江口盐水入侵的模拟计算,计算结果表明:模型计算的潮位、流速和盐度过程与实测资料一致.%A 2D numerical model to simulate tidal flow and salinity in complex estuaries is developed. The grid module is designed under unstructured triangular grid with second order accuracy by cell reconstruction using multiple least square methods to remove stability limitations associated with surface gravity wave. The circulation module is based on semi-implicit Eulerian-Lagrangian method and free from CFL condition constraint, and the wetting and drying are addressed by movable boundary techniques. The salinity module is designed in the frame-work of finite-volume method with a second-order resolution in coordination with the discreted continuity equation, through the cell face concentration reconstructed from surrounding cell averaged by complex interpolation combined with a mono-tonicity criterion. The model has been tested by a pure advection case and a pure diffusion case, which demonstrates that the model has a high accuracy. Finally, this model has been applied to simulating the saline intrusion in the Yangtze (Changjiang) River Estuary and the results show that the simulated tidal levels, velocities and salinities agree well with the measured ones.
A reduction of order two for infinite-order Lagrangians
Jaén, X.; Llosa, J.; Molina, A.
1986-10-01
Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.
In defence of naivete The conceptual status of Lagrangian QFT
Wallace, D
2001-01-01
I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the "naive" quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work.
A Lagrangian particle model to predict the airborne spread of foot-and-mouth disease virus
Mayer, D.; Reiczigel, J.; Rubel, F.
Airborne spread of bioaerosols in the boundary layer over a complex terrain is simulated using a Lagrangian particle model, and applied to modelling the airborne spread of foot-and-mouth disease (FMD) virus. Two case studies are made with study domains located in a hilly region in the northwest of the Styrian capital Graz, the second largest town in Austria. Mountainous terrain as well as inhomogeneous and time varying meteorological conditions prevent from application of so far used Gaussian dispersion models, while the proposed model can handle these realistically. In the model, trajectories of several thousands of particles are computed and the distribution of virus concentration near the ground is calculated. This allows to assess risk of infection areas with respect to animal species of interest, such as cattle, swine or sheep. Meteorological input data like wind field and other variables necessary to compute turbulence were taken from the new pre-operational version of the non-hydrostatic numerical weather prediction model LMK ( Lokal-Modell-Kürzestfrist) running at the German weather service DWD ( Deutscher Wetterdienst). The LMK model provides meteorological parameters with a spatial resolution of about 2.8 km. To account for the spatial resolution of 400 m used by the Lagrangian particle model, the initial wind field is interpolated upon the finer grid by a mass consistent interpolation method. Case studies depict a significant influence of local wind systems on the spread of virus. Higher virus concentrations at the upwind side of the hills and marginal concentrations in the lee are well observable, as well as canalization effects by valleys. The study demonstrates that the Lagrangian particle model is an appropriate tool for risk assessment of airborne spread of virus by taking into account the realistic orographic and meteorological conditions.
Max-Sum Diversification, Monotone Submodular Functions and Dynamic Updates
Borodin, Allan; Ye, Yuli
2012-01-01
Result diversification has many important applications in databases, operations research, information retrieval, and finance. In this paper, we study and extend a particular version of result diversification, known as max-sum diversification. More specifically, we consider the setting where we are given a set of elements in a metric space and a set valuation function $f$ defined on every subset. For any given subset $S$, the overall objective is a linear combination of $f(S)$ and the sum of the distances induced by $S$. The goal is to find a subset $S$ satisfying some constraints that maximizes the overall objective. This problem is first studied by Gollapudi and Sharma for modular set functions and for sets satisfying a cardinality constraint. We consider an extension of the modular case to the monotone submodular case, for which the previous algorithm no longer applies. Interestingly, we are able to match the 2-approximation using a natural, but different greedy algorithm. We then further extend the problem...
Non-monotonicity of trace distance under tensor products
Maziero, Jonas, E-mail: jonas.maziero@ufsm.br [Universidade Federal de Santa Maria (UFSM), RS (Brazil). Departamento de Fisica
2015-10-15
The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable features, its possible non-monotonicity under taking tensor products of its arguments (NMuTP), has been hitherto unexplored. In this article, we advance analytical and numerical investigations of this issue considering different classes of states living in a discrete and finite dimensional Hilbert space. Our results reveal that although this property of TD does not show up for pure states and for some particular classes of mixed states, it is present in a non-negligible fraction of the regarded density operators. Hence, even though the percentage of quartets of states leading to the NMuTP drawback of TD and its strength decrease as the system's dimension grows, this property of TD must be taken into account before using it as a figure of merit for distinguishing mixed quantum states. (author)
Dynamical zeta functions for piecewise monotone maps of the interval
Ruelle, David
2004-01-01
Consider a space M, a map f:M\\to M, and a function g:M \\to {\\mathbb C}. The formal power series \\zeta (z) = \\exp \\sum ^\\infty _{m=1} \\frac {z^m}{m} \\sum _{x \\in \\mathrm {Fix}\\,f^m} \\prod ^{m-1}_{k=0} g (f^kx) yields an example of a dynamical zeta function. Such functions have unexpected analytic properties and interesting relations to the theory of dynamical systems, statistical mechanics, and the spectral theory of certain operators (transfer operators). The first part of this monograph presents a general introduction to this subject. The second part is a detailed study of the zeta functions associated with piecewise monotone maps of the interval [0,1]. In particular, Ruelle gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of \\zeta (z) and the eigenvalues of the transfer operator. He also proves a theorem expressing the largest eigenvalue of the transfer operator in terms of the ergodic properties of (M,f,g).
Completely Monotone Multisequences, Symmetric Probabilities and a Normal Limit Theorem
J C Gupta
2000-11-01
Let G, be the set of all partial completely monotone multisequences of order and degree , i.e., multisequences (1, 2,$\\ldots$ ,k), 1, 2,$\\ldots$ , = 0, 1, 2,$\\ldots$ ,1 + 2 + \\$cdots$ + ≤ n, (0,0,$\\ldots$ ,0) = 1 and $(-1)^{_0}^{_0}$ (1, 2,$\\ldots$ ,)≥ 0 whenever 0 ≤ -(1 + 2 +$\\cdots$ +) where (1, 2,$\\ldots$ ,)=(1+1, 2,$\\ldots$ ,)+ (1,2+1,$\\ldots$ ,)+$\\cdots$ + (1, 2,$\\ldots$ ,+1)-(1,2,$\\ldots$ ,)$. Further, let $\\prod_{n,k}$ be the set of all symmetric probabilities on ${0, 1, 2,\\ldots ,k}^{n}$. We establish a one-to-one correspondence between the sets G, and $\\prod_{n, k}$ and use it to formulate and answer interesting questions about both. Assigning to G, the uniform probability measure, we show that, as → ∞ , any fixed section {(1, 2,$\\ldots$ ,), 1 ≤ $\\sum ≤ }, properly centered and normalized, is asymptotically multivariate normal. That is, $\\left\\{\\sqrt{\\left(\\binom{n+k}{k}\\right)}((1, 2,\\ldots ,)-c_0(1, 2,\\ldots ,), 1≤ _1+2+\\cdots +_k≤ m\\right\\}$ converges weakly to MVN[0,]; the centering constants 0(1, 2,$\\ldots$ ,) and the asymptotic covariances depend on the moments of the Dirichlet $(1, 1,\\ldots ,1; 1)$ distribution on the standard simplex in .
National Aeronautics and Space Administration — After discussions by the organizing committee, and some research using the RSW grids, a modification has been made on the RSW grids. The inflow boundary has now been...
HIRENASD coarse structured grid
National Aeronautics and Space Administration — blockstructured hexahedral grid, 6.7 mio elements, 24 degree minimum grid angle, CGNS format version 2.4, double precision Binary, Plot3D file Please contact...
Grid generation and inviscid flow computation about aircraft geometries
Smith, Robert E.
1989-01-01
Grid generation and Euler flow about fighter aircraft are described. A fighter aircraft geometry is specified by an area ruled fuselage with an internal duct, cranked delta wing or strake/wing combinations, canard and/or horizontal tail surfaces, and vertical tail surfaces. The initial step before grid generation and flow computation is the determination of a suitable grid topology. The external grid topology that has been applied is called a dual-block topology which is a patched C (exp 1) continuous multiple-block system where inner blocks cover the highly-swept part of a cranked wing or strake, rearward inner-part of the wing, and tail components. Outer-blocks cover the remainder of the fuselage, outer-part of the wing, canards and extend to the far field boundaries. The grid generation is based on transfinite interpolation with Lagrangian blending functions. This procedure has been applied to the Langley experimental fighter configuration and a modified F-18 configuration. Supersonic flow between Mach 1.3 and 2.5 and angles of attack between 0 degrees and 10 degrees have been computed with associated Euler solvers based on the finite-volume approach. When coupling geometric details such as boundary layer diverter regions, duct regions with inlets and outlets, or slots with the general external grid, imposing C (exp 1) continuity can be extremely tedious. The approach taken here is to patch blocks together at common interfaces where there is no grid continuity, but enforce conservation in the finite-volume solution. The key to this technique is how to obtain the information required for a conservative interface. The Ramshaw technique which automates the computation of proportional areas of two overlapping grids on a planar surface and is suitable for coding was used. Researchers generated internal duct grids for the Langley experimental fighter configuration independent of the external grid topology, with a conservative interface at the inlet and outlet.
Reyes, Jonathan; Shadwick, B. A.
2016-10-01
Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.
3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"
Douglass, A.
2005-01-01
The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.
Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks.
Pietarila Graham, Jonathan; Mininni, Pablo D; Pouquet, Annick
2009-07-01
We demonstrate that, for the case of quasiequipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics (LAMHD) alpha model reproduces well both the large-scale and the small-scale properties of turbulent flows; in particular, it displays no increased (superfilter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the subfilter scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes alpha model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of superfilter-scale spectral properties. We argue that, as the Lorentz force breaks the conservation of circulation and enables spectrally nonlocal energy transfer (associated with Alfvén waves), it is responsible for the absence of a viscous bottleneck in magnetohydrodynamics (MHD), as compared to the fluid case. As LAMHD preserves Alfvén waves and the circulation properties of MHD, there is also no (superfilter) bottleneck found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of approximately 200 when compared to a direct numerical simulation on a large grid of 1536;{3} points at the same Reynolds number.
The global convergence of the non-quasi-Newton methods with non-monotone line search
无
2006-01-01
The non-quasi-Newton methods for unconstrained optimization was investigated. Non-monotone line search procedure is introduced, which is combined with the non-quasi-Newton family. Under the uniform convexity assumption on objective function, the global convergence of the non-quasi-Newton family was proved.Numerical experiments showed that the non-monotone line search was more effective.
How to project onto the monotone nonnegative cone using Pool Adjacent Violators type algorithms
Németh, A B
2012-01-01
The metric projection onto an order nonnegative cone from the metric projection onto the corresponding order cone is derived. Particularly, we can use Pool Adjacent Violators-type algorithms developed for projecting onto the monotone cone for projecting onto the monotone nonnegative cone too.
An analysis of the stability and monotonicity of a kind of control models
LU Yifa
2013-06-01
Full Text Available The stability and monotonicity of control systems with parameters are considered.By the iterative relationship of the coefficients of characteristic polynomials and the Mathematica software,some sufficient conditions for the monotonicity and stability of systems are given.
Tijs, S.H.; Moretti, S.; Brânzei, R.; Norde, H.W.
2005-01-01
A new way is presented to define for minimum cost spanning tree (mcst-) games the irreducible core, which is introduced by Bird in 1976.The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems i
A novel complex-system-view-based method for system effectiveness analysis: Monotonic indexes space
无
2006-01-01
Based on the characteristics of the complex system, this paper presents a novel method, the monotonic indexes space method, for the effectiveness analysis of the complex system. First, it presents some basic concepts and assumption such as the monotonic indexes space, monotonic indexes requirement locus, etc. Second, based on the assumption that indexes are monotonic for the requirements, an algorithm is proposed and applied to numerical approximation of monotonic indexes requirement locus with hyperboxes. Third, this paper proposes two algorithms for acquiring intersection of several monotonic indexes requirement locus. Fourth, this paper proposes the monotonic-index- space based system analysis model such as the system evaluation model, the sensitivity analysis model for indexes. Based on the practical requirement, the concept of fuzzy monotonic indexes requirement locus and the corresponding analysis model are introduced. Finally, this paper applies the above-mentioned models to analyze the effectiveness of a notional anti-stealth-air-defense information system. And the outputs show that the method is promising.
Effects of temperature on monotonic and fatigue properties of carbon fibre epoxy cross ply laminates
Matsuhisa, Y.; King, J.
1993-01-01
The effects of test temperature on damage accumulation behaviour has been studied using "Torayca" T800H / #3631 in conditions of monotonic and fatigue loading. The damage accumulation behaviour was found to vary as a function of the test temperature, with the effect of temperature on the damage behaviour being different between monotonic and fatigue loading.
