A Refinement of the Kolmogorov-Marcinkiewicz-Zygmund Strong Law of Large Numbers
Li, Deli; Rosalsky, Andrew
2010-01-01
For the partial sums formed from a sequence of i.i.d. random variables having a finite absolute p'th moment for some p in (0,2), we extend the recent and striking discovery of Hechner and Heinkel (Journal of Theoretical Probability (2010)) concerning "complete moment convergence" to the two cases 0
refinement of the celebrated Kolmogorov-Marcinkiewicz-Zygmund strong law of large numbers. Versions of the above results in a Banach space setting are also presented.
Jain, Kartik; Mardal, Kent-Andre
2015-01-01
Most Computational Fluid Dynamics (CFD) studies of hemodynamics in intracranial aneurysms are based on the assumption of laminar flow due to a relatively low (below 500) parent artery Reynolds number. A few studies have recently demonstrated the occurrence of transitional flow in aneurysms, but these studies employed special finite element schemes tailored to capture transitional nature of flow. In this study we investigate the occurrence of transition using a standard Lattice Boltzmann method (LBM). The LBM is used because of its computational efficiency, which in the present study allowed us to perform simulations at a higher resolution than has been done in the context of aneurysms before. The high space-time resolutions of 8{\\mu}m and 0.11 {\\mu}s resulted in nearly one billion cells and 9 million time steps per second and allowed us to quantify the turbulent kinetic energy at resolutions below the Kolmogorov scales. We perform an in-depth space and time refinement study on 2 aneurysms; one was previously ...
Woo-Young Jung
2015-04-01
Full Text Available For the solution of geometrically nonlinear analysis of plates and shells, the formulation of a nonlinear nine-node refined first-order shear deformable element-based Lagrangian shell element is presented. Natural co-ordinate-based higher order transverse shear strains are used in present shell element. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, a refined first-order shear deformation theory for thin and thick shells, which results in parabolic through-thickness distribution of the transverse shear strains from the formulation based on the third-order shear deformation theory, is proposed. This formulation eliminates the need for shear correction factors in the first-order theory. To avoid difficulties resulting from large increments of the rotations, a scheme of attached reference system is used for the expression of rotations of shell normal. Numerical examples demonstrate that the present element behaves reasonably satisfactorily either for the linear or for geometrically nonlinear analysis of thin and thick plates and shells with large displacement but small strain. Especially, the nonlinear results of slit annular plates with various loads provided the benchmark to test the accuracy of related numerical solutions.
Shang, Haibin; Wu, Xiaoyu; Cui, Pingyuan
2017-02-01
Ground observations have found that asynchronous systems constitute most of the population of the near-Earth binary asteroids. This paper concerns the trajectory of a particle in the asynchronous system which is systematically described using periodic ellipsoidal and spherical body models. Due to the non-autonomous characteristics of the asynchronous system, Lagrangian coherent structures (LCS) are employed to identify the various dynamical behaviors. To enhance the accuracy of LCS, a robust LCS finding algorithm is developed incorporating hierarchical grid refinement, one-dimensional search and variational theory verification. In this way, the intricate dynamical transport boundaries are detected efficiently. These boundaries indicate that a total of 15 types of trajectories exist near asynchronous binary asteroids. According to their Kepler energy variations, these trajectories can be grouped into four basic categories, i.e., transitory, escape, impact and flyby trajectories. Furthermore, the influence of the ellipsoid's spin period on the dynamical behavior is discussed in the context of the change of dynamical regions. We found that the transitory and impact motions occur easily in the synchronous-like binary systems, in which the rotation period of the ellipsoid is nearly equal to that of the mutual orbit. Meanwhile, the results confirm a positive correlation between the spinning rate of the ellipsoid and the probability of the escape and flyby trajectories. The LCS also reveal a marked increase in trajectory diversity after a larger initial energy is selected.
Evaluating Kolmogorov\\'s Distribution
George Marsaglia
2003-11-01
Full Text Available Kolmogorov's goodness-of-fit measure, Dn , for a sample CDF has consistently been set aside for methods such as the D+n or D-n of Smirnov, primarily, it seems, because of the difficulty of computing the distribution of Dn . As far as we know, no easy way to compute that distribution has ever been provided in the 70+ years since Kolmogorov's fundamental paper. We provide one here, a C procedure that provides Pr(Dn .999 with n's of several thousand, we provide a quick approximation that gives accuracy to the 7th digit for such cases.
Kolmogorov turbulence by matched asymptotic expansions
Lundgren, Thomas S.
2003-04-01
The Kolmogorov [Dokl. Akad. Nauk. SSSR 30, 299 (1941), hereafter K41] inertial range theory is derived from first principles by analysis of the Navier-Stokes equation using the method of matched asymptotic expansions without assuming isotropy or homogeneity and the Kolmogorov (K62) [J. Fluid Mech. 13, 82 (1962)] refined theory is analyzed. This paper is an extension of Lundgren [Phys. Fluids 14, 638 (2002)], in which the second- and third-order structure functions were determined from the isotropic Karman-Howarth [Proc. R. Soc. London, Ser. A 164, 192 (1938)] equation. The starting point for the present analysis is an equation for the difference in velocity between two points, one of which is a Lagrangian fluid point and the second, slaved to the first by a fixed separation r, is not Lagrangian. The velocity difference, so defined, satisfies the Navier-Stokes equation with spatial variable r. The analysis is carried out in two parts. In the first part the physical hypothesis is made that the mean dissipation is independent of viscosity as viscosity tends to zero, as assumed in K41. This means that the mean dissipation is finite as Reynolds number tends to infinity and leads to the K41 inertial range results. In the second part this dissipation assumption is relaxed in an attempt to duplicate the K62 theory. While the K62 structure is obtained, there are restrictions, resulting from the analysis which shows that there can be no inertial range intermittency as Reynolds number tends to infinity, and therefore the mean dissipation has to be finite as Reynolds number tends to infinity, as assumed in part one. Reynolds number-dependent corrections to the K41 results are obtained in the form of compensating functions of r/λ, which tend to zero slowly like Rλ-2/3 as Rλ→∞.
2006-01-01
The editorial board for the History of Mathematics series has selected for this volume a series of translations from two Russian publications, Kolmogorov in Remembrance and Mathematics and its Historical Development. This book, Kolmogorov in Perspective, includes articles written by Kolmogorov's students and colleagues and his personal accounts of shared experiences and lifelong mathematical friendships. The articles combine to give an excellent personal and scientific biography of this important mathematician. There is also an extensive bibliography with the complete list of Kolmogorov's works-including the articles written for encyclopedias and newspapers. The book is illustrated with photographs and includes quotations from Kolmogorov's letters and conversations, uniquely reflecting his mathematical tastes and opinions.
Berthiaume, A; Laplante, S; Berthiaume, Andre; Dam, Wim van; Laplante, Sophie
2000-01-01
In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the amount of innate randomness (or information) contained in the string. We define the quantum Kolmogorov complexity of a qubit string as the length of the shortest quantum input to a universal quantum Turing machine that produces the initial qubit string with high fidelity. The definition of Vitanyi (Proceedings of the 15th IEEE Annual Conference on Computational Complexity, 2000) measures the amount of classical information, whereas we consider the amount of quantum information in a qubit string. We argue that our definition is natural and is an accurate representation of the amount of quantum information contained in a quantum state.
Kolmogorov Complexity, Causality And Spin
Shayda, Dara O
2012-01-01
A novel topological and computational method for 'motion' is described. Motion is constrained by inequalities in terms of Kolmogorov Complexity. Causality is obtained as the output of a high-pass filter, passing through only high values of Kolmogorov Complexity. Motion under the electromagnetic field described with immediate relationship with Subscript[G, 2] Holonomy group and its corresponding dense free 2-subgroup. Similar to Causality, Spin emerges as an immediate and inevitable consequence of high values of Kolmogorov Complexity. Consequently, the physical laws are nothing but a low-pass filter for small values of Kolmogorov Complexity.
Kolmogorov complexity as a language
Shen, Alexander
2011-01-01
The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we provide (with minimal comments) many different examples where notions and statements that involve Kolmogorov complexity are compared with their counterparts not involving complexity.
Biferale, L.; Meneveau, C.; Verzicco, R.
2014-01-01
Small droplets in turbulent flows can undergo highly variable deformations and orientational dynamics. For neutrally buoyant droplets smaller than the Kolmogorov scale, the dominant effects from the surrounding turbulent flow arise through Lagrangian time histories of the velocity gradient tensor. H
Topological arguments for Kolmogorov complexity
Alexander Shen
2012-08-01
Full Text Available We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some nontrivial algorithmic properties.
Game interpretation of Kolmogorov complexity
Muchnik, Andrej A; Shen, Alexander; Vereshchagin, Nikolay
2010-01-01
The Kolmogorov complexity function K can be relativized using any oracle A, and most properties of K remain true for relativized versions. In section 1 we provide an explanation for this observation by giving a game-theoretic interpretation and showing that all "natural" properties are either true for all sufficiently powerful oracles or false for all sufficiently powerful oracles. This result is a simple consequence of Martin's determinacy theorem, but its proof is instructive: it shows how one can prove statements about Kolmogorov complexity by constructing a special game and a winning strategy in this game. This technique is illustrated by several examples (total conditional complexity, bijection complexity, randomness extraction, contrasting plain and prefix complexities).
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 ...
Fokker-Planck-Kolmogorov equations
Bogachev, Vladimir I; Röckner, Michael; Shaposhnikov, Stanislav V
2015-01-01
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
Self-preservation relation to the Kolmogorov similarity hypotheses
Djenidi, Lyazid; Antonia, Robert A.; Danaila, Luminita
2017-05-01
The relation between self-preservation (SP) and the Kolmogorov similarity hypotheses (Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR 30, 301 (1941) [Proc. R. Soc. London A 434, 9 (1991), 10.1098/rspa.1991.0075]) is investigated through the transport equations for the second- and third-order moments of the longitudinal velocity increments [ δ u (r ,t )=u (x ,t )-u (x +r ,t ) , where x ,t , and r are the spatial point and the time and longitudinal separation between two points, respectively]. It is shown that the fluid viscosity ν and the mean turbulent kinetic energy dissipation rate ɛ ¯ (the overbar represents an ensemble average) emerge naturally from the equations of motion as controlling parameters for the velocity increment moments when SP is assumed. Consequently, the Kolmogorov length scale η [≡(ν3/ɛ¯) 1 /4] and velocity scale vK [≡(νɛ ¯) 1 /4] also emerge as natural scaling parameters in conformity with SP, indicating that Kolmogorov's first hypothesis is subsumed under the more general hypothesis of SP. Further, the requirement for a very large Reynolds number is also relaxed, at least for the first similarity hypothesis. This requirement however is still necessary to derive the two-thirds law (or the four-fifths law) from the analysis. These analytical results are supported by experimental data in wake, jet, and grid turbulence. An expression for the fourth-order moment of the longitudinal velocity increments (δu ) 4¯ is derived from the analysis carried out in the inertial range. The expression, which involves the product of (δu ) 2 and ∂ δ p /∂ x , does not require the use the volume-averaged dissipation ɛ¯r, introduced by Oboukhov [Oboukhov, Some specific features of atmospheric turbulence, J. Fluid Mech. 13, 77 (1962), 10.1017/S0022112062000506] on a phenomenological basis and used by Kolmogorov to derive his refined similarity hypotheses
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.
Music analysis and Kolmogorov complexity
Meredith, David
that the program represents. If such an effective measure of analysis quality can be found, it could be used in a system that automatically finds the optimal analysis for any passage of music. Measuring program length in terms of number of source-code characters is shown to be problematic and an expression......The goal of music analysis is to find the most satisfying explanations for musical works. It is proposed that this can best be achieved by attempting to write computer programs that are as short as possible and that generate representations that are as detailed as possible of the music...... is proposed that overcomes some but not all of these problems. It is suggested that the solutions to the remaining problems may lie either in the field of concrete Kolmogorov complexity or in the design of languages specialized for expressing musical structure....