Effects of temperature on monotonic and fatigue properties of carbon fibre epoxy cross ply laminates
Matsuhisa, Y. (Composite Materials Research Labs., Toray Industries Inc., Ehime (Japan)); King, J.E. (Composite Materials Research Labs., Toray Industries Inc., Ehime (Japan) Dept. of Materials Science and Metallurgy, Univ. of Cambridge (United Kingdom))
1993-11-01
The effects of test temperature on damage accumulation behaviour has been studied using ''Torayca'' T800H/[3631] in conditions of monotonic and fatigue loading. The damage accumulation behaviour was found to vary as a function of the test temperature, with the effect of temperature on the damage behaviour being different between monotonic and fatigue loading. (orig.).
Tijs, S.H.; Moretti, S.; Brânzei, R.; Norde, H.W.
2005-01-01
A new way is presented to define for minimum cost spanning tree (mcst-) games the irreducible core, which is introduced by Bird in 1976.The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems
Kovyrkina, O. A.; Ostapenko, V. V.
2016-05-01
The monotonicity of the CABARET scheme approximating a hyperbolic differential equation with a sign-changing characteristic field is analyzed. Monotonicity conditions for this scheme are obtained in domains where the characteristics have a sign-definite propagation velocity and near sonic lines, on which the propagation velocity changes its sign. These properties of the CABARET scheme are illustrated by test computations.
Tijs, S.H.; Moretti, S.; Brânzei, R.; Norde, H.W.
2005-01-01
A new way is presented to define for minimum cost spanning tree (mcst-) games the irreducible core, which is introduced by Bird in 1976.The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems i
Computation of displacements for nonlinear elastic beam models using monotone iterations
Philip Korman
1988-01-01
Full Text Available We study displacement of a uniform elastic beam subject to various physically important boundary conditions. Using monotone methods, we discuss stability and instability of solutions. We present computations, which suggest efficiency of monotone methods for fourth order boundary value problems.
Lagrangian Volume Deformations around Simulated Galaxies
Robles, S; Oñorbe, J; Martínez-Serrano, F J
2015-01-01
We present a detailed analysis of the local evolution of 206 Lagrangian Volumes (LVs) selected at high redshift around galaxy seeds, identified in a large-volume $\\Lambda$CDM hydrodynamical simulation. The LVs have a mass range of $1 - 1500 \\times 10^{10} M_\\odot$. We follow the dynamical evolution of the density field inside these initially spherical LVs from $z=10$ up to $z_{\\rm low}= 0.05$, witnessing highly non-linear, anisotropic mass rearrangements within them, leading to the emergence of the local cosmic web (CW). These mass arrangements have been analysed in terms of the reduced inertia tensor $I_{ij}^r$, focusing on the evolution of the principal axes of inertia and their corresponding eigen directions, and paying particular attention to the times when the evolution of these two structural elements declines. In addition, mass and component effects along this process have also been investigated. We have found that deformations are led by DM dynamics and they transform most of the initially spherical L...
One-loop effective lagrangians after matching
Aguila, F. del; Santiago, J. [Universidad de Granada, Departamento de Fisica Teorica y del Cosmos and CAFPE, Granada (Spain); Kunszt, Z. [ETH Zuerich, Institute for Theoretical Physics, Zuerich (Switzerland)
2016-05-15
We discuss the limitations of the covariant derivative expansion prescription advocated to compute the one-loop Standard Model (SM) effective lagrangian when the heavy fields couple linearly to the SM. In particular, one-loop contributions resulting from the exchange of both heavy and light fields must be explicitly taken into account through matching because the proposed functional approach alone does not account for them. We review a simple case with a heavy scalar singlet of charge -1 to illustrate the argument. As two other examples where this matching is needed and this functional method gives a vanishing result, up to renormalization of the heavy sector parameters, we re-evaluate the one-loop corrections to the T-parameter due to a heavy scalar triplet with vanishing hypercharge coupling to the Brout-Englert-Higgs boson and to a heavy vector-like quark singlet of charged 2/3 mixing with the top quark, respectively. In all cases we make use of a new code for matching fundamental and effective theories in models with arbitrary heavy field additions. (orig.)
Lagrangian based methods for coherent structure detection
Allshouse, Michael R., E-mail: mallshouse@chaos.utexas.edu [Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, Texas 78712 (United States); Peacock, Thomas, E-mail: tomp@mit.edu [Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2015-09-15
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.
Sigma Decomposition: The CP-Odd Lagrangian
Hierro, I M; Rigolin, and S
2015-01-01
In Alonso et al., JHEP 12 (2014) 034, the CP-even sector of the effective chiral Lagrangian for a generic composite Higgs model with a symmetric coset has been constructed, up to four momenta. In this paper, the CP-odd couplings are studied within the same context. If only the Standard Model bosonic sources of custodial symmetry breaking are considered, then at most six independent operators form a basis. One of them is the weak-$\\theta$ term linked to non-perturbative sources of CP viola- tion, while the others describe CP-odd perturbative couplings between the Standard Model gauge bosons and an Higgs-like scalar belonging to the Goldstone boson sector. The procedure is then applied to three distinct exemplifying frameworks: the original $SU(5)/SO(5)$ Georgi-Kaplan model, the minimal custodial-preserving $SO(5)/SO(4)$ model and the minimal $SU(3)/(SU(2)\\times U(1))$ model, which intrinsically breaks cus- todial symmetry. Moreover, the projection of the high-energy electroweak effective theory to the low-ener...
Sea Fog Forecasting with Lagrangian Models
Lewis, J. M.
2014-12-01
In 1913, G. I. Taylor introduced us to a Lagrangian view of sea fog formation. He conducted his study off the coast of Newfoundland in the aftermath of the Titanic disaster. We briefly review Taylor's classic work and then apply these same principles to a case of sea fog formation and dissipation off the coast of California. The resources used in this study consist of: 1) land-based surface and upper-air observations, 2) NDBC (National Data Buoy Center) observations from moored buoys equipped to measure dew point temperature as well as the standard surface observations at sea (wind, sea surface temperature, pressure, and air temperature), 3) satellite observations of cloud, and 4) a one-dimensional (vertically directed) boundary layer model that tracks with the surface air motion and makes use of sophisticated turbulence-radiation parameterizations. Results of the investigation indicate that delicate interplay and interaction between the radiation and turbulence processes makes accurate forecasts of sea fog onset unlikely in the near future. This pessimistic attitude stems from inadequacy of the existing network of observations and uncertainties in modeling dynamical processes within the boundary layer.
Disentangling the Cosmic Web with Lagrangian Submanifold
Shandarin, Sergei F.; Medvedev, Mikhail V.
2016-10-01
The Cosmic Web is a complicated highly-entangled geometrical object. Remarkably it has formed from practically Gaussian initial conditions, which may be regarded as the simplest departure from exactly uniform universe in purely deterministic mapping. The full complexity of the web is revealed neither in configuration no velocity spaces considered separately. It can be fully appreciated only in six-dimensional (6D) phase space. However, studies of the phase space is complicated by the fact that every projection of it on a three-dimensional (3D) space is multivalued and contained caustics. In addition phase space is not a metric space that complicates studies of geometry. We suggest to use Lagrangian submanifold i.e., x = x(q), where both x and q are 3D vectors instead of the phase space for studies the complexity of cosmic web in cosmological N-body dark matter simulations. Being fully equivalent in dynamical sense to the phase space it has an advantage of being a single valued and also metric space.
Top marine predators track Lagrangian coherent structures.
Tew Kai, Emilie; Rossi, Vincent; Sudre, Joel; Weimerskirch, Henri; Lopez, Cristobal; Hernandez-Garcia, Emilio; Marsac, Francis; Garçon, Veronique
2009-05-19
Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great Frigatebird. Using a newly developed dynamic concept, the finite-size Lyapunov exponent (FSLE), we identified Lagrangian coherent structures (LCSs) present in the surface flow in the channel over a 2-month observation period (August and September 2003). By comparing seabird satellite positions with LCS locations, we demonstrate that frigatebirds track precisely these structures in the Mozambique Channel, providing the first evidence that a top predator is able to track these FSLE ridges to locate food patches. After comparing bird positions during long and short trips and different parts of these trips, we propose several hypotheses to understand how frigatebirds can follow these LCSs. The birds might use visual and/or olfactory cues and/or atmospheric current changes over the structures to move along these biologic corridors. The birds being often associated with tuna schools around foraging areas, a thorough comprehension of their foraging behavior and movement during the breeding season is crucial not only to seabird ecology but also to an appropriate ecosystemic approach to fisheries in the channel.
Sommer, Simon; Ma, Zheng; Jørgensen, Bo Nørregaard
2015-01-01
China is planning to transform its traditional power grid in favour of a smart grid, since it allows a more economically efficient and a more environmentally friendly transmission and distribution of electricity. Thus, a nationwide smart grid is likely to save tremendous amounts of resources...
A Lagrangian, small-scale investigation of turbulent entrainment in an axisymmetric jet
Wolf, M; Luethi, B; Krug, D [Institute of Environmental Engineering, ETH Zurich, 8093 Zurich (Switzerland); Holzner, M [Max Planck Institute for Dynamics and Self-Organisation, 37073 Goettingen (Germany); Liberzon, A; Tsinober, A, E-mail: wolf@ifu.baug.ethz.ch [School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
2011-12-22
Particle tracking velocimetry (PTV) was applied to study turbulent entrainment in an axisymmetric jet at Re = 5000. Several single-point flow statistics are used to characterize the general flow field of our newly designed jet facility, proving that a self-preserving axisymmetric jet could be established. An analysis of the Lagrangian evolution of small scale quantities, such as vorticity and strain, along trajectories passing the entrainment interface is performed. We find that a particle needs on the order of one Kolmogorov time scale to cross the entrainment interface, which is similar to results of grid turbulence without mean shear. Finally, we perform a conditional investigation of invariants of du{sub i}/du{sub j} at the entrainment interface, analyzing joint probability density functions (joint PDFs) evaluated at different times along trajectories crossing the interfacial region.
A Lagrangian, small-scale investigation of turbulent entrainment in an axisymmetric jet
Wolf, M.; Lüthi, B.; Holzner, M.; Liberzon, A.; Krug, D.; Tsinober, A.
2011-12-01
Particle tracking velocimetry (PTV) was applied to study turbulent entrainment in an axisymmetric jet at Re = 5000. Several single-point flow statistics are used to characterize the general flow field of our newly designed jet facility, proving that a self-preserving axisymmetric jet could be established. An analysis of the Lagrangian evolution of small scale quantities, such as vorticity and strain, along trajectories passing the entrainment interface is performed. We find that a particle needs on the order of one Kolmogorov time scale to cross the entrainment interface, which is similar to results of grid turbulence without mean shear. Finally, we perform a conditional investigation of invariants of at the entrainment interface, analyzing joint probability density functions (joint PDFs) evaluated at different times along trajectories crossing the interfacial region.
Flow-Driven Cloud Formation and Fragmentation: Results From Eulerian and Lagrangian Simulations
Heitsch, Fabian; Walch, Stefanie
2011-01-01
The fragmentation of shocked flows in a thermally bistable medium provides a natural mechanism to form turbulent cold clouds as precursors to molecular clouds. Yet because of the large density and temperature differences and the range of dynamical scales involved, following this process with numerical simulations is challenging. We compare two-dimensional simulations of flow-driven cloud formation without self-gravity, using the Lagrangian Smoothed Particle Hydrodynamics (SPH) code VINE and the Eulerian grid code Proteus. Results are qualitatively similar for both methods, yet the variable spatial resolution of the SPH method leads to smaller fragments and thinner filaments, rendering the overall morphologies different. Thermal and hydro-dynamical instabilities lead to rapid cooling and fragmentation into cold clumps with temperatures below 300K. For clumps more massive than 1 Msun/pc, the clump mass function has an average slope of -0.8. The internal velocity dispersion of the clumps is nearly an order of ma...
Multi-stage high order semi-Lagrangian schemes for incompressible flows in Cartesian geometries
Cameron, Alexandre; Dormy, Emmanuel
2016-01-01
Efficient transport algorithms are essential to the numerical resolution of incompressible fluid flow problems. Semi-Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy then determines the properties of the scheme. We introduce a simple multi-stage procedure which can easily be used to increase the order of accuracy of a code based on multi-linear interpolations. This approach is an extension of a corrective algorithm introduced by Dupont \\& Liu (2003, 2007). This multi-stage procedure can be easily implemented in existing parallel codes using a domain decomposition strategy, as the communications pattern is identical to that of the multi-linear scheme. We show how a combination of a forward and backward error correction can provide a third-order accurate scheme, thus significantly reducing diffusive effects while retaining a non-dispersive leading error term.
Large eddy simulation of Rayleigh-Taylor instability using the arbitrary Lagrangian-Eulerian method
Darlington, R
1999-12-01
This research addresses the application of a large eddy simulation (LES) to Arbitrary Lagrangian Eulerian (ALE) simulations of Rayleigh-Taylor instability. First, ALE simulations of simplified Rayleigh-Taylor instability are studied. The advantages of ALE over Eulerian simulations are shown. Next, the behavior of the LES is examined in a more complicated ALE simulation of Rayleigh-Taylor instability. The effects of eddy viscosity and stochastic backscatter are examined. The LES is also coupled with ALE to increase grid resolution in areas where it is needed. Finally, the methods studied above are applied to two sets of experimental simulations. In these simulations, ALE allows the mesh to follow expanding experimental targets, while LES can be used to mimic the effect of unresolved instability modes.
A constraint algorithm for singular Lagrangians subjected to nonholonomic constraints
de Leon, M. [Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); de Diego, D.M. [Departamento de Economia Aplicada Cuantitativa, Facultad de Ciencias Economicas y Empresariales, UNED, 28040 Madrid (Spain)
1997-06-01
We construct a constraint algorithm for singular Lagrangian systems subjected to nonholonomic constraints which generalizes that of Dirac for constrained Hamiltonian systems. {copyright} {ital 1997 American Institute of Physics.}
A Dynamic Job Shop Scheduling Method Based on Lagrangian Relaxation
无
1999-01-01
Due to the complexity of dynamic job shop scheduling in flexible manufacturing s ystem(FMS), many heuristic rules are still used today. A dynamic scheduling appr oach based on Lagrangian relaxation is proposed to improve the quality and guara ntee the real-time capability of dynamic scheduling. The proposed method makes use of the dynamic predictive optimal theory combined with Lagrangian relaxation to obtain a good solution that can be evaluated quantitatively. The Lagrangian multipliers introduced here are capable of describing machine predictive states and system capacity constraints. This approach can evaluate the suboptimality of the scheduling systems. It can also quickly obtain high quality feasible schedu les, thus enabling Lagrangian relaxation to be better used in the dynamic schedu ling of manufacturing system. The efficiency and effectiveness of this method ar e verified by numerical experiments.
Remarks on the Lagrangian representation of bi-Hamiltonian equations
Pavlov, M. V.; Vitolo, R. F.
2017-03-01
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair A1, A2, where A1 is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equivalent to finding a generalized vector field τ such that A2 =LτA1. We use this result in order to find the Lagrangian representation when A2 is a homogeneous third-order Hamiltonian operator, although the method that we use can be applied to any other homogeneous Hamiltonian operator. As an example we provide the Lagrangian representation of a WDVV hydrodynamic-type system in 3 components.
Second post-Newtonian Lagrangian dynamics of spinning compact binaries
Huang, Li; Wu, Xin [Nanchang University, Department of Physics and Institute of Astronomy, Nanchang (China); Ma, DaZhu [Hubei University for Nationalities, School of Science, Enshi (China)
2016-09-15
The leading-order spin-orbit coupling is included in a post-Newtonian Lagrangian formulation of spinning compact binaries, which consists of the Newtonian term, first post-Newtonian (1PN) and 2PN non-spin terms and 2PN spin-spin coupling. This leads to a 3PN spin-spin coupling occurring in the derived Hamiltonian. The spin-spin couplings are mainly responsible for chaos in the Hamiltonians. However, the 3PN spin-spin Hamiltonian is small and has different signs, compared with the 2PN spin-spin Hamiltonian equivalent to the 2PN spin-spin Lagrangian. As a result, the probability of the occurrence of chaos in the Lagrangian formulation without the spin-orbit coupling is larger than that in the Lagrangian formulation with the spin-orbit coupling. Numerical evidences support this claim. (orig.)
Construction of Lagrangians and Hamiltonians from the Equation of Motion
Yan, C. C.
1978-01-01
Demonstrates that infinitely many Lagrangians and Hamiltonians can be constructed from a given equation of motion. Points out the lack of an established criterion for making a proper selection. (Author/GA)
A discrete Lagrangian based direct approach to macroscopic modelling
Sarkar, Saikat; Nowruzpour, Mohsen; Reddy, J. N.; Srinivasa, A. R.
2017-01-01
A direct discrete Lagrangian based approach, designed at a length scale of interest, to characterize the response of a body is proposed. The main idea is to understand the dynamics of a deformable body via a Lagrangian corresponding to a coupled interaction of rigid particles in the reduced dimension. We argue that the usual practice of describing the laws of a deformable body in the continuum limit is redundant, because for most of the practical problems, analytical solutions are not available. Since continuum limit is not taken, the framework automatically relaxes the requirement of differentiability of field variables. The discrete Lagrangian based approach is illustrated by deriving an equivalent of the Euler-Bernoulli beam model. A few test examples are solved, which demonstrate that the derived non-local model predicts lower deflections in comparison to classical Euler-Bernoulli beam solutions. We have also included crack propagation in thin structures for isotropic and anisotropic cases using the Lagrangian based approach.
Don't worry. Lagrangian drift kinetics is OK
Burby, Joshua
2015-11-01
I show that standard Lagrangian (i.e. variational) drift kinetics with uE × B ~vth and Hgc =Ho + ɛH1 +ɛ2H2 has an unphysically-large phase space; where a valid initial condition ought to consist of (F , E , B) specified at t = 0 , Lagrangian drift kinetics requires initial time derivatives of the electromagnetic field to be specified as well. This phenomenon occurs because the guiding center coordinate transformation depends on time derivatives of the electromagnetic field, and this leads to the appearance of a time derivative of E in H2. I also show how to ``renormalize'' the Lagrangian approach to drift kinetics in a way that manifestly preserves the correct structure of the initial value problem. Starting from this modified Lagrangian procedure, I derive the drift kinetic system's Poisson bracket. Work supported by DOE contract # DE-AC02-09CH11466.
Geometry of Lagrangian First-order Classical Field Theories
Echeverría-Enríquez, A; Román-Roy, N; Echeverr\\'ia-Enr\\'iquez, Arturo; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso
1996-01-01
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the {\\sl Euler-Lagrange equations} in two equivalent ways: as the result of a variational problem and developing the {\\sl jet field formalism} (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied.
The complete HEFT Lagrangian after the LHC Run I
Brivio, I; Gonzalez-Garcia, M C; Merlo, L
2016-01-01
The complete effective chiral Lagrangian for a dynamical Higgs is presented and constrained by means of a global analysis including electroweak precision data together with Higgs and triple gauge boson coupling data from the LHC Run~I. The operators' basis up to next-to-leading order in the expansion consists of 148 (188 considering right-handed neutrinos) flavour universal terms and it is presented here making explicit the custodial nature of the operators. This effective Lagrangian provides the most general description of the physical Higgs couplings once the electroweak symmetry is assumed, and it allows for deviations from the $SU(2)_L$ doublet nature of the Standard Model Higgs. The comparison with the effective linear Lagrangian constructed with an exact $SU(2)_L$ doublet Higgs and considering operators with at most canonical dimension six is presented. A promising strategy to disentangle the two descriptions consists in analysing i) anomalous signals present only in the chiral Lagrangian and not expect...
Classical Nonminimal Lagrangians and Kinematic Tests of Special Relativity
Schreck, M
2016-01-01
This article gives a brief summary on recently obtained classical lagrangians for the nonminimal fermion sector of the Standard-Model Extension (SME). Such lagrangians are adequate descriptions of classical particles that are subject to a Lorentz-violating background field based on the SME. Explicitly, lagrangians were obtained for the leading nonminimal contributions of the m, a, c, e, and f coefficients. These results were then used to interpret classical, kinematic tests of Special Relativity in the framework of the nonminimal SME. This led to new constraints on certain nonminimal controlling coefficients. Although the experiments were very sophisticated in the era when they were carried out, their sensitivities for detecting Lorentz violation were still far away from the Planck scale. Obtaining the novel constraints can be considered as a proof-of-principle demonstrating the applicability of the classical lagrangians computed.
Simultaneous temperature and velocity Lagrangian measurements in turbulent thermal convection
Liot, O; Zonta, F; Chibbaro, S; Coudarchet, T; Gasteuil, Y; Pinton, J -F; Salort, J; Chillà, F
2015-01-01
We report joint Lagrangian velocity and temperature measurements in turbulent thermal convection. Measurements are performed using an improved version (extended autonomy) of the neutrally-buoyant instrumented particle that was used by to performed experiments in a parallelepipedic Rayleigh-Benard cell. The temperature signal is obtained from a RFtransmitter. Simultaneously, we determine particle's position and velocity with one camera, which grants access to the Lagrangian heat flux. Due to the extended autonomy of the present particle, we obtain well converged temperature and velocity statistics, as well as pseudo-eulerian maps of velocity and heat flux. Present experimental results have also been compared with the results obtained by a corresponding campaign of Direct Numerical Simulations and Lagrangian Tracking of massless tracers. The comparison between experimental and numerical results show the accuracy and reliability of our experimental measurements. Finally, the analysis of lagrangian velocity and t...
Testing of a new dense gas approach in the Lagrangian Dispersion Model SPRAY.
Mortarini, Luca; Alessandrini, Stefano; Ferrero, Enrico; Anfossi, Domenico; Manfrin, Massimiliano
2013-04-01
A new original method for the dispersion of a positively and negatively buoyant plume is proposed. The buoyant pollutant movement is treated introducing a fictitious scalar inside the Lagrangian Stochastic Particle Model SPRAY. The method is based on the same idea of Alessandrini and Ferrero (Phys. A 388:1375-1387, 2009) for the treatment of a background substance entrainment into the plume. In this application, the fictitious scalar is the density and momentum difference between the plume portions and the environment air that naturally takes into account the interaction between the plume and the environment. As a consequence, no more particles than those inside the plume have to be released to simulate the entrainment of the background air temperature. In this way the entrainment is properly simulated and the plume sink is calculated from the local property of the flow. This new approach is wholly Lagrangian in the sense that the Eulerian grid is only used to compute the propriety of a portion of the plume from the particles contained in every cell. No equation of the bulk plume is solved on a fixed grid. To thoroughly test the turbulent velocity field calculated by the model, the latter is compared with a water tank experiment carried out in the TURLAB laboratory in Turin (Italy). A vertical density driven current was created releasing a saline solution (salt and water) in a water tank with no mean flow. The experiment reproduces in physical similarity, based on the density Froud number, the release of a dense gas in the planetary boundary layer and the Particle Image Velocimetry technique has been used to analyze the buoyancy generated velocity field. The high temporal and spatial resolution of the measurements gives a deep insight to the problems of the bouncing of the dense gas and of the creation of the outflow velocity at the ground.
Flux form Semi-Lagrangian methods for parabolic problems
Bonaventura Luca
2016-09-01
Full Text Available A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and stability analysis is proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection diffusion and nonlinear parabolic problems.
Integration over families of Lagrangian submanifolds in BV formalism
Mikhailov, Andrei
2016-01-01
Gauge fixing is interpreted in BV formalims as a choice of Lagrangian submanifold in an odd symplectic manifold. A natural construction defines an integration procedure on families of Lagrangian submanifolds. In string perturbation theory, the moduli space integrals of higher genus amplitudes can be interpreted this way. We discuss the role of symmetries in this construction. We also discuss its applications to string worldsheet sigma-model, in particular to the construction of vertex operators.
Addendum to "Coherent Lagrangian vortices: The black holes of turbulence"
Haller, G.; Beron-Vera, F. J.
2014-01-01
In Haller and Beron-Vera (2013) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null-geodesics of the Lorentzian metric associated with a generalized Green-Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here we give an improved discussion on this analogy.
Merging matter and geometry in the same Lagrangian
Hendrik Ludwig
2015-12-01
Full Text Available We show that a Lagrangian density proportional to −gLm2/R reduces to a pressuron theory of gravity that is indistinguishable from General Relativity in the dust limit. The combination of matter and geometry in the same Lagrangian density intrinsically satisfies Mach's Principle — since matter cannot exist without curvature and vice versa — while it may have the correct phenomenology in order to describe actual gravity.
Lagrangian formulation of continuum with internal long-range interactions
无
2011-01-01
Based on a new definition of nonlocal variable,this paper establishes the Lagrangian formulation for continuum with internal long-range interactions.Distinguished from the existing theories,the nonlocal term in the Lagrangian formulation automatically satisfies the zero mean condition determined by the action and reaction law.By this formulation,elastic wave in a rod with the internal long-range interactions is investigated.The dispersion of the elastic wave is predicted.