The Kolmogorov-Riesz compactness theorem
Hanche-Olsen, Harald
2009-01-01
We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.
A Short Introduction to Kolmogorov Complexity
Nannen, Volker
2010-01-01
This is a short introduction to Kolmogorov complexity and information theory. The interested reader is referred to the literature, especially the textbooks [CT91] and [LV97] which cover the elds of information theory and Kolmogorov complexity in depth and with all the necessary rigor.
A.N. Kolmogorov's defence of Mendelism
Alan Stark
2011-01-01
Full Text Available In 1939 N.I. Ermolaeva published the results of an experiment which repeated parts of Mendel's classical experiments. On the basis of her experiment she concluded that Mendel's principle that self-pollination of hybrid plants gave rise to segregation proportions 3:1 was false. The great probability theorist A.N. Kolmogorov reviewed Ermolaeva's data using a test, now referred to as Kolmogorov's, or Kolmogorov-Smirnov, test, which he had proposed in 1933. He found, contrary to Ermolaeva, that her results clearly confirmed Mendel's principle. This paper shows that there were methodological flaws in Kolmogorov's statistical analysis and presents a substantially adjusted approach, which confirms his conclusions. Some historical commentary on the Lysenko-era background is given, to illuminate the relationship of the disciplines of genetics and statistics in the struggle against the prevailing politically-correct pseudoscience in the Soviet Union. There is a Brazilian connection through the person of Th. Dobzhansky.
Lakshminarayanan, Vasudevan; Thyagarajan, K
2002-01-01
Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Many features oflight propagation can be analyzed in terms ofrays,ofcourse, subtle effects near foci, caustics or turning points would need an analysis based on the wave natureoflight. Allofgeometric optics can be derived from Fermat's principle which is an extremum principle. The counterpart in classical mechanics is of course Hamilton's principle. There is a very close analogy between mechanics ofparticles and optics oflight rays. Much insight (and useful results) can be obtained by analyzing these analogies. Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, 1956), classical mechanics is only a geometrical optics approximation to a wave theory! In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of ray propagation through various media. Given the ...
Lagrangian Quantum Homology for Lagrangian cobordism
Singer, Berit
2015-01-01
We extend the definition of Lagrangian quantum homology to monotone Lagrangian cobordism and establish its general algebraic properties. In particular we develop a relative version of Lagrangian quantum homology associated to a cobordism relative to a part of its boundary and study relations of this invariant to the ambient quantum homology.
Kolmogorov and Zabih’s Graph Cuts Stereo Matching Algorithm
Vladimir Kolmogorov
2014-10-01
Full Text Available Binocular stereovision estimates the three-dimensional shape of a scene from two photographs taken from different points of view. In rectified epipolar geometry, this is equivalent to a matching problem. This article describes a method proposed by Kolmogorov and Zabih in 2001, which puts forward an energy-based formulation. The aim is to minimize a four-term-energy. This energy is not convex and cannot be minimized except among a class of perturbations called expansion moves, in which case an exact minimization can be done with graph cuts techniques. One noteworthy feature of this method is that it handles occlusion: The algorithm detects points that cannot be matched with any point in the other image. In this method displacements are pixel accurate (no subpixel refinement.
Simultaneous DOA estimation based on Kolmogorov's theorem
Nájar Martón, Montserrat; Lagunas Hernandez, Miguel A.
1993-01-01
The design of a new architecture for signal processing, based on the Kolmogorov's theorem (1957), is addressed. This architecture is applied to solve the problem of source separation. Particularly, an adaptive algorithm is proposed to separate simultaneously all the unknown impinging sources on an aperture of sensors. The implemented framework is composed of two different stages: the first one is the inhibition stage, which turns the problem of estimating simultaneous DOAs (directions of arri...
Kolmogorov Dissipation scales in Weakly Ionized Plasmas
Krishan, V
2009-01-01
In a weakly ionized plasma, the evolution of the magnetic field is described by a "generalized Ohm's law" that includes the Hall effect and the ambipolar diffusion terms. These terms introduce additional spatial and time scales which play a decisive role in the cascading and the dissipation mechanisms in magnetohydrodynamic turbulence. We determine the Kolmogorov dissipation scales for the viscous, the resistive and the ambipolar dissipation mechanisms. The plasma, depending on its properties and the energy injection rate, may preferentially select one of the these dissipation scales. thus determining the shortest spatial scale of the supposedly self-similar spectral distribution of the magnetic field. The results are illustrated taking the partially ionized part of the solar atmosphere as an example. Thus the shortest spatial scale of the supposedly self-similar spectral distribution of the solar magnetic field is determined by any of the four dissipation scales given by the viscosity, the Spizer resistivity...
Rate distortion and denoising of individual data using Kolmogorov complexity
Vereshchagin, N.K.; Vitányi, P.M.B.
2010-01-01
We examine the structure of families of distortion balls from the perspective of Kolmogorov complexity. Special attention is paid to the canonical rate-distortion function of a source word which returns the minimal Kolmogorov complexity of all distortion balls containing that word subject to a bound
Fedotov, Sergei
1998-10-01
An asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of the path-integral approach, scaling procedure, and the singular perturbation techniques involving the large deviations theory for the Poisson random walk. The exact formula for the position and speed of reaction front is derived. It is found that the reaction front dynamics is formally associated with the relativistic Hamiltonian/Lagrangian mechanics.
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.
Kolmogorov-Chaitin Complexity of Digital Controller Implementations
James F. Whidborne; John McKernan; Da-Wei Gu
2006-01-01
The complexity of linear, fixed-point arithmetic digital controllers is investigated from a Kolmogorov-Chaitin perspective. Based on the idea of Kolmogorov-Chaitin complexity, practical measures of complexity are developed for state-space realizations, parallel and cascade realizations, and for a newly proposed generalized implicit state-space realization.The complexity of solutions to a restricted complexity controller benchmark problem is investigated using this measure.The results show that from a Kolmogorov-Chaitin viewpoint, higher-order controllers with a shorter word-length may have lower complexity and better performance, than lower-order controllers with longer word-length.
Kolmogorov-Sinai and Bekenstein-Hawking entropies
Ropotenko, K
2007-01-01
It is shown that instability of stringy matter near the event horizon of a black hole (the spreading effect) can be characterized by the Lyapunov exponents. For a homogeneous and isotropic horizon the (average) Lyapunov exponent coincides with the Kolmogorov-Sinai entropy of stringy matter. Due to identity of phase space volume of the string with the area of the horizon the relation between the Kolmogorov-Sinai and Bekenstein-Hawking entropies is established. The Kolmogorov-Sinai entropy measures the rate at which information about the string state is lost as the string spreads over the horizon.
SLM-based laboratory simulations of Kolmogorov and non-Kolmogorov anisotropic turbulence.
Toselli, Italo; Korotkova, Olga; Xiao, Xifeng; Voelz, David G
2015-05-20
In this paper, we present a laboratory setup to simulate anisotropic, non-Kolmogorov turbulence. A sequence of numerical phase screens that incorporate the turbulence characteristics were applied to a spatial light modulator placed in the path of a laser beam with a Gaussian intensity profile and the resulting far-field intensity patterns were recorded by a CCD camera. The values of scintillation at the position of the maximum intensity were extracted from the images and compared with theoretical values. Our experimental results show a trend that is in agreement with known theoretical expressions; however, the turbulence rescaling due to anisotropy shows some discrepancy with theory and requires more investigation.
Optimal control problem for the extended Fisher–Kolmogorov equation
Ning Duan
2016-02-01
In this paper, the optimal control problem for the extended Fisher–Kolmogorov equation is studied. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved and the optimality system is established.
Numerical solution of the Kolmogorov-Feller equation with singularities
Baranov, N. A.; Turchak, L. I.
2010-02-01
A method is proposed for solving the Kolmogorov-Feller integro-differential equation with kernels containing delta function singularities. The method is based on a decomposition of the solution into regular and singular parts.
Quantum Kolmogorov complexity and the quantum Turing machine
Mueller, M.
2007-08-31
The purpose of this thesis is to give a formal definition of quantum Kolmogorov complexity and rigorous mathematical proofs of its basic properties. Classical Kolmogorov complexity is a well-known and useful measure of randomness for binary strings. In recent years, several different quantum generalizations of Kolmogorov complexity have been proposed. The most natural generalization is due to A. Berthiaume et al. (2001), defining the complexity of a quantum bit (qubit) string as the length of the shortest quantum input for a universal quantum computer that outputs the desired string. Except for slight modifications, it is this definition of quantum Kolmogorov complexity that we study in this thesis. We start by analyzing certain aspects of the underlying quantum Turing machine (QTM) model in a more detailed formal rigour than was done previously. Afterwards, we apply these results to quantum Kolmogorov complexity. Our first result is a proof of the existence of a universal QTM which simulates every other QTM for an arbitrary number of time steps and than halts with probability one. In addition, we show that every input that makes a QTM almost halt can be modified to make the universal QTM halt entirely, by adding at most a constant number of qubits. It follows that quantum Kolmogorov complexity has the invariance property, i.e. it depends on the choice of the universal QTM only up to an additive constant. Moreover, the quantum complexity of classical strings agrees with classical complexity, again up to an additive constant. The proofs are based on several analytic estimates. Furthermore, we prove several incompressibility theorems for quantum Kolmogorov complexity. Finally, we show that for ergodic quantum information sources, complexity rate and entropy rate coincide with probability one. The thesis is finished with an outlook on a possible application of quantum Kolmogorov complexity in statistical mechanics. (orig.)
Zilberman, Arkadi; Golbraikh, Ephim; Kopeika, Norman S
2008-12-01
Turbulence properties of communication links (optical and microwave) in terms of log-amplitude variance are studied on the basis of a three-layer model of refractive index fluctuation spectrum in the free atmosphere. We suggest a model of turbulence spectra (Kolmogorov and non-Kolmogorov) changing with altitude on the basis of obtained experimental and theoretical data for turbulence profile in the troposphere and lower stratosphere.
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.
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.
Forbidden substrings, Kolmogorov complexity and almost periodic sequences
Rumyantsev, Andrey
2010-01-01
Assume that for some $\\alpha<1$ and for all nutural $n$ a set $F_n$ of at most $2^{\\alpha n}$ "forbidden" binary strings of length $n$ is fixed. Then there exists an infinite binary sequence $\\omega$ that does not have (long) forbidden substrings. We prove this combinatorial statement by translating it into a statement about Kolmogorov complexity and compare this proof with a combinatorial one based on Laslo Lovasz local lemma. Then we construct an almost periodic sequence with the same property (thus combines the results of Levin and Muchnik-Semenov-Ushakov). Both the combinatorial proof and Kolmogorov complexity argument can be generalized to the multidimensional case.
Limit cycles and Hopf bifurcations in a Kolmogorov type system
Simona Muratori
1989-04-01
Full Text Available The paper is devoted to the study of a class of Kolmogorov type systems which can be used to represent the dynamic behaviour of prey and predators. The model is an extension of the classical prey-predator model since it allows intra-specific competition for the predator's species. The analysis shows that the system can only have Kolmogorov's two modes of behaviour: a globally stable equilibrium or a globally stable limit cycle. Moreover, the transition from one of these two modes to the other is a non-catastrophic Hopf bifurcation which can be specified analytically.
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
Kolmogorov complexity, Lovasz local lemma and critical exponents
Rumyantsev, Andrey
2010-01-01
D. Krieger and J. Shallit have proved that every real number greater than 1 is a critical exponent of some sequence. We show how this result can be derived from some general statements about sequences whose subsequences have (almost) maximal Kolmogorov complexity. In this way one can also construct a sequence that has no "approximate" fractional powers with exponent that exceeds a given value.
Asymptotical Behaviors of Nonautonomous Discrete Kolmogorov System with Time Lags
Shengqiang Liu
2010-01-01
Full Text Available We discuss a general n-species discrete Kolmogorov system with time lags. We build some new results about the sufficient conditions for permanence, extinction, and balancing survival. When applying these results to some Lotka-Volterra systems, we obtain the criteria on harmless delay for the permanence as well as profitless delay for balancing survival.
Asymptotical Behaviors of Nonautonomous Discrete Kolmogorov System with Time Lags
Liu Shengqiang
2010-01-01
Full Text Available We discuss a general -species discrete Kolmogorov system with time lags. We build some new results about the sufficient conditions for permanence, extinction, and balancing survival. When applying these results to some Lotka-Volterra systems, we obtain the criteria on harmless delay for the permanence as well as profitless delay for balancing survival.
The Inveterate Tinkerer: 2. Instability of Kolmogorov Flow
Aditi Kambli; Chirag Kalelkar
2017-04-01
In this series of articles, the authors discuss various phenomenain fluid dynamics, which may be investigated via tabletopexperiments using low-cost or home-made instruments.The second article in this series is about a simple set-up fordemonstrating the instability of Kolmogorov Flow.
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.
Spandan, Vamsi; Lohse, Detlef
2016-01-01
The influence of the underlying flow topology on the shape and size of sub-Kolmogorov droplets dispersed in a turbulent flow is of considerable interest in many industrial and scientific applications. In this work we study the deformation and orientation statistics of sub-Kolmogorov droplets dispersed into a turbulent Taylor-Couette flow. Along with Direct Numerical Simulations (DNS) of the carrier phase and Lagrangian tracking of the dispersed droplets, we solve a phenomenological equation proposed by Maffettone and Minale (\\emph{J. Fluid Mech.} 78, 227-241 (1998)) to track the shape evolution and orientation of approximately $10^5$ ellipsoidal droplets. By varying the capillary number $Ca$ and viscosity ratio $\\hat \\mu$ of the droplets we find that the droplets deform more with increasing capillary number $Ca$ and this effect is more pronounced in the boundary layer regions. This indicates that along with a capillary number effect there is also a strong correlation between spatial position and degree of def...
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.
Kolmogorov Complexity, String Information, Panspermia and the Fermi Paradox
Gurzadyan, V G
2005-01-01
Bit strings rather than byte files can be a mode of transmission both for intelligent signals and for travels of extraterrestrial life. Kolmogorov complexity, i.e. the minimal length of a binary coded string completely defining a system, can then, due to its universality, become a key concept in the strategy of the search of extraterrestrials. Evaluating, for illustration, the Kolmogorov complexity of the human genome, one comes to an unexpected conclusion that a low complexity compressed string - analog of Noah's ark - will enable the recovery of the totality of terrestrial life. The recognition of bit strings of various complexity up to incompressible Martin-L\\"{o}f random sequences, will require a different strategy for the analysis of the cosmic signals. The Fermi paradox "Where is Everybody?" can be viewed under in the light of such information panspermia, i.e. a Universe full of traveling life streams.
Kolmogorov entropy of magnetic field lines in the percolation regime
Zimbardo, G; Bitane, R; Pommois, P; Veltri, P [Physics Department, University of Calabria, Arcavacata di Rende (Italy)
2009-01-15
We report the first numerical computation of the Kolmogorov entropy h of magnetic field lines extending from the quasilinear up to the percolation regime, using a numerical code where one can change both the turbulence level {delta}B/B{sub 0} and the turbulence anisotropy l{sub ||}/l{sub p}erpendicular. We find that the proposed percolation scaling of h is not reproduced, but rather a saturation of h is obtained. Also, we find that the Kolmogorov entropy depends solely on the Kubo number R = ({delta}B/B{sub 0})(l{sub ||}/l{sub p}erpendicular), and not separately on {delta}B/B{sub 0} and l{sub ||}/l{sub p}erpendicular. We apply the results to electron transport in solar coronal loops, which involves the use of the Rechester and Rosenbluth diffusion coefficient, and show that the study of transport in the percolation regime is required.
An Improved Evaluation of Kolmogorovs Distribution
Luis Carvalho
2015-06-01
Full Text Available We propose a new algorithm for computing extreme probabilities of Kolmogorov's goodness-of-fit measure, Dn . This algorithm is an improved version of the method originally proposed by Wang, Tsang, and Marsaglia (2003 based on a result from Durbin (1973. The new algorithm keeps the same numerical precision of the Wang et al. (2003 method, but is more efficient: it features linear instead of quadratic space complexity and has better time complexity for a common range of input parameters of practical importance. The proposed method is implemented in the R package kolmim, which also includes an improved routine to perform one-sample two-sided exact Kolmogorov-Smirnov tests.
The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium
Van Beijeren, H; Posch, H A; Dellago, C; Dellago, Ch.
1997-01-01
We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy per particle for a dilute gas in equilibrium. For an equilibrium system, the KS entropy, h_KS is the sum of all of the positive Lyapunov exponents characterizing the chaotic behavior of the gas. We compute h_KS/N, where N is the number of particles in the gas. This quantity has a density expansion of the form h_KS/N = a\
Hypocoercivity for Kolmogorov backward evolution equations and applications
Grothaus, Martin; Stilgenbauer, Patrik
2012-01-01
In this article we extend the modern, powerful and simple abstract Hilbert space strategy for proving hypocoercivity that has been developed originally by Dolbeault, Mouhot and Schmeiser. As well-known, hypocoercivity methods imply an exponential decay to equilibrium with explicit computable rate of convergence. Our extension is now made for studying the long-time behavior of some strongly continuous semigroup generated by a (degenerate) Kolmogorov backward operator L. Additionally, we introd...
INTEGRABILITY AND LINEARIZABILITY FOR A CLASS OF CUBIC KOLMOGOROV SYSTEMS
无
2010-01-01
The integrability and linearizability for a class of cubic Kolmogorov systems are studied. A recursive formula to compute the saddle quantities of the systems is deduced firstly, and integrable conditions for the systems are obtained. Then a recursive formula to compute the coefficients of the normal form for saddle points of the systems is also applied. Finally linearizable conditions of the origin for the systems are given. Both formulas to find necessary conditions are all linear and readily done using c...
Complexity measurement based on information theory and kolmogorov complexity.
Lui, Leong Ting; Terrazas, Germán; Zenil, Hector; Alexander, Cameron; Krasnogor, Natalio
2015-01-01
In the past decades many definitions of complexity have been proposed. Most of these definitions are based either on Shannon's information theory or on Kolmogorov complexity; these two are often compared, but very few studies integrate the two ideas. In this article we introduce a new measure of complexity that builds on both of these theories. As a demonstration of the concept, the technique is applied to elementary cellular automata and simulations of the self-organization of porphyrin molecules.
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.
Adaptive mesh refinement for stochastic reaction-diffusion processes
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2011-01-01
We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction-diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction-diffusion processes as described by the Fisher-Kolmogorov and Gray-Scott equations.
HE JiFeng
2008-01-01
This paper presents a refinement calculus for service components. We model the behaviour of individual service by a guarded design, which enables one to separate the responsibility of clients from the commitment made by the system, and to iden-tify a component by a set of failures and divergences. Protocols are introduced to coordinate the interactions between a component with the external environment. We adopt the notion of process refinement to formalize the substitutivity of components, and provide a complete proof method based on the notion of simulations.
Exact values of Kolmogorov widths of classes of analytic functions
Serdyuk, A. S.; Bodenchuk, V. V.
2014-01-01
We prove that kernels of analytic functions of kind $H_{h,\\beta}(t)=\\sum\\limits_{k=1}^{\\infty}\\frac{1}{\\cosh kh}\\cos\\Big(kt-\\frac{\\beta\\pi}{2}\\Big)$, $h>0$, ${\\beta\\in\\mathbb{R}}$, satisfies Kushpel's condition $C_{y,2n}$ beginning with some number $n_h$ which is explicitly expressed by parameter $h$ of smoothness of the kernel. As a consequence, for all $n\\geqslant n_h$ we obtain lower bounds for Kolmogorov widths $d_{2n}$ of functional classes that are representable as convolutions of kerne...
Kolmogorov Equation in a Fully Developed Turbulence Experiment
Moisy, F; Willaime, H
1999-01-01
The Kolmogorov equation with a forcing term is compared to experimental measurements, in low temperature helium gas, in a range of microscale Reynolds numbers $R_{\\lambda}$ between 120 and 1200. We show that the relation is accurately verified by the experiment (i.e. within +/- 3 % relative error, over ranges of scales extending up to three decades). Two scales are extracted from the analysis, and revealed experimentally, one characterizing the external forcing, and the other, varying as $R_{\\lambda}^{-3/5}$, defining the position of the maximum of the function $- S_{3}(r)/r$, and for which a physical interpretation is offered.
Average-Case Analysis of Algorithms Using Kolmogorov Complexity
姜涛; 李明
2000-01-01
Analyzing the average-case complexity of algorithms is a very prac tical but very difficult problem in computer science. In the past few years, we have demonstrated that Kolmogorov complexity is an important tool for analyzing the average-case complexity of algorithms. We have developed the incompressibility method. In this paper, several simple examples are used to further demonstrate the power and simplicity of such method. We prove bounds on the average-case number of stacks (queues) required for sorting sequential or parallel Queuesort or Stacksort.
Diffusion coefficient and Kolmogorov entropy of magnetic field lines
Zimbardo, G.; Veltri, P.; Malara, F. (Cosenza Univ. (Italy). Dip. di Fisica)
1984-08-01
A diffusion equation for magnetic field lines of force in a turbulent magnetic field, which describes both the random walk of a single line and how two nearby lines separate from each other, has been obtained using standard statistical techniques. Starting from such an equation, a closed set of equations for the moments may be obtained, in general, with suitable assumptions. From such a set of equations the Kolmogorov entropy may be explicitly calculated. The results have been applied to the most interesting examples of magnetic field geometries.
On Kolmogorov's superpositions and Boolean functions
Beiu, V.
1998-12-31
The paper overviews results dealing with the approximation capabilities of neural networks, as well as bounds on the size of threshold gate circuits. Based on an explicit numerical (i.e., constructive) algorithm for Kolmogorov's superpositions they will show that for obtaining minimum size neutral networks for implementing any Boolean function, the activation function of the neurons is the identity function. Because classical AND-OR implementations, as well as threshold gate implementations require exponential size (in the worst case), it will follow that size-optimal solutions for implementing arbitrary Boolean functions require analog circuitry. Conclusions and several comments on the required precision are ending the paper.
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
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.
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...
A spectral-based numerical method for Kolmogorov equations in Hilbert spaces
Delgado-Vences, Francisco; Flandoli, Franco
2016-08-01
We propose a numerical solution for the solution of the Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein-Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as an infinite system of ordinary differential equations, and by truncating it we set a linear finite system of differential equations. The solution of such system allow us to build an approximation to the solution of the Kolmogorov equations. We test the numerical method with the Kolmogorov equations associated with a stochastic diffusion equation, a Fisher-KPP stochastic equation and a stochastic Burgers equation in dimension 1.