BRST Lagrangian construction for spin-2 field in Einstein space
Buchbinder, I.L., E-mail: joseph@tspu.edu.r [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation); Krykhtin, V.A., E-mail: krykhtin@tspu.edu.r [Department of Theoretical Physics, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation); Laboratory of Mathematical Physics, Tomsk Polytechnic University, Tomsk 634034 (Russian Federation); Lavrov, P.M., E-mail: lavrov@tspu.edu.r [Department of Mathematical Analysis, Tomsk State Pedagogical University, Tomsk 634061 (Russian Federation)
2010-03-01
We explore a new possibility of BRST construction in higher spin field theory to obtain a consistent Lagrangian for massive spin-2 field in Einstein space. Such approach automatically leads to gauge invariant Lagrangian with suitable auxiliary and Stueckelberg fields. It is proved that in this case a propagation of spin-2 field is hyperbolic and causal. Also we extend notion of partial masslessness for spin-2 field in the background under consideration.
Forecasting Future Sea Ice Conditions: A Lagrangian Approach
2014-09-30
that survives the summer melt season in each of the Arctic peripheral seas. The Lagrangian Model is forced with weekly mean satellite-derived sea- ice ...GCM to drive the Lagrangian code and map the regions for the multi-year ice surviving the summer melt in each of the Arctic peripheral seas in todays...1995, Emery et al. 1997, Meier et al. 2000, Tschudi et al. 2010) 3- Assess whether the source region of sea ice melting in peripheral seas in the
Interactive Lagrangian density between massive photons and gravitons
DENG Yan-bin
2006-01-01
The interactive Lagrangian density of massive photons and gravitons is proposed after an investigation into the interaction between photons with or without mass under the influence of gravity either as classical field, gravitational wave, or gravitons from a perspective of quantum field. This interactive Lagrangian density can provide a step-stone for further research of gravitational wave and the possible rest mass of photon.
Probabilistic Analysis of Pattern Formation in Monotonic Self-Assembly.
Moore, Tyler G; Garzon, Max H; Deaton, Russell J
2015-01-01
Inspired by biological systems, self-assembly aims to construct complex structures. It functions through piece-wise, local interactions among component parts and has the potential to produce novel materials and devices at the nanoscale. Algorithmic self-assembly models the product of self-assembly as the output of some computational process, and attempts to control the process of assembly algorithmically. Though providing fundamental insights, these computational models have yet to fully account for the randomness that is inherent in experimental realizations, which tend to be based on trial and error methods. In order to develop a method of analysis that addresses experimental parameters, such as error and yield, this work focuses on the capability of assembly systems to produce a pre-determined set of target patterns, either accurately or perhaps only approximately. Self-assembly systems that assemble patterns that are similar to the targets in a significant percentage are "strong" assemblers. In addition, assemblers should predominantly produce target patterns, with a small percentage of errors or junk. These definitions approximate notions of yield and purity in chemistry and manufacturing. By combining these definitions, a criterion for efficient assembly is developed that can be used to compare the ability of different assembly systems to produce a given target set. Efficiency is a composite measure of the accuracy and purity of an assembler. Typical examples in algorithmic assembly are assessed in the context of these metrics. In addition to validating the method, they also provide some insight that might be used to guide experimentation. Finally, some general results are established that, for efficient assembly, imply that every target pattern is guaranteed to be assembled with a minimum common positive probability, regardless of its size, and that a trichotomy exists to characterize the global behavior of typical efficient, monotonic self-assembly systems
Probabilistic Analysis of Pattern Formation in Monotonic Self-Assembly.
Tyler G Moore
Full Text Available Inspired by biological systems, self-assembly aims to construct complex structures. It functions through piece-wise, local interactions among component parts and has the potential to produce novel materials and devices at the nanoscale. Algorithmic self-assembly models the product of self-assembly as the output of some computational process, and attempts to control the process of assembly algorithmically. Though providing fundamental insights, these computational models have yet to fully account for the randomness that is inherent in experimental realizations, which tend to be based on trial and error methods. In order to develop a method of analysis that addresses experimental parameters, such as error and yield, this work focuses on the capability of assembly systems to produce a pre-determined set of target patterns, either accurately or perhaps only approximately. Self-assembly systems that assemble patterns that are similar to the targets in a significant percentage are "strong" assemblers. In addition, assemblers should predominantly produce target patterns, with a small percentage of errors or junk. These definitions approximate notions of yield and purity in chemistry and manufacturing. By combining these definitions, a criterion for efficient assembly is developed that can be used to compare the ability of different assembly systems to produce a given target set. Efficiency is a composite measure of the accuracy and purity of an assembler. Typical examples in algorithmic assembly are assessed in the context of these metrics. In addition to validating the method, they also provide some insight that might be used to guide experimentation. Finally, some general results are established that, for efficient assembly, imply that every target pattern is guaranteed to be assembled with a minimum common positive probability, regardless of its size, and that a trichotomy exists to characterize the global behavior of typical efficient, monotonic
Fused Lasso Screening Rules via the Monotonicity of Subdifferentials.
Wang, Jie; Fan, Wei; Ye, Jieping
2015-09-01
Fused Lasso is a popular regression technique that encodes the smoothness of the data. It has been applied successfully to many applications with a smooth feature structure. However, the computational cost of the existing solvers for fused Lasso is prohibitive when the feature dimension is extremely large. In this paper, we propose novel screening rules that are able to quickly identity the adjacent features with the same coefficients. As a result, the number of variables to be estimated can be significantly reduced, leading to substantial savings in computational cost and memory usage. To the best of our knowledge, the proposed approach is the first attempt to develop screening methods for the fused Lasso problem with general data matrix. Our major contributions are: 1) we derive a new dual formulation of fused Lasso that comes with several desirable properties; 2) we show that the new dual formulation of fused Lasso is equivalent to that of the standard Lasso by two affine transformations; 3) we propose a novel framework for developing effective and efficient screening rules for fused Lasso via the monotonicity of the subdifferentials (FLAMS). Some appealing features of FLAMS are: 1) our methods are safe in the sense that the detected adjacent features are guaranteed to have the same coefficients; 2) the dataset needs to be scanned only once to run the screening, whose computational cost is negligible compared to that of solving the fused Lasso; (3) FLAMS is independent of the solvers and can be integrated with any existing solvers. We have evaluated the proposed FLAMS rules on both synthetic and real datasets. The experiments indicate that FLAMS is very effective in identifying the adjacent features with the same coefficients. The speedup gained by FLAMS can be orders of magnitude.
Local Monotonicity and Isoperimetric Inequality on Hypersurfaces in Carnot groups
Francesco Paolo Montefalcone
2010-12-01
Full Text Available Let G be a k-step Carnot group of homogeneous dimension Q. Later on we shall present some of the results recently obtained in [32] and, in particular, an intrinsic isoperimetric inequality for a C2-smooth compact hypersurface S with boundary @S. We stress that S and @S are endowed with the homogeneous measures n????1 H and n????2 H , respectively, which are actually equivalent to the intrinsic (Q - 1-dimensional and (Q - 2-dimensional Hausdor measures with respect to a given homogeneous metric % on G. This result generalizes a classical inequality, involving the mean curvature of the hypersurface, proven by Michael and Simon [29] and Allard [1], independently. One may also deduce some related Sobolev-type inequalities. The strategy of the proof is inspired by the classical one and will be discussed at the rst section. After reminding some preliminary notions about Carnot groups, we shall begin by proving a linear isoperimetric inequality. The second step is a local monotonicity formula. Then we may achieve the proof by a covering argument.We stress however that there are many dierences, due to our non-Euclidean setting.Some of the tools developed ad hoc are, in order, a \\blow-up" theorem, which holds true also for characteristic points, and a smooth Coarea Formula for the HS-gradient. Other tools are the horizontal integration by parts formula and the 1st variation formula for the H-perimeter n????1H already developed in [30, 31] and then generalized to hypersurfaces having non-empty characteristic set in [32]. These results can be useful in the study of minimal and constant horizontal mean curvature hypersurfaces in Carnot groups.
Taft, Jeffrey D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2016-01-01
The report describes work done on Grid Architecture under the auspices of the Department of Electricity Office of Electricity Delivery and Reliability in 2015. As described in the first Grid Architecture report, the primary purpose of this work is to provide stakeholder insight about grid issues so as to enable superior decision making on their part. Doing this requires the creation of various work products, including oft-times complex diagrams, analyses, and explanations. This report provides architectural insights into several important grid topics and also describes work done to advance the science of Grid Architecture as well.
Generalized Lagrangian dynamics of physical and non-physical systems
Sandler, U.
2014-12-01
In this paper, we show how to study the evolution of a complex system, given imprecise knowledge about the state of the system and the dynamics laws. It will be shown that dynamics of these systems is equivalent to Lagrangian (or Hamiltonian) mechanics in a n+1-dimensional space, where n is a system's dimensionality. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's equations gain a non-zero right side proportional to the derivative of the Lagrangian with respect to the action. Examples of such systems are unstable systems, systems with dissipation and systems which can remember their history. Moreover, in certain situations, the Lagrangian could be a set-valued function. The corresponding equations of motion then become differential inclusions instead of differential equations. We will also show that the principal of least action is a consequence of the causality principle and the local topology of the state space and not an independent axiom of classical mechanics. We emphasize that our adaptation of Lagrangian mechanics does not use or depend on specific properties of the physical system being modeled. Therefore, this Lagrangian approach may be equally applied to non-physical systems. An example of such an application is presented as well.
Lagrangian structures in time-periodic vortical flows
S. V. Kostrykin
2006-01-01
Full Text Available The Lagrangian trajectories of fluid particles are experimentally studied in an oscillating four-vortex velocity field. The oscillations occur due to a loss of stability of a steady flow and result in a regular reclosure of streamlines between the vortices of the same sign. The Eulerian velocity field is visualized by tracer displacements over a short time period. The obtained data on tracer motions during a number of oscillation periods show that the Lagrangian trajectories form quasi-regular structures. The destruction of these structures is determined by two characteristic time scales: the tracers are redistributed sufficiently fast between the vortices of the same sign and much more slowly transported into the vortices of opposite sign. The observed behavior of the Lagrangian trajectories is quantitatively reproduced in a new numerical experiment with two-dimensional model of the velocity field with a small number of spatial harmonics. A qualitative interpretation of phenomena observed on the basis of the theory of adiabatic chaos in the Hamiltonian systems is given. The Lagrangian trajectories are numerically simulated under varying flow parameters. It is shown that the spatial-temporal characteristics of the Lagrangian structures depend on the properties of temporal change in the streamlines topology and on the adiabatic parameter corresponding to the flow. The condition for the occurrence of traps (the regions where the Lagrangian particles reside for a long time is obtained.
Lagrangian Coherent Structures in a Non-Euclidean Global Thermosphere
Wang, N.; Ramirez, U.; Flores, F.; Datta-Barua, S.
2016-12-01
Lagrangian Coherent Structures (LCSs) are manifolds of maximum divergence or convergence in 2D or 3D time-varying flow fields. The study of LCSs has been used to predict material transport in numerous geophysical flows. The most commonly used computational method for finding LCSs is to compute the finite time Lyapunov exponent (FTLE), a scalar field measuring the ratio of stretching after a given interval of time among neighboring particles, relative to their initial separation. LCS ridges are located at the local maxima of the FTLE. The LCS must be objective (frame-invariant for different observers), and the technique for computing the FTLE that determines the LCS typically assumes a Euclidean domain. Previous work showed that LCSs are likely to exist globally at high latitudes using the Euclidean norm. Here we refine that calculation by deriving the FTLE calculation for the Riemannian manifold of a spherical surface, and applying it to the thermospheric layer of the atmosphere globally. The thermosphere is treated as a closed spherical 2D domain on which the fluid flows, assuming negligible vertical flow. The domain is discretized in longitude and latitude, and the Horizontal Wind Model 2014 (HWM14) is used to generate the 2D velocity field at each grid point, each of which is a ground speed in the local east-north-up (ENU) frame. To make the LCS objective, the ground speed in each local ENU frame is converted to angular velocity in the earth-centered earth-fixed (ECEF) coordinates. Using bilinear interpolation and including the rotational velocity of Earth to transform to an inertial frame, we trace the trajectory of each particle to compute the final positions after the integration time. Replacing the Euclidean distance between particles with the great circle distance gives the FTLE scalar field from which the LCSs can be identified. We find and illustrate objective LCSs in the neutral wind flow field at high latitudes by applying this algorithm for the
Framework for Grid Manufacturing
陈笠; 邓宏; 邓倩妮; 吴振宇
2004-01-01
With the development of networked manufacturing, it is more and more imminent to solve problems caused by inherent limitations of network technology, such as heterogeneity, collaboration collision, and decentralized control.This paper presents a framework for grid manufacturing, which neatly combines grid technology with the infrastructure of advanced manufacturing technology.The paper studies grid-oriented knowledge description and acquisition, and constructs a distributed knowledge grid model.The paper also deals with the protocol of node description in collaborative design, and describes a distributed collaborative design model.The protocol and node technology leads to a collaborative production model for grid manufacturing.The framework for grid manufacturing offers an effective and feasible solution for the problems of networked manufacturing.The grid manufacturing will become an advanced distributed manufacturing model and promote the development of advanced manufacturing technologies.
Atkinson, C.; Hackl, J.; Stegeman, P.; Borrell, G.; Soria, J.
2014-04-01
The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.
Bates, J. R.; Moorthi, S.; Higgins, R. W.
1993-01-01
An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.
Angelis, G I; Kotasidis, F A; Matthews, J C [Imaging, Proteomics and Genomics, MAHSC, University of Manchester, Wolfson Molecular Imaging Centre, Manchester (United Kingdom); Reader, A J [Montreal Neurological Institute, McGill University, Montreal (Canada); Lionheart, W R, E-mail: georgios.angelis@mmic.man.ac.uk [School of Mathematics, University of Manchester, Alan Turing Building, Manchester (United Kingdom)
2011-07-07
Iterative expectation maximization (EM) techniques have been extensively used to solve maximum likelihood (ML) problems in positron emission tomography (PET) image reconstruction. Although EM methods offer a robust approach to solving ML problems, they usually suffer from slow convergence rates. The ordered subsets EM (OSEM) algorithm provides significant improvements in the convergence rate, but it can cycle between estimates converging towards the ML solution of each subset. In contrast, gradient-based methods, such as the recently proposed non-monotonic maximum likelihood (NMML) and the more established preconditioned conjugate gradient (PCG), offer a globally convergent, yet equally fast, alternative to OSEM. Reported results showed that NMML provides faster convergence compared to OSEM; however, it has never been compared to other fast gradient-based methods, like PCG. Therefore, in this work we evaluate the performance of two gradient-based methods (NMML and PCG) and investigate their potential as an alternative to the fast and widely used OSEM. All algorithms were evaluated using 2D simulations, as well as a single [{sup 11}C]DASB clinical brain dataset. Results on simulated 2D data show that both PCG and NMML achieve orders of magnitude faster convergence to the ML solution compared to MLEM and exhibit comparable performance to OSEM. Equally fast performance is observed between OSEM and PCG for clinical 3D data, but NMML seems to perform poorly. However, with the addition of a preconditioner term to the gradient direction, the convergence behaviour of NMML can be substantially improved. Although PCG is a fast convergent algorithm, the use of a (bent) line search increases the complexity of the implementation, as well as the computational time involved per iteration. Contrary to previous reports, NMML offers no clear advantage over OSEM or PCG, for noisy PET data. Therefore, we conclude that there is little evidence to replace OSEM as the algorithm of choice
Securing smart grid technology
Chaitanya Krishna, E.; Kosaleswara Reddy, T.; Reddy, M. YogaTeja; Reddy G. M., Sreerama; Madhusudhan, E.; AlMuhteb, Sulaiman
2013-03-01
In the developing countries electrical energy is very important for its all-round improvement by saving thousands of dollars and investing them in other sector for development. For Growing needs of power existing hierarchical, centrally controlled grid of the 20th Century is not sufficient. To produce and utilize effective power supply for industries or people we should have Smarter Electrical grids that address the challenges of the existing power grid. The Smart grid can be considered as a modern electric power grid infrastructure for enhanced efficiency and reliability through automated control, high-power converters, modern communications infrastructure along with modern IT services, sensing and metering technologies, and modern energy management techniques based on the optimization of demand, energy and network availability and so on. The main objective of this paper is to provide a contemporary look at the current state of the art in smart grid communications as well as critical issues on smart grid technologies primarily in terms of information and communication technology (ICT) issues like security, efficiency to communications layer field. In this paper we propose new model for security in Smart Grid Technology that contains Security Module(SM) along with DEM which will enhance security in Grid. It is expected that this paper will provide a better understanding of the technologies, potential advantages and research challenges of the smart grid and provoke interest among the research community to further explore this promising research area.
Cuellar, Jorge (ed.) [Siemens AG, Muenchen (Germany). Corporate Technology
2013-11-01
The engineering, deployment and security of the future smart grid will be an enormous project requiring the consensus of many stakeholders with different views on the security and privacy requirements, not to mention methods and solutions. The fragmentation of research agendas and proposed approaches or solutions for securing the future smart grid becomes apparent observing the results from different projects, standards, committees, etc, in different countries. The different approaches and views of the papers in this collection also witness this fragmentation. This book contains the following papers: 1. IT Security Architecture Approaches for Smart Metering and Smart Grid. 2. Smart Grid Information Exchange - Securing the Smart Grid from the Ground. 3. A Tool Set for the Evaluation of Security and Reliability in Smart Grids. 4. A Holistic View of Security and Privacy Issues in Smart Grids. 5. Hardware Security for Device Authentication in the Smart Grid. 6. Maintaining Privacy in Data Rich Demand Response Applications. 7. Data Protection in a Cloud-Enabled Smart Grid. 8. Formal Analysis of a Privacy-Preserving Billing Protocol. 9. Privacy in Smart Metering Ecosystems. 10. Energy rate at home Leveraging ZigBee to Enable Smart Grid in Residential Environment.
Potechin, Aaron
2011-01-01
L (Logarithmic space) versus NL (Non-deterministic logarithmic space) is one of the great open problems in computational complexity theory. In the paper "Bounds on monotone switching networks for directed connectivity", we separated monotone analogues of L and NL using a model called the switching network model. In particular, by considering inputs consisting of just a path and isolated vertices, we proved that any monotone switching network solving directed connectivity on $N$ vertices must have size at least $N^{\\Omega(\\lg(N))}$ and this bound is tight. If we could show a similar result for general switching networks solving directed connectivity, then this would prove that $L \
Huang, Bo; Chen, Dehui; Li, Xingliang; Li, Chao
2014-05-01
The Global/Regional Assimilation and PrEdiction System (GRAPES) is the new-generation numerical weather prediction (NWP) system developed by the China Meteorological Administration. It is a fully compressible non-hydrostatical global/regional unified model that uses a traditional semi-Lagrangian advection scheme with cubic Lagrangian interpolation (referred to as the SL_CL scheme). The SL_CL scheme has been used in many operational NWP models, but there are still some deficiencies, such as the damping effects due to the interpolation and the relatively low accuracy. Based on Reich's semi-Lagrangian advection scheme (referred to as the R2007 scheme), the Re_R2007 scheme that uses the low- and high-order B-spline function for interpolation at the departure point, is developed in this paper. One- and two-dimensional idealized tests in the rectangular coordinate system with uniform grid cells were conducted to compare the Re_R2007 scheme and the SL_CL scheme. The numerical results showed that: (1) the damping effects were remarkably reduced with the Re_R2007 scheme; and (2) the normalized errors of the Re_R2007 scheme were about 7.5 and 3 times smaller than those of the SL_CL scheme in one- and two-dimensional tests, respectively, indicating the higher accuracy of the Re_R2007 scheme. Furthermore, two solid-body rotation tests were conducted in the latitude-longitude spherical coordinate system with nonuniform grid cells, which also verified the Re_R2007 scheme's advantages. Finally, in comparison with other global advection schemes, the Re_R2007 scheme was competitive in terms of accuracy and flow independence. An encouraging possibility for the application of the Re_R2007 scheme to the GRAPES model is provided.
Rosy Mondardini Producer
2003-01-01
The Grid : . Sharing resources owned by many different organizations to access remote computers, software, and data efficiently and automatically . Secure access to establish the identity of a user or resource, after defining conditions under which sharing occurs . Bridging distance using high-speed connections between computers to create a global Grid . Open standards to allow applications designed for one Grid to run on all others
Geometric deviation modeling by kinematic matrix based on Lagrangian coordinate
Liu, Weidong; Hu, Yueming; Liu, Yu; Dai, Wanyi
2015-09-01
Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it's expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.
Multi-symplectic, Lagrangian, one-dimensional gas dynamics
Webb, G. M.
2015-05-01
The equations of Lagrangian, ideal, one-dimensional, compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate m and time t as independent variables, and in which the Eulerian position of the fluid element x = x(m, t) is one of the dependent variables. This approach differs from the Eulerian, multi-symplectic approach using Clebsch variables. Lagrangian constraints are used to specify equations for xm, xt, and St consistent with the Lagrangian map, where S is the entropy of the gas. We require St = 0 corresponding to advection of the entropy S with the flow. We show that the Lagrangian Hamiltonian equations are related to the de Donder-Weyl multi-momentum formulation. The pullback conservation laws and the symplecticity conservation laws are discussed. The pullback conservation laws correspond to invariance of the action with respect to translations in time (energy conservation) and translations in m in Noether's theorem. The conservation law due to m-translation invariance gives rise to a novel nonlocal conservation law involving the Clebsch variable r used to impose ∂S(m, t)/∂t = 0. Translation invariance with respect to x in Noether's theorem is associated with momentum conservation. We obtain the Cartan-Poincaré form for the system, and use it to obtain a closed ideal of two-forms representing the equation system.
P.Cerello; T.Anticic; 等
2001-01-01
The challenge of LHC computing,with data rates in the range of several PB/year,requires the development of GRID technologies,to optimize the exploitation of distributed computing power and the authomatic access to distributed data storage.In the framework of the EU-DataGrid project,the ALICE experiment is one of the selected test applications for the early development and implementation of GRID Services.Presently,about 15 ALICE sites are makin use of available GRID tools and a large scale test production involving 9 of them was carried out with our simulation program.Results are discussed in detail,as well as future plans.
Challenges facing production grids
Pordes, Ruth; /Fermilab
2007-06-01
Today's global communities of users expect quality of service from distributed Grid systems equivalent to that their local data centers. This must be coupled to ubiquitous access to the ensemble of processing and storage resources across multiple Grid infrastructures. We are still facing significant challenges in meeting these expectations, especially in the underlying security, a sustainable and successful economic model, and smoothing the boundaries between administrative and technical domains. Using the Open Science Grid as an example, I examine the status and challenges of Grids operating in production today.
Fogh, Rune; Johansen, Asger
2013-01-01
In this paper we propose The Play Grid, a model for systemizing different play types. The approach is psychological by nature and the actual Play Grid is based, therefore, on two pairs of fundamental and widely acknowledged distinguishing characteristics of the ego, namely: extraversion vs...... at the Play Grid. Thus, the model has four quadrants, each of them describing one of four play types: the Assembler, the Director, the Explorer, and the Improviser. It is our hope that the Play Grid can be a useful design tool for making entertainment products for children....
Monotone Iterative Technique for Duffie-Epstein Type Backward Stochastic Differential Equations
SUN Xiao-jun; WU Yue
2005-01-01
For Duffle-Epstein type Backward Stochastic Differential Equations, the comparison theorem is proved. Based on the comparison theorem, by monotone iterative technique, the existence of the minimal and maximal solutions of the equations are proved.
Monotonicity in the Sample Size of the Length of Classical Confidence Intervals
Kagan, Abram M
2012-01-01
It is proved that the average length of standard confidence intervals for parameters of gamma and normal distributions monotonically decrease with the sample size. The proofs are based on fine properties of the classical gamma function.
Criteria for Response Monotonicity Preserving in Approximation of Fractional Order Systems
Mohammad Saleh Tavazoei
2016-01-01
In approximation of fractional order systems,a significant objective is to preserve the important properties of the original system.The monotonicity of time/frequency responses is one of these properties whose preservation is of great importance in approximation process.Considering this importance,the issues of monotonicity preservation of the step response and monotonicity preservation of the magnitude-frequency response are independently investigated in this paper.In these investigations,some conditions on approximating filters of fractional operators are found to guarantee the preservation of step/magnitude-frequency response monotonicity in approximation process.These conditions are also simplified in some special cases.In addition,numerical simulation results are presented to show the usefulness of the obtained conditions.
Monotone methods for solving a boundary value problem of second order discrete system
Wang Yuan-Ming
1999-01-01
Full Text Available A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.
On the rate of convergence of the maximum likelihood estimator of a k-monotone density
WELLNER; Jon; A
2009-01-01
Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0,A] are obtained under both the Hellinger distance and the Lp(Q) distance,where 1 p < ∞ and Q is a probability measure on [0,A].The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.
On the rate of convergence of the maximum likelihood estimator of a K-monotone density
GAO FuChang; WELLNER Jon A
2009-01-01
Bounds for the bracketing entropy of the classes of bounded K-monotone functions on [0, A] are obtained under both the Hellinger distance and the LP(Q) distance, where 1 ≤ p < ∞ and Q is a probability measure on [0, A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a K-monotone density.
Cuong LE VAN; Morhaim, Lisa; Vailakis, Yiannis
2008-01-01
We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel’skii (1964) and Krasnosel’skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.
MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES
王良龙; 王志成
2004-01-01
This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.
Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces
Kalabušić S
2009-01-01
Full Text Available We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation , where satisfies mixed-monotone conditions with respect to the given ordering.
Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces
Dž. Burgić
2009-01-01
Full Text Available We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation zn+1=F(zn,zn−1, n=2,3,…, where F satisfies mixed-monotone conditions with respect to the given ordering.