Markov vs. Hurst-Kolmogorov behaviour identification in hydroclimatic processes
Dimitriadis, Panayiotis; Gournari, Naya; Koutsoyiannis, Demetris
2016-04-01
Hydroclimatic processes are usually modelled either by exponential decay of the autocovariance function, i.e., Markovian behaviour, or power type decay, i.e., long-term persistence (or else Hurst-Kolmogorov behaviour). For the identification and quantification of such behaviours several graphical stochastic tools can be used such as the climacogram (i.e., plot of the variance of the averaged process vs. scale), autocovariance, variogram, power spectrum etc. with the former usually exhibiting smaller statistical uncertainty as compared to the others. However, most methodologies including these tools are based on the expected value of the process. In this analysis, we explore a methodology that combines both the practical use of a graphical representation of the internal structure of the process as well as the statistical robustness of the maximum-likelihood estimation. For validation and illustration purposes, we apply this methodology to fundamental stochastic processes, such as Markov and Hurst-Kolmogorov type ones. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.
The Kolmogorov equation with time-measurable coefficients
Jay Kovats
2003-07-01
Full Text Available Using both probabilistic and classical analytic techniques, we investigate the parabolic Kolmogorov equation $$ L_t v +frac {partial v}{partial t}equiv frac 12 a^{ij}(tv_{x^ix^j} +b^i(t v_{x^i} -c(t v+ f(t +frac {partial v}{partial t}=0 $$ in $H_T:=(0,T imes E_d$ and its solutions when the coefficients are bounded Borel measurable functions of $t$. We show that the probabilistic solution $v(t,x$ defined in $ar H_T$, is twice differentiable with respect to $x$, continuously in $(t,x$, once differentiable with respect to $t$, a.e. $t in [0,T$ and satisfies the Kolmogorov equation $L_t v +frac {partial v}{partial t}=0$ a.e. in $ar H_T$. Our main tool will be the Aleksandrov-Busemann-Feller Theorem. We also examine the probabilistic solution to the fully nonlinear Bellman equation with time-measurable coefficients in the simple case $bequiv 0,,cequiv 0$. We show that when the terminal data function is a paraboloid, the payoff function has a particularly simple form.
Storage Enforcement with Kolmogorov Complexity and List Decoding
Husain, Mohammad Iftekhar; Rudra, Atri; Uurtamo, Steve
2011-01-01
We consider the following problem that arises in outsourced storage: a user stores her data $x$ on a remote server but wants to audit the server at some later point to make sure it actually did store $x$. The goal is to design a (randomized) verification protocol that has the property that if the server passes the verification with some reasonably high probability then the user can rest assured that the server is storing $x$. In this work we present an optimal solution (in terms of the user's storage and communication) while at the same time ensuring that a server that passes the verification protocol with any reasonable probability will store, to within a small \\textit{additive} factor, $C(x)$ bits of information, where $C(x)$ is the plain Kolmogorov complexity of $x$. (Since we cannot prevent the server from compressing $x$, $C(x)$ is a natural upper bound.) The proof of security of our protocol combines Kolmogorov complexity with list decoding and unlike previous work that relies upon cryptographic assumpt...
Spandan, Vamsi; Lohse, Detlef; Verzicco, Roberto
2016-12-01
The influence of the underlying flow topology on the shape and size of sub-Kolmogorov droplets dispersed in a turbulent flow is of considerable interest in many industrial and scientific applications. In this work we study the deformation and orientation statistics of sub-Kolmogorov droplets dispersed into a turbulent Taylor-Couette flow. Along with Direct Numerical Simulations (DNS) of the carrier phase and Lagrangian tracking of the dispersed droplets, we solve a phenomenological equation proposed by Maffettone and Minale (\\emph{J. Fluid Mech.} 78, 227-241 (1998)) to track the shape evolution and orientation of approximately $10^5$ ellipsoidal droplets. By varying the capillary number $Ca$ and viscosity ratio $\\hat \\mu$ of the droplets we find that the droplets deform more with increasing capillary number $Ca$ and this effect is more pronounced in the boundary layer regions. This indicates that along with a capillary number effect there is also a strong correlation between spatial position and degree of deformation of the droplet. Regardless of the capillary number $Ca$, the major-axis of the ellipsoids tends to align with the stream-wise direction and the extensional strain rate eigen direction in the boundary layer region while the distribution is highly isotropic in the bulk. When the viscosity ratio between the droplet and the carrier fluid is increased we find that there is no preferential stretched axis which is due to the increased influence of rotation over stretching and relaxation. Droplets in high viscosity ratio systems are thus less deformed and oblate (disk-like) as compared to highly deformed prolate (cigar-like) droplets in low viscosity ratio systems.
Gyrotactic trapping in laminar and turbulent Kolmogorov flow
Santamaria, Francesco; Cencini, Massimo; Boffetta, Guido
2014-01-01
Phytoplankton patchiness, namely the heterogeneous distribution of microalgae over multiple spatial scales, dramatically impacts marine ecology. A spectacular example of such heterogeneity occurs in thin phytoplankton layers (TPLs), where large numbers of photosynthetic microorganisms are found within a small depth interval. Some species of motile phytoplankton can form TPLs by gyrotactic trapping due to the interplay of their particular swimming style (directed motion biased against gravity) and the transport by a flow with shear along the direction of gravity. Here we consider gyrotactic swimmers in numerical simulations of the Kolmogorov shear flow, both in laminar and turbulent regimes. In the laminar case, we show that the swimmer motion is integrable and the formation of TPLs can be fully characterized by means of dynamical systems tools. We then study the effects of rotational Brownian motion or turbulent fluctuations (appearing when the Reynolds number is large enough) on TPLs. In both cases we show t...
Kolmogorov complexities Kmax, Kmin on computable partially ordered sets
Ferbus-Zanda, Marie
2008-01-01
We introduce a machine free mathematical framework to get a natural formalization of some general notions of infinite computation in the context of Kolmogorov complexity. Namely, the classes Max^{X\\to D}_{PR} and Max^{X\\to D}_{Rec} of functions X \\to D which are pointwise maximum of partial or total computable sequences of functions where D = (D,_{ct} K^{0',D}. We characterize the orders leading to each case. We also show that K^D_{min}, K^D_{max} cannot be both much smaller than K^D at any point. These results are proved in a more general setting with two orders on D, one extending the other.
On the Kolmogorov-Chaitin Complexity for short sequences
Delahaye, Jean Pierre
2007-01-01
A drawback to Kolmogorov-Chaitin complexity $(K)$ is that it is uncomputable in general, and that limits its range of applicability. Another critique concerns the dependence of $K$ on a particular universal Turing machine $U$ for which predictions for short sequences -shorter for example than typical compiler lengths- can be arbitrary. In practice one can approximate it by computable compression methods. However, such compression methods do not provide a good approximation for short sequences. Herein is suggested an empirical approach to overcome the problem that compression approximations do not work well for short sequences. Additionally, our results demonstrate that there is a strong correlation in terms of sequence frequencies across the output of several systems including such abstract systems as cellular automata and Turing machines, as well as repositories containing a sample of real-world information such as images and human DNA fragments. Our results suggest that behind all such systems is a shared -...
Kolmogorov-Smirnov test for spatially correlated data
Olea, R.A.; Pawlowsky-Glahn, V.
2009-01-01
The Kolmogorov-Smirnov test is a convenient method for investigating whether two underlying univariate probability distributions can be regarded as undistinguishable from each other or whether an underlying probability distribution differs from a hypothesized distribution. Application of the test requires that the sample be unbiased and the outcomes be independent and identically distributed, conditions that are violated in several degrees by spatially continuous attributes, such as topographical elevation. A generalized form of the bootstrap method is used here for the purpose of modeling the distribution of the statistic D of the Kolmogorov-Smirnov test. The innovation is in the resampling, which in the traditional formulation of bootstrap is done by drawing from the empirical sample with replacement presuming independence. The generalization consists of preparing resamplings with the same spatial correlation as the empirical sample. This is accomplished by reading the value of unconditional stochastic realizations at the sampling locations, realizations that are generated by simulated annealing. The new approach was tested by two empirical samples taken from an exhaustive sample closely following a lognormal distribution. One sample was a regular, unbiased sample while the other one was a clustered, preferential sample that had to be preprocessed. Our results show that the p-value for the spatially correlated case is always larger that the p-value of the statistic in the absence of spatial correlation, which is in agreement with the fact that the information content of an uncorrelated sample is larger than the one for a spatially correlated sample of the same size. ?? Springer-Verlag 2008.
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.
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.
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.
Holzner, Markus; Liberzon, A.; Nikitin, N.; L?Thi, B.; Kinzelbach, W.; Tsinober, A.
We report an analysis of small-scale enstrophy = 50. The results are based on the Lagrangian viewpoint with the main focus on flow particle tracers crossing the turbulent/non-turbulent interface. This approach allowed a direct investigation of the key physical processes underlying the entrainment phenomenon and revealed the role of small-scale non-local, inviscid and viscous processes. We found that the entrainment mechanism is initiated by self-amplification of s2 through the combined effect of strain production and pressure--strain interaction. This process is followed by a sharp change of 2. Finally, shortly after the crossing of the turbulent/non-turbulent interface, production and dissipation of both enstrophy and strain reach a balance. The characteristic time scale of the described processes is the Kolmogorov time scale, . Locally, the characteristic velocity of the fluid relative to the turbulent/non-turbulent interface is the Kolmogorov velocity, uη.
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 .
Spectral slope and Kolmogorov constant of MHD turbulence.
Beresnyak, A
2011-02-18
The spectral slope of strong MHD turbulence has recently been a matter of controversy. While the Goldreich-Sridhar model predicts a -5/3 slope, shallower slopes have been observed in numerics. We argue that earlier numerics were affected by driving due to a diffuse locality of energy transfer. Our highest-resolution simulation (3072(2)×1024) exhibited the asymptotic -5/3 scaling. We also discover that the dynamic alignment, proposed in models with -3/2 slope, saturates and cannot modify the asymptotic, high Reynolds number slope. From the observed -5/3 scaling we measure the Kolmogorov constant C(KA)=3.27±0.07 for Alfvénic turbulence and C(K)=4.2±0.2 for full MHD turbulence, which is higher than the hydrodynamic value of 1.64. This larger C(K) indicates inefficient energy transfer in MHD turbulence, which is in agreement with diffuse locality.
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.
He Xue-Mei; L(u) Bai-Da
2011-01-01
The propagation properties of partially coherent Hermite-Gaussian beams through non-Kolmogorov atmospheric turbulence are studied. The effects of non-Kolmogorov turbulence and beam nonparaxiality on the average intensity evolution and the beam-width spreading are stressed. It is found that the evolution of the average intensity distribution and the beam-width spreading depends on the generalized exponent factor,namely,on the non-Kolmogorov turbulence strength for the paraxial case. For the non-paraxial case the effect of the turbulence is negligible,while the beamwidth spreading becomes very large. The analytical results are illustrated numerically and interpreted physically.
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.
Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation
Ma, W.
1996-05-01
Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and further two solutions to describe nonlinear interaction of traveling waves are generated. B\\"acklund transformations of the linear form and some special cases are considered.
Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation
Ma, Wen-Xiu; Fuchssteiner, Benno
1995-01-01
Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and further two solutions to describe nonlinear interaction of traveling waves are generated. B\\"acklund transformations of the linear form and some special cases are considered.
A Lagrangian particle/panel method for the barotropic vorticity equations on a rotating sphere
Bosler, Peter; Krasny, Robert [Department of Mathematics, University of Michigan, Ann Arbor, MI 48109 (United States); Wang, Lei [Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201 (United States); Christiane Jablonowski, E-mail: krasny@umich.edu [Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, MI 48109 (United States)
2014-06-01
We present a Lagrangian particle/panel method for geophysical fluid flow described by the barotropic vorticity equations on a rotating sphere. The particles carry vorticity and the panels are used in discretizing the Biot–Savart integral for the velocity. Adaptive panel refinement and a new Lagrangian remeshing scheme are applied to reduce the computational cost and maintain accuracy as the flow evolves. Computed examples include a Rossby–Haurwitz wave, a Gaussian vortex, and a perturbed zonal jet. To validate the method, a comparison is made with results obtained using the Lin–Rood finite–volume scheme. (papers)
Lagrangian Submanifolds Foliated by (n-1)-spheres in R2n
Henri ANCIAUX; Ildefonso CASTRO; Pascal ROMON
2006-01-01
We study Lagrangian submanifolds foliated by (n-1)-spheres in R2n for n≥3. We give a general parametrization for such submanifolds, and refine that description when the submanifold is special Lagrangian, self-similar, Hamiltonian stationary or has mean curvature vector of constant length. In all these cases, the submanifold is centered, i.e. invariant under the action of SO(n). It suffices then to solve a simple ODE in two variables to describe the geometry of the solutions.