Totally Optimal Decision Trees for Monotone Boolean Functions with at Most Five Variables
Chikalov, Igor
2013-01-01
In this paper, we present the empirical results for relationships between time (depth) and space (number of nodes) complexity of decision trees computing monotone Boolean functions, with at most five variables. We use Dagger (a tool for optimization of decision trees and decision rules) to conduct experiments. We show that, for each monotone Boolean function with at most five variables, there exists a totally optimal decision tree which is optimal with respect to both depth and number of nodes.
Heinz Werner Höppel
2012-02-01
Full Text Available The monotonic and cyclic deformation behavior of ultrafine-grained metastable austenitic steel AISI 304L, produced by severe plastic deformation, was investigated. Under monotonic loading, the martensitic phase transformation in the ultrafine-grained state is strongly favored. Under cyclic loading, the martensitic transformation behavior is similar to the coarse-grained condition, but the cyclic stress response is three times larger for the ultrafine-grained condition.
Trends in life science grid: from computing grid to knowledge grid
Konagaya Akihiko
2006-01-01
Abstract Background Grid computing has great potential to become a standard cyberinfrastructure for life sciences which often require high-performance computing and large data handling which exceeds the computing capacity of a single institution. Results This survey reviews the latest grid technologies from the viewpoints of computing grid, data grid and knowledge grid. Computing grid technologies have been matured enough to solve high-throughput real-world life scientific problems. Data grid...
A Lagrangian fluctuation-dissipation relation for scalar turbulence
Drivas, Theodore D
2016-01-01
An exact relation is derived between the dissipation of scalar fluctuations and the variance of the scalar inputs (due to initial scalar values, scalar sources, and boundary fluxes) as those are sampled by stochastic Lagrangian trajectories. Previous work on the Kraichnan (1968) model of turbulent scalar advection has shown that anomalous scalar dissipation, non-vanishing in the limit of vanishing viscosity and diffusivity, is in that model due to Lagrangian spontaneous stochasticity, or non-determinism of the Lagrangian particle trajectories in the limit. We here extend this result to scalars advected by any incompressible velocity field. For fluid flows in domains without walls (e.g. periodic boxes) and for insulating/impermeable walls with zero scalar fluxes, we prove that anomalous scalar dissipation and spontaneous stochasticity are completely equivalent. For flows with imposed scalar values or non-vanishing scalar fluxes at the walls, spontaneous stochasticity still implies anomalous scalar dissipation ...
A new approach to Lagrangian investigations of isotropic turbulence
Barjona, Manuel; B. da Silva, Carlos; Idmec Team
2016-11-01
A new numerical approach is used in conjunction with direct numerical simulations (DNS) of statistically stationary (forced) isotropic turbulence to investigate the high Reynolds number scaling properties of turbulence characteristics in a Lagrangian frame. The new method provides an alternative route to the determination of the classical Lagrangian turbulence quantities, such as the second order Lagrangian velocity structure function and two point particle separation, at a much higher Reynolds number than as obtained in previous numerical simulations, and displays excellent agreement with the classical theoretical predictions and existing numerical simulations and experimental data. The authors acknowledge the Laboratory for Advanced Computing at University of Coimbra for providing HPC, computing, consulting resources that have contributed to the research results reported within this paper. URL http://www.lca.uc.pt.
Tracing the Cosmic Web substructure with Lagrangian submanifold
Shandarin, Sergei F
2014-01-01
A new computational paradigm for the analysis of substructure of the Cosmic Web in cosmological cold dark matter simulations is proposed. We introduce a new data-field --- the flip-flop field ---which carries wealth of information about the history and dynamics of the structure formation in the universe. The flip-flop field is an ordered data set in Lagrangian space representing the number of turns inside out sign reversals of an elementary volume of each collisionless fluid element represented by a computational particle in a N-body simulation. This field is computed using the Lagrangian submanifold, i.e. the three-dimensional dark matter sheet in the six-dimensional space formed by three Lagrangian and three Eulerian coordinates of the simulation particles. It is demonstrated that the very rich substructure of dark matter haloes and the void regions can be reliably and unambiguously recovered from the flip-flop field.
Does a Functional Integral Really Need a Lagrangian?
D. Kochan
2010-01-01
Full Text Available Path integral formulation of quantum mechanics (and also other equivalent formulations depends on a Lagrangian and/or Hamiltonian function that is chosen to describe the underlying classical system. The arbitrariness presented in this choice leads to a phenomenon called Quantization ambiguity. For example both L1 = ˙q2 and L2 = eq˙ are suitable Lagrangians on a classical level (δL1 = δL2, but quantum mechanically they are diverse. This paper presents a simple rearrangement of the path integral to a surface functional integral. It is shown that the surface functional integral formulation gives transition probability amplitude which is free of any Lagrangian/Hamiltonian and requires just the underlying classical equations of motion. A simple example examining the functionality of the proposed method is considered.
Collaborative production planning between supply chain partners by Lagrangian relaxation
无
2007-01-01
A collaborative planning framework based on the Lagrangian Relaxation was developed to coordinate and optimize the production planning of independent partners in multiple tier supply chains. Linking constraints and dependent demand constraints were added to the monolithic Multi-Level, multi-item Capacitated Lot Sizing Problem (MLCLSP). MLCLSP was Lagrangian relaxed and decomposed into facility-separable subproblems.Surrogate gradient algorithm was used to update Lagrangian multipliers, which coordinate decentralized decisions of the facilities. Production planning of independent partners could be appropriately coordinated and optimized by this framework without intruding their decision authorities and private information. Experimental results show that the proposed coordination mechanism and procedure come close to optimal results as obtained by central coordination.
Local Lagrangian Formalism and Discretization of the Heisenberg Magnet Model
Karpeev, D
2004-01-01
In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global Lagrangian density, a local variational formulation allows one to derive local conservation laws using a version of N\\"other's theorem from the formal variational calculus of Gelfand-Dikii. Using the local Lagrangian form we extend the method of Marsden, Patrick and Schkoller to derive local multisymplectic discretizations directly from the variational principle. We employ a version of the finite element method to discretize the space of sections of the trivial magnetic spin bundle $N = M\\times S^2$ over an appropriate space-time $M$. Since sections do not form a vector space, the usual FEM bases can be used only locally with coordinate transformations intervening on element boundaries, and conservation properties are guaranteed only within an element. We discuss possible w...
Minimal Local Lagrangians for Higher-Spin Geometry
Francia, D
2005-01-01
The Fronsdal Lagrangians for free totally symmetric rank-s tensors rest on suitable trace constraints for their gauge parameters and gauge fields. Only when these constraints are removed, however, the resulting equations reflect the expected free higher-spin geometry. We show that geometric equations, in both their local and non-local forms, can be simply recovered from local Lagrangians with only two additional fields, a rank-(s-3) compensator and a rank-(s-4) Lagrange multiplier. In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n-2) compensator and a rank-(n-3) Lagrange multiplier.
Health inequality and non-monotonicity of the health related social welfare function.
Dutta, Indranil
2007-03-01
In a recent paper in this journal Abasolo and Tsuchiya [Abasolo, I., Tsuchiya, A., 2004. Exploring social welfare functions and violation of monotonicity: an example from inequalities in health. Journal of Health Economics 23, 313-329] have strongly argued for the use of a non-monotonic health related social welfare function. This note discusses both the limitations of the measure proposed by Abasolo and Tsuchiya [Abasolo, I., Tsuchiya, A., 2004. Exploring social welfare functions and violation of monotonicity: an example from inequalities in health. Journal of Health Economics 23, 313-329] and the problems associated with their empirics. We are able to show how non-monotonicity may lead to paradoxical results and policies. Further we examine the empirics of Abasolo and Tsuchiya [Abasolo, I., Tsuchiya, A., 2004. Exploring social welfare functions and violation of monotonicity: an example from inequalities in health. Journal of Health Economics 23, 313-329] and provide an alternative explanation to the observed patterns in the data that do not violate monotonicity. Finally we briefly mention why the Atkinson-Sen framework may be more appropriate as a way forward.
Ramos, Juan David Hincapie; Tabard, Aurélien; Bardram, Jakob
2010-01-01
We introduce GridOrbit, a public awareness display that visualizes the activity of a community grid used in a biology laboratory. This community grid executes bioin-formatics algorithms and relies on users to donate CPU cycles to the grid. The goal of GridOrbit is to create a shared awareness about...
Lagrangian statistics and flow topology in forced 2-D turbulence
Kadoch, B. [Universite d' Aix-Marseille; Del-Castillo-Negrete, Diego B [ORNL; Bos, W.J.T. [CNRS, Ecole Centrale de Lyon, Universite Claude Bernard Lyon; Schneider, Kai [Universite d' Aix-Marseille
2011-01-01
A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order - 2.
Baranov, Alexander
2016-01-01
The LHCb Grid access if based on the LHCbDirac system. It provides access to data and computational resources to researchers with different geographical locations. The Grid has a hierarchical topology with multiple sites distributed over the world. The sites differ from each other by their number of CPUs, amount of disk storage and connection bandwidth. These parameters are essential for the Grid work. Moreover, job scheduling and data distribution strategy have a great impact on the grid performance. However, it is hard to choose an appropriate algorithm and strategies as they need a lot of time to be tested on the real grid. In this study, we describe the LHCb Grid simulator. The simulator reproduces the LHCb Grid structure with its sites and their number of CPUs, amount of disk storage and bandwidth connection. We demonstrate how well the simulator reproduces the grid work, show its advantages and limitations. We show how well the simulator reproduces job scheduling and network anomalies, consider methods ...
Humphrey, Marty; Thompson, Mary R.; Jackson, Keith R.
2005-08-14
Securing a Grid environment presents a distinctive set of challenges. This paper groups the activities that need to be secured into four categories: naming and authentication; secure communication; trust, policy, and authorization; and enforcement of access control. It examines the current state of the art in securing these processes and introduces new technologies that promise to meet the security requirements of Grids more completely.
Silvano de Gennaro
2003-01-01
DataGrid is a project funded by the European Union that aims to enable access to geographically distributed computing power and storage facilities belonging to different institutions. This will provide scientists with an unprecedented computing and data management tool. DataGrid is led by CERN, together with 20 other scientific and industrial partners.
New Lagrangian diagnostics for characterizing fluid flow mixing
Mundel, Ruty; Gildor, Hezi; Rom-Kedar, Vered
2014-01-01
A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two- (and potentially three-) dimensional unsteady flows in both bounded and open domains. Its computation is much easier than all other Lagrangian diagnostics known to us and provides new insights regarding the mixing properties on both short and long time scales and on both spatial plots and distribution diagrams. We demonstrate its applicability to two dimensional flows using two toy models and a data set of surface currents from the Mediterranean Sea.
Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations
Deriglazov, Alexei A
2015-01-01
We obtain Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body with given values of spin and momentum starting from Lagrangian action without auxiliary variables. MPTD-equations correspond to minimal interaction of our spinning particle with gravity. We shortly discuss some novel properties deduced from the Lagrangian form of MPTD-equations: emergence of an effective metric instead of the original one, non-commutativity of coordinates of representative point of the body, spin corrections to Newton potential due to the effective metric as well as spin corrections to the expression for integrals of motion of a given isometry.
Using Upper Tolerances in Lagrangian Relaxation for the DCMSTP
Turkensteen, Marcel
-constraints, the Minimum Spanning Tree Problem (MSTP), is polynomially solvable. We solve the DCMSTP using Lagrangian relaxation. This is the approach in which constraint violations are penalized in the objective function. In an iterative process, the penalty values of violated constraints are increased...... used to approximate the optimal solution value. We present a Lagrangian approach that, as in Volgenant (1989), penalizes violations of the degree-constraints of each vertex. The penalty of a vertex is added to the costs of all edges adjacent to the vertex. Our approach uses upper tolerances...
An extended Lagrangian support vector machine for classifications
YANG Xiaowei; SHU Lei; HAO Zhifeng; LIANG Yanchun; LIU Guirong; HAN Xu
2004-01-01
Lagrangian support vector machine (LSVM) cannot solve large problems for nonlinear kernel classifiers. In order to extend the LSVM to solve very large problems, an extended Lagrangian support vector machine (ELSVM) for classifications based on LSVM and SVMlight is presented in this paper. Our idea for the ELSVM is to divide a large quadratic programming problem into a series of subproblems with small size and to solve them via LSVM. Since the LSVM can solve small and medium problems for nonlinear kernel classifiers, the proposed ELSVM can be used to handle large problems very efficiently. Numerical experiments on different types of problems are performed to demonstrate the high efficiency of the ELSVM.
The anomalous chiral Lagrangian of order $p^6$
Bijnens, J; Talavera, P
2002-01-01
We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$. The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavors, 23 terms for three and five for two flavors. In the two flavor case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well.
Experimental investigation of Lagrangian structure functions in turbulence
Berg, Jacob; Ott, Søren; Mann, Jakob
2009-01-01
Lagrangian properties obtained from a particle tracking velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian structure functions and to measure intermittency at small...... temporal scales. The finiteness of the measurement volume can bias the results significantly. We present a robust way to overcome this obstacle. Despite no fully developed inertial range, we observe strong intermittency at the scale of dissipation. The multifractal model is only partially able to reproduce...
Lagrangian Approach to Dispersionless KdV Hierarchy
Amitava Choudhuri
2007-09-01
Full Text Available We derive a Lagrangian based approach to study the compatible Hamiltonian structure of the dispersionless KdV and supersymmetric KdV hierarchies and claim that our treatment of the problem serves as a very useful supplement of the so-called r-matrix method. We suggest specific ways to construct results for conserved densities and Hamiltonian operators. The Lagrangian formulation, via Noether's theorem, provides a method to make the relation between symmetries and conserved quantities more precise. We have exploited this fact to study the variational symmetries of the dispersionless KdV equation.
Large N duality, lagrangian cycles, and algebraic knots
Diaconescu, D -E; Vafa, C
2011-01-01
We consider knot invariants in the context of large $N$ transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicity constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.
Large N Duality, Lagrangian Cycles, and Algebraic Knots
Diaconescu, D.-E.; Shende, V.; Vafa, C.
2013-05-01
We consider knot invariants in the context of large N transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicitly constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.
Unifying Ghost-Free Lorentz-Invariant Lagrangians
Li, Wenliang
2015-01-01
We present the details of the novel framework for Lagrangian field theories that are Lorentz-invariant and lead to at most second order equations of motion. The use of antisymmetric structure is of crucial importance. The general ghost-free Lagrangians are constructed and then translated into the language of differential forms. The ghost-freeness has a geometric nature. A novel duality is proposed which generalizes the Hodge duality in Maxwell's theory. We discuss how the well-established theories are reformulated and propose many new theories.
Particles within extended-spin space: Lagrangian connection
Besprosvany, J
2015-01-01
A spin-space extension is reviewed, which provides information on the standard model. Its defining feature is a common matrix space that describes symmetries and representations, and leads to limits on these, for given dimension. The model provides additional information on the standard model, whose interpretation requires an interactive formulation. Within this program, we compare the model's lepton-W generated interactive Lagrangian in (5+1)-dimensions, and that of the standard model. We derive the conditions for this matching, which apply to other Lagrangian terms. We also discuss the advantages of this extension, as compared to others.
Upper Tolerances and Lagrangian Relaxation for the DCMSTP
Turkensteen, Marcel
The Degree-Constrained Minimum Spanning Tree Problem (DCMSTP) is the problem of connecting a set of vertices against minimum cost, where no more than a prespecified number of edges may enter or leave each vertex. The DCMSTP is an NP-hard problem with many practical applications in the design...... of networks. Many efficient solution methods for the DCMSTP rely on Lagrangian relaxation for the tight lower bounds needed to solve instances. Lagrangian procedures for the DCMSTP solve a modified version of the regular Minimum Spanning Tree Problem (MSTP) in which the degree constraint violations...
Lagrangian Fuzzy Dynamics of Physical and Non-Physical Systems
Sandler, Uziel
2014-01-01
In this paper, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the \\emph{Fuzzy Dynamics} of a $n$-dimensional system is equivalent to Lagrangian (or Hamiltonian) mechanics in a $n+1$-dimensional space. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's eq...
Moore, Reagan W.; Studham, Ronald S.; Rajasekar, Arcot; Watson, Chip; Stockinger, Heinz; Kunszt, Peter; Charlie Catlett and Ian Foster
2002-02-27
Data grids link distributed, heterogeneous storage resources into a coherent data management system. From a user perspective, the data grid provides a uniform name space across the underlying storage systems, while supporting retrieval and storage of files. In the high energy physics community, at least six data grids have been implemented for the storage and distribution of experimental data. Data grids are also being used to support projects as diverse as digital libraries (National Library of Medicine Visible Embryo project), federation of multiple astronomy sky surveys (NSF National Virtual Observatory project), and integration of distributed data sets (Long Term Ecological Reserve). Data grids also form the core interoperability mechanisms for creating persistent archives, in which data collections are migrated to new technologies over time. The ability to provide a uniform name space across multiple administration domains is becoming a critical component of national-scale, collaborative projects.
Liseikin, Vladimir D
2017-01-01
This new edition provides a description of current developments relating to grid methods, grid codes, and their applications to actual problems. Grid generation methods are indispensable for the numerical solution of differential equations. Adaptive grid-mapping techniques, in particular, are the main focus and represent a promising tool to deal with systems with singularities. This 3rd edition includes three new chapters on numerical implementations (10), control of grid properties (11), and applications to mechanical, fluid, and plasma related problems (13). Also the other chapters have been updated including new topics, such as curvatures of discrete surfaces (3). Concise descriptions of hybrid mesh generation, drag and sweeping methods, parallel algorithms for mesh generation have been included too. This new edition addresses a broad range of readers: students, researchers, and practitioners in applied mathematics, mechanics, engineering, physics and other areas of applications.
Sommer, Simon; Ma, Zheng; Jørgensen, Bo Nørregaard
2015-01-01
China is planning to transform its traditional power grid in favour of a smart grid, since it allows a more economically efficient and a more environmentally friendly transmission and distribution of electricity. Thus, a nationwide smart grid is likely to save tremendous amounts of resources...... and costs. This paper elaborates on the key stakeholders, crucial polices and general challenges in the context of the Chinese smart grid development. The paper finds that the Chinese energy market is a state monopoly and foreign companies can only become key stakeholders in the role of suppliers or service...... providers. It can be concluded that the Chinese smart grid development has still to overcome technological and political issues, such as overlapping authority structures, not installed or immature key technologies, the absence of standards and governmental market protectionism....
BSCW Unstructured Grids - VGRID software
National Aeronautics and Space Administration — These grids were constructed using VGRID software from NASA Langley. The grids designed for node based (labeled 'nc') and cell-centered solvers are supplied. Grids...
HIRENASD Unstructured Grids - VGRID software
National Aeronautics and Space Administration — These grids were constructed using VGRID software from NASA Langley. The grids designed for node based (labeled 'nc') and cell-centered solvers are supplied. Grids...
Zhou, Chunlüe; Wang, Kaicun
2016-05-01
Most studies on global warming rely on global mean surface temperature, whose change is jointly determined by anthropogenic greenhouse gases (GHGs) and natural variability. This introduces a heated debate on whether there is a recent warming hiatus and what caused the hiatus. Here, we presented a novel method and applied it to a 5° × 5° grid of Northern Hemisphere land for the period 1900 to 2013. Our results show that the coldest 5% of minimum temperature anomalies (the coldest deviation) have increased monotonically by 0.22 °C/decade, which reflects well the elevated anthropogenic GHG effect. The warmest 5% of maximum temperature anomalies (the warmest deviation), however, display a significant oscillation following the Atlantic Multidecadal Oscillation (AMO), with a warming rate of 0.07 °C/decade from 1900 to 2013. The warmest (0.34 °C/decade) and coldest deviations (0.25 °C/decade) increased at much higher rates over the most recent decade than last century mean values, indicating the hiatus should not be interpreted as a general slowing of climate change. The significant oscillation of the warmest deviation provides an extension of previous study reporting no pause in the hottest temperature extremes since 1979, and first uncovers its increase from 1900 to 1939 and decrease from 1940 to 1969.
Mixing model with multi-particle interactions for Lagrangian simulations of turbulent mixing
Watanabe, T.; Nagata, K.
2016-08-01
We report on the numerical study of the mixing volume model (MVM) for molecular diffusion in Lagrangian simulations of turbulent mixing problems. The MVM is based on the multi-particle interaction in a finite volume (mixing volume). A priori test of the MVM, based on the direct numerical simulations of planar jets, is conducted in the turbulent region and the interfacial layer between the turbulent and non-turbulent fluids. The results show that the MVM predicts well the mean effects of the molecular diffusion under various numerical and flow parameters. The number of the mixing particles should be large for predicting a value of the molecular diffusion term positively correlated to the exact value. The size of the mixing volume relative to the Kolmogorov scale η is important in the performance of the MVM. The scalar transfer across the turbulent/non-turbulent interface is well captured by the MVM especially with the small mixing volume. Furthermore, the MVM with multiple mixing particles is tested in the hybrid implicit large-eddy-simulation/Lagrangian-particle-simulation (LES-LPS) of the planar jet with the characteristic length of the mixing volume of O(100η). Despite the large mixing volume, the MVM works well and decays the scalar variance in a rate close to the reference LES. The statistics in the LPS are very robust to the number of the particles used in the simulations and the computational grid size of the LES. Both in the turbulent core region and the intermittent region, the LPS predicts a scalar field well correlated to the LES.
Schäfer, Benjamin; Matthiae, Moritz; Timme, Marc; Witthaut, Dirk
2015-01-01
Stable operation of complex flow and transportation networks requires balanced supply and demand. For the operation of electric power grids—due to their increasing fraction of renewable energy sources—a pressing challenge is to fit the fluctuations in decentralized supply to the distributed and temporally varying demands. To achieve this goal, common smart grid concepts suggest to collect consumer demand data, centrally evaluate them given current supply and send price information back to customers for them to decide about usage. Besides restrictions regarding cyber security, privacy protection and large required investments, it remains unclear how such central smart grid options guarantee overall stability. Here we propose a Decentral Smart Grid Control, where the price is directly linked to the local grid frequency at each customer. The grid frequency provides all necessary information about the current power balance such that it is sufficient to match supply and demand without the need for a centralized IT infrastructure. We analyze the performance and the dynamical stability of the power grid with such a control system. Our results suggest that the proposed Decentral Smart Grid Control is feasible independent of effective measurement delays, if frequencies are averaged over sufficiently large time intervals.
Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems
CHEN Jing; BAI Yuzhen
2006-01-01
Ma(n)é conjectured that every minimal measure in the generic Lagrangian systems is by analyzing the structure of the supports of minimal probability measures for some kinds of the Lagrangian systems.
Low energy effective Lagrangians in open superstring theory
Medina, Ricardo [Universidade Federal de Itajuba, MG (Brazil). Inst. de Ciencias Exatas
2008-07-01
The low energy effective Lagrangian describes the interactions of the massless modes of String Theory. Present work is being done to obtain all alpha'{sup 3} terms (bosonic and fermionic) by means of the known 5-point amplitudes and SUSY.
Towards Selective Tidal-Stream Transport for Lagrangian profilers
Jouffroy, Jerome; Zhou, Qiuyang; Zielinski, Oliver
2011-01-01
Autonomous Lagrangian profilers are widely used as measurement and monitoring platforms. In their current mode of operation, the profilers usually drift passively at their parking depth before making a vertical profile to go back to the surface. This paper presents a control strategy to actively...
Structure of Lanczos-Lovelock Lagrangians in critical dimensions
Yale, Alexandre; Padmanabhan, T.
2011-06-01
The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D-dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general covariance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension D = 2 m and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in D = 2 m. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, {R √{-g} = partial_j R^j} for a doublet of functions R j = ( R 0, R 1) which depends only on the metric and its first derivatives. We explicitly construct families of such R j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in D = 4. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.
Lagrangianity for log extendable overconvergent $F$-isocrystals
Caro, Daniel
2015-01-01
In the framework of Berthelot's theory of arithmetic $\\mathcal{D}$-modules, we prove that Berthelot's characteristic variety associated with a holonomic $\\mathcal{D}$-modules endowed with a Frobenius structure has pure dimension. As an application, we get the lagrangianity of the characteristic variety of a log extendable overconvergent $F$-isocrystal.
Extended Lagrangian formalism for rheonomic systems with variable mass
Mušicki Đorđe
2017-01-01
Full Text Available In this paper the extended Lagrangian formalism for the rheonomic systems (Dj. Mušicki, 2004, which began with the modification of the mechanics of such systems (V. Vujičić, 1987, is extended to the systems with variable mass, with emphasis on the corresponding energy relations. This extended Lagrangian formalism is based on the extension of the set of chosen generalized coordinates by new quantities, suggested by the form of nonstationary constraints, which determine the position of the frame of reference in respect to which these generalized coordinates refer. As a consequence, an extended system of the Lagrangian equations is formulated, accommodated to the variability of the masses of particles, where the additional ones correspond to the additional generalized coordinates. By means of these equations, the energy relations of such systems have been studied, where it is demonstrated that here there are four types of energy conservation laws. The obtained energy laws are more complete and natural than the corresponding ones in the usual Lagrangian formulation for such systems. It is demonstrated that the obtained energy laws, are in full accordance with the energy laws in the corresponding vector formulation, if they are expressed in terms of the quantities introduced in this formulation of mechanics. The obtained results are illustrated by an example: the motion of a rocket, which ejects the gasses backwards, while this rocket moves up a straight line on an oblique plane, which glides uniformly in a horizontal direction.