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.
Atkey, Robert; Ghani, Neil
2012-01-01
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the N-indexed type of vectors refines lists by their lengths. Other data types may be refined in similar ways, but programmers must produce purpose-specific refinements on an ad hoc basis, developers must anticipate which refinements to include in libraries, and implementations must often store redundant information about data and their refinements. In this paper we show how to generically derive inductive characterisations of refinements of inductive types, and argue that these characterisations can alleviate some of the aforementioned difficulties associated with ad hoc refinements. Our characterisations also ensure that standard techniques for programming with and reasoning about inductive types are applicable to refinements, and that refinements can the...
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.
Mihailovic, Dragutin T; Nikolic-Djoric, Emilija; Arsenic, Ilija
2013-01-01
We have proposed novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We have considered background of the Kolmogorov complexity and also we have discussed meaning of the physical as well as other complexities. To get better insights into the complexity of complex systems and time series analysis we have introduced the three novel measures based on the Kolmogorov complexity: (i) the Kolmogorov complexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and (iii) the overall Kolmogorov complexity. The characteristics of these measures have been tested using a generalized logistic equation. Finally, the proposed measures have been applied on different time series originating from: the model output (the biochemical substance exchange in a multi-cell system), four different geophysical phenomena (dynamics of: river flow, long term precipitation, indoor 222Rn concentration and UV radiation dose) and economy (stock prices dynamics). Re...
Mihailović Dragutin T.
2015-01-01
Full Text Available We propose novel metrics based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We consider the origins of the Kolmogorov complexity and discuss its physical meaning. To get better insights into the nature of complex systems and time series analysis we introduce three novel measures based on the Kolmogorov complexity: (i the Kolmogorov complexity spectrum, (ii the Kolmogorov complexity spectrum highest value and (iii the overall Kolmogorov complexity. The characteristics of these measures have been tested using a generalized logistic equation. Finally, the proposed measures have been applied to different time series originating from: a model output (the biochemical substance exchange in a multi-cell system, four different geophysical phenomena (dynamics of: river flow, long term precipitation, indoor 222Rn concentration and UV radiation dose and the economy (stock price dynamics. The results obtained offer deeper insights into the complexity of system dynamics and time series analysis with the proposed complexity measures.
Gao, Lin; Wang, Jue; Chen, Longwei
2013-06-01
Objective. Various approaches have been applied for the quantification of event-related desynchronization/synchronization (ERD/ERS) in EEG/MEG data analysis, but most of them are based on band power analysis. In this paper, we sought a novel method using a nonlinear measurement to quantify the ERD/ERS time course of motor-related EEG. Approach. We applied Kolmogorov entropy to quantify the ERD/ERS time course of motor-related EEG in relation to hand movement imagination and execution for the first time. To further test the validity of the Kolmogorov entropy measure, we tested it on five human subjects for feature extraction to classify the left and right hand motor tasks. Main results. The results show that the relative increase and decrease of Kolmogorov entropy indicates the ERD and ERS respectively. An average classification accuracy of 87.3% was obtained for five subjects. Significance. The results prove that Kolmogorov entropy can effectively quantify the dynamic process of event-related EEG, and it also provides a novel method of classifying motor imagery tasks from scalp EEG by Kolmogorov entropy measurement with promising classification accuracy.
Kolmogorov Behavior of Near-Wall Turbulence and Its Application in Turbulence Modeling
Shih, Tsan-Hsing; Lumley, John L.
1992-01-01
The near-wall behavior of turbulence is re-examined in a way different from that proposed by Hanjalic and Launder and followers. It is shown that at a certain distance from the wall, all energetic large eddies will reduce to Kolmogorov eddies (the smallest eddies in turbulence). All the important wall parameters, such as friction velocity, viscous length scale, and mean strain rate at the wall, are characterized by Kolmogorov microscales. According to this Kolmogorov behavior of near-wall turbulence, the turbulence quantities, such as turbulent kinetic energy, dissipation rate, etc. at the location where the large eddies become Kolmogorov eddies, can be estimated by using both direct numerical simulation (DNS) data and asymptotic analysis of near-wall turbulence. This information will provide useful boundary conditions for the turbulent transport equations. As an example, the concept is incorporated in the standard k-epsilon model which is then applied to channel and boundary flows. Using appropriate boundary conditions (based on Kolmogorov behavior of near-wall turbulence), there is no need for any wall-modification to the k-epsilon equations (including model constants). Results compare very well with the DNS and experimental data.
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
A Lagrangian approach to classical thermodynamics
Stokes, A.
2017-02-01
The specification of microstates of interacting dynamical systems is different in Lagrangian and Hamiltonian approaches whenever the interaction Lagrangian depends on generalised velocities. In almost all cases of physical interest however, velocity-dependent interaction Lagrangians do not couple velocities belonging to different subsystems. For these cases we define reduced system and bath Lagrangian macrostates, which like the underlying microstates differ from their Hamiltonian counterparts. We then derive exact first and second laws of thermodynamics without any modification of the original system and bath quantities. This approach yields manifestly gauge-invariant definitions of work and free energy, and a gauge-invariant Jarzynski equality is derived. The formalism is applied in deriving the thermodynamic laws for a material system within the radiation reservoir. The Lagrangian partition of the total energy is manifestly gauge-invariant and is in accordance with Poynting's theorem.
On Attracting Lagrangian Coherent Structures
Karrasch, Daniel
2013-01-01
In this note, we show that in the autonomous, two-dimensional incompressible saddle flow, contrary to common intuition, also attracting Lagrangian Coherent Structures (LCSs) can show up as ridges of the forward finite-time Lyapunov exponent (FTLE) field. This raises the issue of characterization of attracting LCSs from forward time FTLE analysis. First, we extend recent results of Haller & Sapsis (2011) [11] on the relation between forward and backward maximal and minimal stretching rates to the whole finite-time Lyapunov spectrum and to stretching directions by considering the singular value decomposition (SVD) of the deformation gradient. We show two significant advantages of the SVD compared to the usual eigendecomposition of the Cauchy-Green strain tensor: (1) one gains theoretical insight into local deformation under a finite-time dynamical system, and (2) one obtains both complete forward and backward strain information from a single grid advection. Furthermore, we give a short and direct proof of t...
Time-Dependent Lagrangian Biomechanics
Ivancevic, Tijana T
2009-01-01
In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. On this extended configuration space we develop time-dependent biomechanical Lagrangian dynamics, using derived jet spaces of velocities and accelerations, as well as the underlying geometric evolution of the mass-inertia matrix. Keywords: Human time-dependent biomechanics, configuration manifold, jet spaces, geometric evolution
Kolmogorov complexity as a hidden factor of scientific discourse: from Newton's law to data mining
Manin, Yuri I
2013-01-01
The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that must be taken into account; visible "chaotic" character of these data and/or space distribution/time evolution of a system etc. This talk is centered around the precise mathematical notion of "Kolmogorov complexity", originated in the early theoretical computer science and measuring the degree to which an available information can be compressed. In the first part, I will argue that a characteristic feature of basic scientific theories, from Ptolemy's epicycles to the Standard Model of elementary particles, is their splitting into two very distinct parts: the part of relatively small Kolmogorov complexity ("laws", "basic equations", "periodic table", "natural selection, genotypes, mutations") and another part, of indefinitely large Kolmogorov complexity ("initial and boundary c...
李玉梅; 李宝毅; 宋媛媛
2015-01-01
利用常微分方程定性理论分析了Kolmogorov-Petrovskii-Piskunov方程(KPP方程)和Zhiber-Shabat方程(ZS方程)的行波解.证明了KPP方程在一定的条件下存在扭波解,给出了ZS方程存在扭波解或反扭波解的充分条件.
José A. Adell
2009-01-01
Full Text Available We give efficient algorithms, as well as sharp estimates, to compute the Kolmogorov distance between the binomial and Poisson laws with the same mean λ. Such a distance is eventually attained at the integer part of λ+1/2−λ+1/4. The exact Kolmogorov distance for λ≤2−2 is also provided. The preceding results are obtained as a concrete application of a general method involving a differential calculus for linear operators represented by stochastic processes.
Levchenko, E. A.; Shapovalov, A. V.; Trifonov, A. Yu
2016-07-01
In this paper we construct asymptotic solutions for the nonlocal multidimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation in the class of functions concentrated on a one-dimensional manifold (curve) using a semiclassical approximation technique. We show that the construction of these solutions can be reduced to solving a similar problem for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov in the class of functions concentrated at a point (zero-dimensional manifold) together with an additional operator condition. The general approach is exemplified by constructing a two-dimensional two-parametric solution, which describes quasi-steady-state patterns on a circumference.
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.
Vickers, Trevor
1992-01-01
On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.
Domingues M. O.
2013-12-01
Full Text Available We present a new adaptive multiresoltion method for the numerical simulation of ideal magnetohydrodynamics. The governing equations, i.e., the compressible Euler equations coupled with the Maxwell equations are discretized using a finite volume scheme on a two-dimensional Cartesian mesh. Adaptivity in space is obtained via Harten’s cell average multiresolution analysis, which allows the reliable introduction of a locally refined mesh while controlling the error. The explicit time discretization uses a compact Runge–Kutta method for local time stepping and an embedded Runge-Kutta scheme for automatic time step control. An extended generalized Lagrangian multiplier approach with the mixed hyperbolic-parabolic correction type is used to control the incompressibility of the magnetic field. Applications to a two-dimensional problem illustrate the properties of the method. Memory savings and numerical divergences of magnetic field are reported and the accuracy of the adaptive computations is assessed by comparing with the available exact solution.
An augmented Lagrangian multi-scale dictionary learning algorithm
Ye Meng
2011-01-01
Full Text Available Abstract Learning overcomplete dictionaries for sparse signal representation has become a hot topic fascinated by many researchers in the recent years, while most of the existing approaches have a serious problem that they always lead to local minima. In this article, we present a novel augmented Lagrangian multi-scale dictionary learning algorithm (ALM-DL, which is achieved by first recasting the constrained dictionary learning problem into an AL scheme, and then updating the dictionary after each inner iteration of the scheme during which majorization-minimization technique is employed for solving the inner subproblem. Refining the dictionary from low scale to high makes the proposed method less dependent on the initial dictionary hence avoiding local optima. Numerical tests for synthetic data and denoising applications on real images demonstrate the superior performance of the proposed approach.
Eulerian-Lagrangian Simulations of Bubbly Flows in A Vertical Square Duct
Liu, Rui; Vanka, Surya P.; Thomas, Brian G.
2013-11-01
We report results of Eulerian-Lagrangian simulations of developing upward and downward bubbly flows in a vertical square duct with a bulk Reynolds number of 5000. The continuous fluid is simulated with DNS, solving the Navier-Stokes equations by a second-order accurate finite volume fractional step method. Bubbles of sizes comparable to the Kolmogorov scale are injected at the duct entrance with a mean bulk volume fraction below 10-2. A two-way coupling approach is adopted for the interaction between the continuous fluid phase and dispersed bubble phase. The bubbles are tracked by a Lagrangian method including drag and lift forces due to buoyancy and Saffman lift. A in-house code, CU-FLOW, implemented on Graphic Processing Unit (GPU) is used for simulations in this work. The preferential distributions of bubbles and their impact on local turbulence structures and their effects on turbulent kinetic energy budgets are studied. Results between an upward flow and a downward flow with the bubbles are compared. Work Supported by Continuous Casting Consortium at UIUC.