Kepler Problem in Lagrangian Formulation Discussed from Topological Viewpoint
XU Gong-Ou; XU Ming-Jie
2005-01-01
@@ The Kepler problem in Lagrangian formulation is discussed from the topological viewpoint. Essential points are analysed. Along the same line of thoughts, it is possible to study the Kepler problem in Hamiltonian formulation as well as in quantum mechanics from the topological viewpoint for showing quantum-classical correspondence.
Effective weak Lagrangians in the Standard Model and B decays
Grozin, Andrey
2013-01-01
Weak processes (e.g., B decays) with characteristic energies <
Some Three-body force cancellations in Chiral Lagrangians
Arriola, E Ruiz
2016-01-01
The cancellation between off-shell two body forces and three body forces implies a tremendous simplification in the study of three body resonances in two meson-one baryon systems. While this can be done by means of Faddeev equations we provide an alternative and simpler derivation using just the chiral Lagrangian and the field re-parametrization invariance.
The 3D Lagrangian Integral Method. Henrik Koblitz Rasmussen
Rasmussen, Henrik Koblitz
2003-01-01
. This are processes such as thermo-forming, gas-assisted injection moulding and all kind of simultaneous multi-component polymer processing operations. Though, in all polymer processing operations free surfaces (or interfaces) are present and the dynamic of these surfaces are of interest. In the "3D Lagrangian...
Physical unitarity in the lagrangian Sp(2)-symmetric formalism
Lavrov, P M
1996-01-01
The structure of state vector space for a general (non-anomalous) gauge theory is studied within the Lagrangian version of the Sp(2)-symmetric quantization method. The physical {\\it S}-matrix unitarity conditions are formulated. The general results are illustrated on the basis of simple gauge theory models.
A remapped particle-mesh semi-Lagrangian advection scheme
Cotter, C.J.; Frank, J.E.; Reich, S.
2007-01-01
We describe the remapped particle-mesh advection method, a new mass-conserving method for solving the density equation which is suitable for combining with semi-Lagrangian methods for compressible flow applied to numerical weather prediction. In addition to the conservation property, the remapped pa
Bohr--Sommerfeld Lagrangians of moduli spaces of Higgs bundles
Biswas, Indranil; Gammelgaard, Niels Leth; Logares, Marina
Let $X$ be a compact connected Riemann surface of genus at least two. Let $M_H(r,d)$ denote the moduli space of semistable Higgs bundles on $X$ of rank $r$ and degree $d$. We prove that the compact complex Bohr-Sommerfeld Lagrangians of $M_H(r,d)$ are precisely the irreducible components of the n...
Classical dynamical variables for the Wess-Zumino matter Lagrangian
Domenech, G.; Levinas, M.; Umerez, N.
1989-05-01
We study the macroscopic behaviour of the Wess-Zumino matter multiplet. The Lagrangian and the energy-momentum tensor are obtained in terms of densities and velocities of an interacting fluid in N=1 supergravity background. Equations of motion and conditions for consistency are found.
Baryon magnetic moments in the effective quark Lagrangian approach
Simonov, YA; Tjon, JA; Weda, J; Simonov, Yu A.
2002-01-01
An effective quark Lagrangian is derived from first principles through bilocal gluon field correlators. It is used to write down equations for baryons, containing both perturbative and nonperturbative fields. As a result one obtains magnetic moments of octet and decuplet baryons without the introduc
Using Lagrangian Coherent Structures to understand coastal water quality
Fiorentino, L. A.; Olascoaga, M. J.; Reniers, A.; Feng, Z.; Beron-Vera, F. J.; MacMahan, J. H.
2012-09-01
The accumulation of pollutants near the shoreline can result in low quality coastal water with negative effects on human health. To understand the role of mixing by tidal flows in coastal water quality we study the nearshore Lagrangian circulation. Specifically, we reveal Lagrangian Coherent Structures (LCSs), i.e., distinguished material curves which shape global mixing patterns and thus act as skeletons of the Lagrangian circulation. This is done using the recently developed geodesic theory of transport barriers. Particular focus is placed on Hobie Beach, a recreational subtropical marine beach located in Virginia Key, Miami, Florida. According to studies of water quality, Hobie Beach is characterized by high microbial levels. Possible sources of pollution in Hobie Beach include human bather shedding, dog fecal matter, runoff, and sand efflux at high tides. Consistent with the patterns formed by satellite-tracked drifter trajectories, the LCSs extracted from simulated currents reveal a Lagrangian circulation favoring the retention near the shoreline of pollutants released along the shoreline, which can help explain the low quality water registered at Hobie Beach.
Matter composition at high density by effective scaled lagrangian
Hyun, Chang Ho; Min, Dong Pil [Dept. of Physics, Seoul National Univ., Seoul (Korea, Republic of)
1998-06-01
We investigate the matter composition at around the neutron star densities with a model lagrangian satisfying Brown-Rho scaling law. We calculate the neutron star properties such as maximum mass, radius, hyperon compositions and central density. We compare our results with those of Walecka model. (orig.)
Lagrangian Fuzzy Dynamics of Physical and Non-Physical Systems
Sandler, Uziel
2014-01-01
In this paper, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the \\emph{Fuzzy Dynamics} of a $n$-dimensional system is equivalent to Lagrangian (or Hamiltonian) mechanics in a $n+1$-dimensional space. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's equations gain a non-zero right side proportional to the derivative of the Lagrangian with respect to the action. Examples of such systems are unstable systems, systems with dissipation and systems which can remember their history. Moreover, in certain situations, the Lagrangian could be a set-valued function. The corresponding equations of motion then become differential inclusions instead of differential equations. We will also show that the principal of least action is a consequence of the causality principle and the loc...
Haarla, Liisa; Hirvonen, Ritva; Labeau, Pierre-Etienne
2011-01-01
In response to the growing importance of power system security and reliability, ""Transmission Grid Security"" proposes a systematic and probabilistic approach for transmission grid security analysis. The analysis presented uses probabilistic safety assessment (PSA) and takes into account the power system dynamics after severe faults. In the method shown in this book the power system states (stable, not stable, system breakdown, etc.) are connected with the substation reliability model. In this way it is possible to: estimate the system-wide consequences of grid faults; identify a chain of eve
Tres, Diego
2013-01-01
Get to grips with a new technology, understand what it is and what it can do for you, and then get to work with the most important features and tasks. Instant 960 Grid System uses step-by-step instructions, covering the basic understanding needed to create a quick, high quality responsive website prototype using the 960 Grid System.The book is intended for beginner web developers and information architects looking to create a quick responsive website prototype. Basic knowledge of web development and a little understanding of grids is encouraged.
Cerin, Christophe
2012-01-01
Desktop Grid Computing presents common techniques used in numerous models, algorithms, and tools developed during the last decade to implement desktop grid computing. These techniques enable the solution of many important sub-problems for middleware design, including scheduling, data management, security, load balancing, result certification, and fault tolerance. The book's first part covers the initial ideas and basic concepts of desktop grid computing. The second part explores challenging current and future problems. Each chapter presents the sub-problems, discusses theoretical and practical
2017-03-28
GridAPPS-D is an open-source, open architecture, standards based platform for development of advanced electric power system planning and operations applications. GridAPPS-D provides a documented data abstraction for the application developer enabling creation of applications that can be run in any compliant system or platform. This enables development of applications that are platform vendor independent applications and applications that take advantage of the possibility of data rich and data driven applications based on deployment of smart grid devices and systems.
Three dimensional Lagrangian structures in the Antarctic Polar Vortex.
Mancho, Ana M.; Garcia-Garrido, Victor J.; Curbelo, Jezabel; Niang, Coumba; Mechoso, Carlos R.; Wiggins, Stephen
2017-04-01
Dynamical systems theory has supported the description of transport processes in fluid dynamics. For understanding trajectory patterns in chaotic advection the geometrical approach by Poincaré seeks for spatial structures that separate regions corresponding to qualitatively different types of trajectories. These structures have been referred to as Lagrangian Coherent Structures (LCS), which typically in geophysical flows are well described under the approach of incompressible 2D flows. Different tools have been used to visualize LCS. In this presentation we use Lagrangian Descriptors [1,2,3,4] (function M) for visualizing 3D Lagrangian structures in the atmosphere, in particular in the Antarctic Polar Vortex. The function M is computed in a fully 3D incompressible flow obtained from data provided by the European Centre for Medium-Range Weather Forecast and it is represented in 2D surfaces. We discuss the findings during the final warming that took place in the spring of 1979 [5]. This research is supported by MINECO grant MTM2014-56392-R. Support is acknowledged also from CSIC grant COOPB20265, U.S. NSF grant AGS-1245069 and ONR grant No. N00014- 01-1-0769. C. Niang acknowledges Fundacion Mujeres por Africa and ICMAT Severo Ochoa project SEV-2011-0087 for financial support. [1] C. Mendoza, A. M. Mancho. The hidden geometry of ocean flows. Physical Review Letters 105 (2010), 3, 038501-1-038501-4. [2] A. M. Mancho, S. Wiggins, J. Curbelo, C. Mendoza. Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems. Communications in Nonlinear Science and Numerical Simulation. 18 (2013) 3530-3557. [3] C. Lopesino, F. Balibrea-Iniesta, S. Wiggins and A. M. Mancho. Lagrangian descriptors for two dimensional, area preserving autonomous and nonautonomous maps. Communications in Nonlinear Science and Numerical Simulations, 27 (2015) (1-3), 40-51. [4] C. Lopesino, F. Balibrea-Iniesta, V. J. García-Garrido, S. Wiggins, and A
Evaluation of the Eulerian-Lagrangian spray atomisation (ELSA) in spray simulations
Hoyas, S.; Pastor Enguídanos, José Manuel; KHUONG, ANH DUNG; MOMPÓ LABORDA, JUAN MANUEL; Ravet, Frederic
2011-01-01
Many approaches have been used to simulate the spray structure especially in modelling fuel sprays, i.e., Eulerian, Lagrangian, Lagrangian- Eulerian, Eulerian-Eulerian and Eulerian-Lagrangian approaches. The present study uses an Eulerian-Lagrangian spray atomisation (ELSA) method which is an integrated model for capturing the whole spray evolution starting directly from injector nozzle still the end. Our goal in this study is to evaluate the ELSA model which is implementing into the commerci...
An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems Techniques
2016-06-07
An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems Techniques Christopher K. R. T. Jones Department of... technology for assimilating Lagrangian data. This new Lagrangian data assimilation platform is expected to be particularly effective in ocean regions where...COVERED 00-00-2006 to 00-00-2006 4. TITLE AND SUBTITLE An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems
Scaling Effect of Area-Averaged NDVI: Monotonicity along the Spatial Resolution
Hiroki Yoshioka
2012-01-01
Full Text Available Changes in the spatial distributions of vegetation across the globe are routinely monitored by satellite remote sensing, in which the reflectance spectra over land surface areas are measured with spatial and temporal resolutions that depend on the satellite instrumentation. The use of multiple synchronized satellite sensors permits long-term monitoring with high spatial and temporal resolutions. However, differences in the spatial resolution of images collected by different sensors can introduce systematic biases, called scaling effects, into the biophysical retrievals. This study investigates the mechanism by which the scaling effects distort normalized difference vegetation index (NDVI. This study focused on the monotonicity of the area-averaged NDVI as a function of the spatial resolution. A monotonic relationship was proved analytically by using the resolution transform model proposed in this study in combination with a two-endmember linear mixture model. The monotonicity allowed the inherent uncertainties introduced by the scaling effects (error bounds to be explicitly determined by averaging the retrievals at the extrema of theresolutions. Error bounds could not be estimated, on the other hand, for non-monotonic relationships. Numerical simulations were conducted to demonstrate the monotonicity of the averaged NDVI along spatial resolution. This study provides a theoretical basis for the scaling effects and develops techniques for rectifying the scaling effects in biophysical retrievals to facilitate cross-sensor calibration for the long-term monitoring of vegetation dynamics.
High-Order Hamilton's Principle and the Hamilton's Principle of High-Order Lagrangian Function
ZHANG Ming-Jiang; ZHAO Hong-Xia; FANG Jian-Hui; MA Shan-Jun; LU Kai
2008-01-01
In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton's principle. Finally, the Hamilton's principle of high-order Lagrangian function is given.
National Aeronautics and Space Administration — New cell centered grids are generated to complement the node-centered ones uploaded. Six tarballs containing the coarse, medium, and fine mixed-element and pure tet....
Grid Computing Education Support
Steven Crumb
2008-01-15
The GGF Student Scholar program enabled GGF the opportunity to bring over sixty qualified graduate and under-graduate students with interests in grid technologies to its three annual events over the three-year program.