The Contributions of A. N. Kolmogorov to the theory of turbulence
Jiménez, Javier
2004-08-01
Full Text Available Two of the papers published by Kolmogorov in 1941 are generally considered to be the origin of modern turbulence theory, including the concepts of scale similarity and of a universal inertial cascade. His third important paper, in 1962, although later superseded, was in the same way the origin of the modern investigations on intermittency. This note summarizes the history of turbulence theory before Kolmogorov, his contributions in these three papers, and his influence on the present understanding of turbulence in fluids.
Dos de los artículos publicados por Kolmogorov en 1941 son considerados generalmente como el origen de la teoría moderna de la turbulencia. Estos artículos incluyen los conceptos de semejanza de escala y de una cascada universal inercial. Su tercer artículo importante sobre el tema, publicado en 1962, es igualmente el origen de las investigaciones modernas sobre intermitencia. En esta nota se resume la historia de las teorías sobre la turbulencia antes de Kolmogorov, sus aportaciones en estos tres artículos, y su influencia sobre la comprensión actual del movimiento turbulento de los fluidos.
Rosestolato, M.; Święch, A.
2017-02-01
We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are C 1 + α regular on special finite dimensional subspaces. The problem has origins in hedging derivatives of risky assets in mathematical finance.
Scintillation of Light from Distant Objects due to Anisotropic and Non-Kolmogorov Turbulence
2013-09-01
8. A. Silverman, E. Golbraikh, and N. S. Kopeika, “ Lidar studies of aerosols and non-Kolmogorov turbulence in the Mediterranean troposphere,” Proc...Propagation with Examples in MATLAB ”, (SPIE Press, Bellingham, Washington, 2010). 29. M. Vorontsov, V. S. Rao Gudimetla, G. Carhart, T. Weyrauch, S
Experimental Generation of non-Kolmogorov Turbulence using a Liquid Crystal Spatial Light Modulator
2011-01-01
Experimental generation of non-Kolmogorov Turbulence using a Liquid Crystal Spatial Light Modulator * Italo Tosellia, Brij N. Agrawala...performance evaluations. ACKNOWLEDGEMENTS This research was performed while the author Italo Toselli holds a National Research Council Research...REFERENCES 1. Larry C. Andrews, Ronald L. Phillips. Laser Beam Propagation through Random Media, 2nd ed. (SPIE, 2005). 2. Italo Toselli, Larry C
A Short Introduction to Model Selection, Kolmogorov Complexity and Minimum Description Length (MDL)
Nannen, Volker
2010-01-01
The concept of overtting in model selection is explained and demon- strated. After providing some background information on information theory and Kolmogorov complexity, we provide a short explanation of Minimum Description Length and error minimization. We conclude with a discussion of the typical
Caceres, Manuel O [Abdus Salam International Centre for Theoretical Physics, Strada Costiera, 11-34014 Trieste (Italy); Lobos, Alejandro M [Centro Atomico Bariloche, Instituto Balseiro, CNEA, Universidad Nacional de Cuyo, and CONICET, Av E Bustillo Km 9.5, 8400 Bariloche (Argentina)
2006-02-17
We present an eigenvalue theory to study the stochastic dynamics of non-stationary time-periodic Markov processes. The analysis is carried out by solving an integral operator of the Fredholm type, i.e. considering complex-valued functions fulfilling the Kolmogorov compatibility condition. We show that the asymptotic behaviour of the stochastic process is characterized by the smaller time-scale associated with the spectrum of the Kolmogorov operator. The presence of time-periodic elements in the evolution equation for the semigroup leads to a Floquet analysis. The first non-trivial Kolmogorov's eigenvalue is interpreted from a physical point of view. This non-trivial characteristic time-scale strongly depends on the interplay between the stochastic behaviour of the process and the time-periodic structure of the Fokker-Planck equation for continuous processes, or the periodically modulated master equation for discrete Markov processes. We present pedagogical examples in a finite-dimensional vector space to calculate the Kolmogorov characteristic time-scale for discrete Markov processes.
Levchenko, E. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2015-11-01
Asymptotic solutions of the multidimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation with an influence function that is invariant with respect to a spatial shift are constructed. The asymptotic solutions are perturbations of a spatially-homogeneous quasistationary exact solution. General expressions are illustrated by the example of a two-dimensional equation with a Gaussian initial condition.
Lotka's Law and the Kolmogorov-Smirnov Test: An Error in Calculation.
Loughner, William
1992-01-01
Corrects an error in the calculation of the Kolmogorov-Smirnov (KS) statistic when it is used to empirically confirm or deny the generalized Lotka's law. Examples from the literature are given of both correct and incorrect uses of the KS test and Lotka equations with cumulative distribution functions (CDFs). (six references) (LRW)
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...
OPTIMIZING EUCALYPTUS PULP REFINING
Vail Manfredi
2004-01-01
This paper discusses the refining of bleached eucalyptus kraft pulp (BEKP).Pilot plant tests were carried out in to optimize the refining process and to identify the effects of refining variables on final paper quality and process costs.The following parameters are discussed: pulp consistency, disk pattern design, refiner speed,energy input, refiner configuration (parallel or serial)and refining intensity.The effects of refining on pulp fibers were evaluated against the pulp quality properties, such as physical strengths, bulk, opacity and porosity, as well as the interactions with papermaking process, such as paper machine runnability, paper breaks and refining control.The results showed that process optimization,considering pulp quality and refining costs, were obtained when eucalyptus pulp is refined under the lowest intensity and the highest pulp consistency possible. Changes on the operational refining conditions will have the highest impact on total energy requirements (costs) without any significant effect on final paper properties.It was also observed that classical ways to control the industrial operation, such as those based on drainage measurements, do not represent the best alternative to maximize the final paper properties neither the paper machine runability.
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.
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.
On the Existence of the Kolmogorov Inertial Range in the Terrestrial Magnetosheath Turbulence
Huang, S. Y.; Hadid, L. Z.; Sahraoui, F.; Yuan, Z. G.; Deng, X. H.
2017-02-01
In the solar wind, power spectral density (PSD) of the magnetic field fluctuations generally follow the so-called Kolmogorov spectrum f ‑5/3 in the inertial range, where the dynamics is thought to be dominated by nonlinear interactions between counter-propagating incompressible Alfvén wave parquets. These features are thought to be ubiquitous in space plasmas. The present study gives a new and more complex picture of magnetohydrodynamic (MHD) turbulence as observed in the terrestrial magnetosheath. The study uses three years of in situ data from the Cluster mission to explore the nature of the magnetic fluctuations at MHD scales in different locations within the magnetosheath, including flanks and subsolar regions. It is found that the magnetic field fluctuations at MHD scales generally have a PSD close to f ‑1 (shallower than the Kolmogorov one f ‑5/3) down to the ion characteristic scale, which recalls the energy-containing scales of solar wind turbulence. The Kolmogorov spectrum is observed only away from the bow shock toward the flank and the magnetopause regions in 17% of the analyzed time intervals. Measuring the magnetic compressibility, it is shown that only a fraction (35%) of the observed Kolmogorov spectra was populated by shear Alfvénic fluctuations, whereas the majority of the events (65%) was found to be dominated by compressible magnetosonic-like fluctuations, which contrasts with well-known turbulence properties in the solar wind. This study gives a first comprehensive view of the origin of the f ‑1 and the transition to the Kolmogorov inertial range; both questions remain controversial in solar wind turbulence.
张强; 雷开洪; 向丽
2013-01-01
运用规范化的Lyapunov-Schmidt约化方法,在Direchlet边界条件下证明了Fisher-Kolmogorov-Petrovskii-Piskunov方程产生分歧,得到了分歧解的具体表达式和分歧解的正则性；在Neumann边界条件下得到了该方程产生超临界分歧和次临界分歧的完整判据、分歧解的具体表达式以及分歧解的正则性.%With normalized Lyapunov-Schmidt reduction method, the bifurcation for Fisher-Kolmogorov-Petrovskii-Piskunov equation with Direchlet boundary condition is proved and the exact expression and the regularity of solutions are obtained. Meanwhile a complete criterion both for supercritical and sub-critical bifurcation of the equation with Neumann boundary condition are derived. Furthermore, the exact form and the regularity of solutions are also obtained.
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.
Zollanvari, Amin
2013-05-24
We provide a fundamental theorem that can be used in conjunction with Kolmogorov asymptotic conditions to derive the first moments of well-known estimators of the actual error rate in linear discriminant analysis of a multivariate Gaussian model under the assumption of a common known covariance matrix. The estimators studied in this paper are plug-in and smoothed resubstitution error estimators, both of which have not been studied before under Kolmogorov asymptotic conditions. As a result of this work, we present an optimal smoothing parameter that makes the smoothed resubstitution an unbiased estimator of the true error. For the sake of completeness, we further show how to utilize the presented fundamental theorem to achieve several previously reported results, namely the first moment of the resubstitution estimator and the actual error rate. We provide numerical examples to show the accuracy of the succeeding finite sample approximations in situations where the number of dimensions is comparable or even larger than the sample size.
Zollanvari, Amin; Genton, Marc G
2013-08-01
We provide a fundamental theorem that can be used in conjunction with Kolmogorov asymptotic conditions to derive the first moments of well-known estimators of the actual error rate in linear discriminant analysis of a multivariate Gaussian model under the assumption of a common known covariance matrix. The estimators studied in this paper are plug-in and smoothed resubstitution error estimators, both of which have not been studied before under Kolmogorov asymptotic conditions. As a result of this work, we present an optimal smoothing parameter that makes the smoothed resubstitution an unbiased estimator of the true error. For the sake of completeness, we further show how to utilize the presented fundamental theorem to achieve several previously reported results, namely the first moment of the resubstitution estimator and the actual error rate. We provide numerical examples to show the accuracy of the succeeding finite sample approximations in situations where the number of dimensions is comparable or even larger than the sample size.
Truchetet, F.; Léni, P. E.; Fougerolle, Y.
2013-05-01
Mastering the sorting of the data in signal (nD) can lead to multiple applications like new compression, transmission, watermarking, encryption methods and even new processing methods for image. Some authors in the past decades have proposed to use these approaches for image compression, indexing, median filtering, mathematical morphology, encryption. A mathematical rigorous way for doing such a study has been introduced by Andrei Nikolaievitch Kolmogorov (1903-1987) in 1957 and recent results have provided constructive ways and practical algorithms for implementing the Kolmogorov theorem. We propose in this paper to present those algorithms and some preliminary results obtained by our team by applying them to image processing problems such as compression, progressive transmission and watermarking.
Spatially inhomogeneous structures in the solution of Fisher-Kolmogorov equation with delay
Aleshin, S. V.; Glyzin, S. D.; Kaschenko, S. A.
2016-02-01
We consider the problem of density wave propagation in a logistic equation with delay and diffusion (Fisher-Kolmogorov equation with delay). A Ginzburg-Landau equation was constructed in order to study the qualitative behavior of the solution near the equilibrium state. The numerical analysis of wave propagation shows that for a sufficiently small delay this equation has a solution similar to the solution of a classical Fisher-Kolmogorov equation. The delay increasing leads to existence of the oscillatory component in spatial distribution of solutions. A further increase of delay leads to destruction of the traveling wave. That is expressed in the fact that undamped spatio-temporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the delay is sufficiently large we observe intensive spatio-temporal fluctuations in the whole area of wave propagation.
Global Weak Solutions for Kolmogorov-Vicsek Type Equations with Orientational Interactions
Gamba, Irene M.; Kang, Moon-Jin
2016-10-01
We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov-Vicsek models that can be considered as non-local, non-linear, Fokker-Planck type equations describing the dynamics of individuals with orientational interactions. This model is derived from the discrete Couzin-Vicsek algorithm as mean-field limit (Bolley et al., Appl Math Lett, 25:339-343, 2012; Degond et al., Math Models Methods Appl Sci 18:1193-1215, 2008), which governs the interactions of stochastic agents moving with a velocity of constant magnitude, that is, the corresponding velocity space for these types of Kolmogorov-Vicsek models is the unit sphere. Our analysis for L p estimates and compactness properties take advantage of the orientational interaction property, meaning that the velocity space is a compact manifold.
Zhang, Yongtao; Zhao, Zhiguo; Ding, Chaoliang; Pan, Liuzhan
2017-02-01
We have investigated the correlation singularities of a partially coherent radially polarized beam propagating through non-Kolmogorov turbulence. An analytical expression for the radius of a ring dislocation is derived. It is shown that the dependence of the radius of a ring dislocation on spatial coherence width in non-Kolmogorov turbulence is quite different from that in free space. The relation between spatial coherence width and beam width affects the change trends of the radius of a ring dislocation versus spatial coherence width. For different value ranges of the power law, the change of the radius of a ring dislocation with power law has an opposite trend. It is also found that the propagation distance plays an important role in determining the change of the radius of a ring dislocation. Our results will be useful in measuring the statistical properties of a random medium or a random field.
Sulis, William H
2017-10-01
Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.
State-space-split method for some generalized Fokker-Planck-Kolmogorov equations in high dimensions.
Er, Guo-Kang; Iu, Vai Pan
2012-06-01
The state-space-split method for solving the Fokker-Planck-Kolmogorov equations in high dimensions is extended to solving the generalized Fokker-Planck-Kolmogorov equations in high dimensions for stochastic dynamical systems with a polynomial type of nonlinearity and excited by Poissonian white noise. The probabilistic solution of the motion of the stretched Euler-Bernoulli beam with cubic nonlinearity and excited by uniformly distributed Poissonian white noise is analyzed with the presented solution procedure. The numerical analysis shows that the results obtained with the state-space-split method together with the exponential polynomial closure method are close to those obtained with the Monte Carlo simulation when the relative value of the basic system relaxation time and the mean arrival time of the Poissonian impulse is in some limited range.
Lyapunov Exponents and Kolmogorov-Sinai Entropy for the Lorentz Gas at Low Densities
van Beijeren, Henk; Dorfman, J. R.
1995-05-01
The Lyapunov exponents and the Kolmogorov-Sinai (KS) entropy for a two-dimensional Lorentz gas at low densities are defined for general nonequilibrium states and calculated with the use of a Lorentz-Boltzmann type equation. In equilibrium the density dependence of these quantities, predicted by Krylov, is recovered and explicit expressions are obtained. The relationship between KS entropy, Lyapunov exponents, and diffusion coefficients, developed by Gaspard and Nicolis, is generalized to a wide class of nonequilibrium states.
Randomness Representation of Turbulence in Canopy Flows Using Kolmogorov Complexity Measures
Dragutin Mihailović
2017-09-01
Full Text Available Turbulence is often expressed in terms of either irregular or random fluid flows, without quantification. In this paper, a methodology to evaluate the randomness of the turbulence using measures based on the Kolmogorov complexity (KC is proposed. This methodology is applied to experimental data from a turbulent flow developing in a laboratory channel with canopy of three different densities. The methodology is even compared with the traditional approach based on classical turbulence statistics.
Edward, Jimenez; Hector, Mosquera; Marco, Cortez; Jimenez, Esteban; Ayala, Carlos E.; Gustavo, Lopez; Ullrich, Stahl
2016-01-01
In this work we show that the dynamics of chemical reactions of order zero, one and two have a representation through logistics probability. This probability is robust, stable and complies systemically with the differential equation of Fisher Kolmogorov (F K). It is robust, because in theorem 1 and theorem 3 differential equations of diffusion and heat transfer are obtained, where the temperature plays a key role. Also, the Eikonal equation of wave mechanics allows us to construct the heat eq...
Levchenko, E. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2014-04-01
A class of nonlinear symmetry operators has been constructed for the many-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation quadratic in independent variables and derivatives. The construction of each symmetry operator includes an interwining operator for the auxiliary linear equations and additional nonlinear algebraic conditions. Symmetry operators for the one-dimensional equation with a constant influence function have been constructed in explicit form and used to obtain a countable set of exact solutions.
Levchenko, E. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2017-06-01
The one-dimensional Fokker-Planck-Kolmogorov equation with a special type of nonlocal quadratic nonlinearity is represented as a consistent system of differential equations, including a dynamical system describing the evolution of the moments of the unknown function. Lie symmetries are found for the consistent system using methods of classical group analysis. An example of an invariant-group solution obtained with an additional integral constraint imposed on the system is considered.
Towards events recognition in a distributed fiber-optic sensor system: Kolmogorov-Zurbenko filtering
Fedorov, Aleksey; Zhirnov, Andrey; Nesterov, Evgeniy; Namiot, Dmitry; Pnev, Alexey; Karasik, Valery
2015-01-01
The paper is about de-noising procedures aimed on events recognition in signals from a distributed fiber-optic vibration sensor system based on the phase-sensitive optical time-domain reflectometry. We report experimental results on recognition of several classes of events in a seismic background. A de-noising procedure uses the framework of the time-series analysis and Kolmogorov-Zurbenko filtering. We demonstrate that this approach allows revealing signatures of several classes of events.
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...
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.
On the Existence of the Kolmogorov Inertial Range in the Terrestrial Magnetosheath Turbulence
Huang, S Y; Sahraoui, F; Yuan, Z G; Deng, X H
2016-01-01
In the solar wind, power spectral density (PSD) of the magnetic field fluctuations generally follow the so-called Kolmogorov spectrum f^-5/3 in the inertial range, where the dynamics is thought to be dominated by nonlinear interactions between counter-propagating incompressible Alfv\\'en wave parquets. These features are thought to be ubiquitous in space plasmas. The present study gives a new and more complex picture of magnetohydrodynamics (MHD) turbulence as observed in the terrestrial magnetosheath. The study uses three years of in-situ data from the Cluster mission to explore the nature of the magnetic fluctuations at MHD scales in different locations within the magnetosheath, including flanks and subsolar regions. It is found that the magnetic field fluctuations at MHD scales generally have a PSD close to f^-1 (shallower than the Kolmogorov one f^-5/3) down to the ion characteristic scale, which recalls the energy containing scales of solar wind turbulence. The Kolmogorov spectrum is observed only away fr...
Tao, Rumao; Si, Lei; Ma, Yanxing; Zhou, Pu; Liu, Zejin
2012-08-10
The propagation properties of coherently combined truncated laser beam arrays with beam distortions through non-Kolmogorov turbulence are studied in detail both analytically and numerically. The analytical expressions for the average intensity and the beam width of coherently combined truncated laser beam arrays with beam distortions propagating through turbulence are derived based on the combination of statistical optics methods and the extended Huygens-Fresnel principle. The effect of beam distortions, such as amplitude modulation and phase fluctuation, is studied by numerical examples. The numerical results reveal that phase fluctuations have significant influence on the spreading of coherently combined truncated laser beam arrays in non-Kolmogorov turbulence, and the effects of the phase fluctuations can be negligible as long as the phase fluctuations are controlled under a certain level, i.e., a>0.05 for the situation considered in the paper. Furthermore, large phase fluctuations can convert the beam distribution rapidly to a Gaussian form, vary the spreading, weaken the optimum truncation effects, and suppress the dependence of spreading on the parameters of the non-Kolmogorov turbulence.
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.
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.
OPTIMIZING EUCALYPTUS PULP REFINING
VailManfredi
2004-01-01
This paper discusses the refining of bleachedeucalyptus kraft pulp (BEKP).Pilot plant tests were carded out in to optimize therefining process and to identify the effects of refiningvariables on final paper quality and process costs.The following parameters are discussed: pulpconsistency, disk pattern design, refiner speed,energy input, refiner configuration (parallel or serial)and refining intensity.The effects of refining on pulp fibers were evaluatedagainst the pulp quality properties, such as physicalstrengths, bulk, opacity and porosity, as well as theinteractions with papermaking process, such as papermachine runnability, paper breaks and refiningcontrol.The results showed that process optimization,considering pulp quality and refining costs, wereobtained when eucalyptus pulp is refined under thelowest intensity and the highest pulp consistencypossible. Changes on the operational refiningconditions will have the highest impact on totalenergy requirements (costs) without any significanteffect on final paper properties.It was also observed that classical ways to control theindustrial operation, such as those based on drainagemeasurements, do not represent the best alternative tomaximize the final paper properties neither the papermachine runability.
A Lagrangian particle method with remeshing for tracer transport on the sphere
Bosler, Peter A.; Kent, James; Krasny, Robert; Jablonowski, Christiane
2017-07-01
A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracer integral, and preservation of nonlinear correlation in a pair of tracers. We compare results obtained using LPM and the Lin-Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.
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.
李向正; 张卫国; 原三领
2013-01-01
作为一种重要的反应扩散方程, Kolmogorov-Pet rovskii-Piskunov方程(简称KPP方程)具有重要的研究价值.KPP方程行波系统的无穷远奇点是高阶奇点中的不定号情形,以往对这种情形的处理不够简洁.提出了一种新的处理方法,以简洁的方式获得了该行系统无穷远奇点的定性结构.这一方法还可用于其它一些系统.
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
Refined Semilattices of Semigroups
Liang Zhang; K.P. Shum; Ronghua Zhang
2001-01-01
In this paper, we introduce the concept of refined semilattices of semigroups. This is a modified concept of the generally strong semilattice of semigroups initiated by Zhang and Huang. By using the concept of generally strong semilattice, Zhang and Huang showed that a regular band can be expressed by a generally strong semilattice of rectangular bands. However, the proof of the associativity for the multiplication is not complete and there exist some gaps in their construction of regular bands. We now revise the generally strong semilattices and call them refined semilattices. In this way, we are able to remove the gaps,and the associative law of the multiplication can be verified. As an application, we prove that a band is regular if and only if it is a refined semilattice of rectangular bands. In fact, refined semilattices provide a new device in the construction of new semigroups from the old ones.
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.
Refinement by interface instantiation
Hallerstede, Stefan; Hoang, Thai Son
2012-01-01
be easily refined. Our first contribution hence is a proposal for a new construct called interface that encapsulates the external variables, along with a mechanism for interface instantiation. Using the new construct and mechanism, external variables can be refined consistently. Our second contribution...... is an approach for verifying the correctness of Event-B extensions using the supporting Rodin tool. We illustrate our approach by proving the correctness of interface instantiation....
NAFTA opportunities: Petroleum refining
1993-01-01
The North American Free Trade Agreement (NAFTA) creates a more transparent environment for the sale of refined petroleum products to Mexico, and locks in access to Canada's relatively open market for these products. Canada and Mexico are sizable United States export markets for refined petroleum products, with exports of $556 million and $864 million, respectively, in 1992. These markets represent approximately 24 percent of total U.S. exports of these goods.
Bozzelli, Laura; French, Tim; Hales, James; Pinchinat, Sophie
2012-01-01
In this paper we present refinement modal logic. A refinement is like a bisimulation, except that from the three relational requirements only 'atoms' and 'back' need to be satisfied. Our logic contains a new operator 'forall' in additional to the standard modalities 'Box' for each agent. The operator 'forall' acts as a quantifier over the set of all refinements of a given model. We call it the refinement operator. As a variation on a bisimulation quantifier, it can be seen as a refinement quantifier over a variable not occurring in the formula bound by the operator. The logic combines the simplicity of multi-agent modal logic with some powers of monadic second order quantification. We present a sound and complete axiomatization of multiagent refinement modal logic. We also present an extension of the logic to the modal mu-calculus, and an axiomatization for the single-agent version of this logic. Examples and applications are also discussed: to software verification and design (the set of agents can also be s...
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.
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.
Use of the 4/5 Kolmogorov equation for describing some characteristics of fully developed turbulence
Tatarskii, V. I.
2005-03-01
The Kolmogorov equation, which relates the second-order structure function Dll(r ) and the third-ordrer structure function Dlll(r ), may be presented as a closed linear integrodifferential equation for the probability distribution function W(U ,r) of longitudinal velocity difference U. In general, without any restrictions, the function of two variables W(U ,r) may be presented as [Dll(r )]-1/2F(U/√Dll(r ) ,r). As a first approximation, we neglect dependence of F on the second argument r. In this approximation (self-similarity of the probability density function), the integrodifferential equation for W reduces to the ordinary nonlinear differential equation for Dll(r ). It follows from this equation that for r →∞ the function Dll(r )˜r2/3. This consideration does not use the 1941 Kolmogorov hypothesis that is based on dimension analysis. Any deviations from the 2/3 law, including intermittency effects, must be related to the violation of the above-mentioned self-similarity of W, i.e., with the additional dependence of F on the second argument r. On the basis of experimental data, we suggest a simple model of W, which allows us to describe deviations from the 2/3 law, caused by intermittency, and describe the local exponents κ in the structure functions ⟨∣U(r)∣ρ⟩˜rκ(ρ ) for moderate ρ. The so called "bottleneck effect" also can be described by 4/5 Kolmogorov equation.
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.
Towards a definition of the Quantum Ergodic Hierarchy: Kolmogorov and Bernoulli systems
Gomez, Ignacio; Castagnino, Mario
2014-01-01
In this paper we translate the two higher levels of the Ergodic Hierarchy [11], the Kolmogorov level and the Bernoulli level, to quantum language. Moreover, this paper can be considered as the second part of [3]. As in [3], we consider the formalism where the states are positive functionals on the algebra of observables and we use the properties of the Wigner transform [12]. We illustrate the physical relevance of the Quantum Ergodic Hierarchy with two emblematic examples of the literature: the Casati-Prosen model [13,14] and the kicked rotator [6-8].
LT^2C^2: A language of thought with Turing-computable Kolmogorov complexity
Santiago Figueira
2013-03-01
Full Text Available In this paper, we present a theoretical effort to connect the theory of program size to psychology by implementing a concrete language of thought with Turing-computable Kolmogorov complexity (LT^2C^2 satisfying the following requirements: 1 to be simple enough so that the complexity of any given finite binary sequence can be computed, 2 to be based on tangible operations of human reasoning (printing, repeating,. . . , 3 to be sufficiently powerful to generate all possible sequences but not too powerful as to identify regularities which would be invisible to humans. We first formalize LT^2C^2, giving its syntax and semantics, and defining an adequate notion of program size. Our setting leads to a Kolmogorov complexity function relative to LT^2C^2 which is computable in polynomial time, and it also induces a prediction algorithm in the spirit of Solomonoff’s inductive inference theory. We then prove the efficacy of this language by investigating regularities in strings produced by participants attempting to generate random strings. Participants had a profound understanding of randomness and hence avoided typical misconceptions such as exaggerating the number of alternations. We reasoned that remaining regularities would express the algorithmic nature of human thoughts, revealed in the form of specific patterns. Kolmogorov complexity relative to LT^2C^2 passed three expected tests examined here: 1 human sequences were less complex than control PRNG sequences, 2 human sequences were not stationary showing decreasing values of complexity resulting from fatigue 3 each individual showed traces of algorithmic stability since fitting of partial data was more effective to predict subsequent data than average fits. This work extends on previous efforts to combine notions of Kolmogorov complexity theory and algorithmic information theory to psychology, by explicitly proposing a language which may describe the patterns of human thoughts.Received: 12
Finite sampling inequalities: an application to two-sample Kolmogorov-Smirnov statistics.
Greene, Evan; Wellner, Jon A
2016-12-01
We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our development complements recent results by Wei and Dudley (2012) concerning exponential bounds for two-sided Kolmogorov - Smirnov statistics by giving corresponding results for one-sided statistics with emphasis on "adjusted" inequalities of the type proved originally by Dvoretzky et al. (1956) and by Massart (1990) for one-sample versions of these statistics.
Detecting changes in maps of gamma spectra with Kolmogorov-Smirnov tests
Reinhart, Alex; Athey, Alex
2015-01-01
Various security, regulatory, and consequence management agencies are interested in continuously monitoring wide areas for unexpected changes in radioactivity. Existing detection systems are designed to search for radioactive sources but are not suited to repeat mapping and change detection. Using a set of daily spectral observations collected at the Pickle Research Campus, we improved on the prior Spectral Comparison Ratio Anomaly Mapping (SCRAM) algorithm and developed a new method based on two-sample Kolmogorov-Smirnov tests to detect sudden spectral changes. We also designed simulations and visualizations of statistical power to compare methods and guide deployment scenarios.
Prozorov, A. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2015-07-01
Asymptotic solutions of the nonlocal, one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald-Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.
Scaling and renormalization for the Kolmogorov-Petrovskii-Piskunov equationwith turbulent convection
Fedotov, Sergei
1997-03-01
The problem of determining the upper bounds for the ensemble-averaged reaction front position and speed in a fully developed three-dimensional turbulent flow has been examined, in which the reaction is of Kolmogorov-Petrovskii-Piskunov type and turbulent velocity is a Gaussian random field exhibiting long-range correlations and infrared divergence in the limit of large Reynolds number. An asymptotic method has been developed that gives the general formalism for determining the upper bounds for reaction front in the long-time, large-distance limit. Two anomalous scaling regimes and corresponding scaling functions have been determined by the use of exact renormalization procedure.
Dynamics, integrability and topology for some classes of Kolmogorov Hamiltonian systems in R+4
Llibre, Jaume; Xiao, Dongmei
2017-02-01
In this paper we first give the sufficient and necessary conditions in order that two classes of polynomial Kolmogorov systems in R+4 are Hamiltonian systems. Then we study the integrability of these Hamiltonian systems in the Liouville sense. Finally, we investigate the global dynamics of the completely integrable Lotka-Volterra Hamiltonian systems in R+4. As an application of the invariant subsets of these systems, we obtain topological classifications of the 3-submanifolds in R+4 defined by the hypersurfaces axy + bzw + cx2 y + dxy2 + ez2 w + fzw2 = h, where a , b , c , d , e , f , w and h are real constants.
Javaheri Javid, Mohammad Ali; Blackwell, Tim; Zimmer, Robert; Majid al-Rifaie, Mohammad
2016-04-01
Shannon entropy fails to discriminate structurally different patterns in two-dimensional images. We have adapted information gain measure and Kolmogorov complexity to overcome the shortcomings of entropy as a measure of image structure. The measures are customised to robustly quantify the complexity of images resulting from multi-state cellular automata (CA). Experiments with a two-dimensional multi-state cellular automaton demonstrate that these measures are able to predict some of the structural characteristics, symmetry and orientation of CA generated patterns.
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.
Mabied, Ahmed F; Müller, Melanie; Dinnebier, Robert E; Nozawa, Shunsuke; Hoshino, Manabu; Tomita, Ayana; Sato, Tokushi; Adachi, Shin-ichi
2012-08-01
The [4π + 4π] photodimerization process of the 9-substituted anthracene derivative crystalline 9-methylanthracene (9-MA) was investigated using time-resolved X-ray powder diffraction. The study was carried out in-situ using a CCD area detector. Sequential and parametric Rietveld refinement was applied for quantitative phase analysis. The results of traditional sequential Rietveld refinement showed that the evolution of the dimerization process can be described using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. The parameters of the JMAK equation were obtained successfully by parametric Rietveld refinement and suggest that the reaction follows heterogeneous nucleation and one-dimensional growth with a decreasing nucleation rate.
Constancio, Silva
2006-07-01
In 2004, refining margins showed a clear improvement that persisted throughout the first three quarters of 2005. This enabled oil companies to post significantly higher earnings for their refining activity in 2004 compared to 2003, with the results of the first half of 2005 confirming this trend. As for petrochemicals, despite a steady rise in the naphtha price, higher cash margins enabled a turnaround in 2004 as well as a clear improvement in oil company financial performance that should continue in 2005, judging by the net income figures reported for the first half-year. Despite this favorable business environment, capital expenditure in refining and petrochemicals remained at a low level, especially investment in new capacity, but a number of projects are being planned for the next five years. (author)
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.
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...
Coupled Eulerian-Lagrangian transport of large debris by tsunamis
Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos
2016-04-01
Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-Eulerian coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian and Eulerian solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed Eulerian-Lagrangian formulation and the resolution of the mesh used in the Eulerian solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the
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.
Verborgh, Ruben
2013-01-01
The book is styled on a Cookbook, containing recipes - combined with free datasets - which will turn readers into proficient OpenRefine users in the fastest possible way.This book is targeted at anyone who works on or handles a large amount of data. No prior knowledge of OpenRefine is required, as we start from the very beginning and gradually reveal more advanced features. You don't even need your own dataset, as we provide example data to try out the book's recipes.
Lagrangian methods of cosmic web classification
Fisher, J. D.; Faltenbacher, A.; Johnson, M. S. T.
2016-05-01
The cosmic web defines the large-scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid-based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or haloes) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian nature admits a straightforward inclusion of the Hubble flow negating the necessity of a visually defined threshold value which is commonly employed by grid-based classification methods.
Inverse Variational Problem for Nonstandard Lagrangians
Saha, A.; Talukdar, B.
2014-06-01
In the mathematical physics literature the nonstandard Lagrangians (NSLs) were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of the equation of motion and solve the associated inverse problem to obtain some of the existing results for NSLs. In addition, we provide a number of alternative Lagrangian representations. The case studies envisaged by us include (i) the usual modified Emden-type equation, (ii) Emden-type equation with dissipative term quadratic in velocity, (iii) Lotka-Volterra model and (vi) a number of the generic equations for dissipative-like dynamical systems. Our method works for nonstandard Lagrangians corresponding to the usual action integral of mechanical systems but requires modification for those associated with the modified actions like S =∫abe L(x ,x˙ , t) dt and S =∫abL 1 - γ(x ,x˙ , t) dt because in the latter case one cannot construct expressions for the Jacobi integrals.
Lagrangian approach and dissipative magnetic systems
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.
Cellular Signaling Networks Function as Generalized Wiener-Kolmogorov Filters to Suppress Noise
Hinczewski, Michael; Thirumalai, D.
2014-10-01
Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers. We show that this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov optimal noise filter. Using concepts from umbral calculus, we generalize the linear Wiener-Kolmogorov theory, originally introduced in the context of communication and control engineering, to take nonlinear signal transduction and discrete molecule populations into account. This allows us to derive rigorous constraints for efficient noise reduction in this biochemical system. Our mathematical formalism yields bounds on filter performance in cases important to cellular function—such as ultrasensitive response to stimuli. We highlight features of the system relevant for optimizing filter efficiency, encoded in a single, measurable, dimensionless parameter. Our theory, which describes noise control in a large class of signal transduction networks, is also useful both for the design of synthetic biochemical signaling pathways and the manipulation of pathways through experimental probes such as oscillatory input.
Cellular Signaling Networks Function as Generalized Wiener-Kolmogorov Filters to Suppress Noise
Michael Hinczewski
2014-10-01
Full Text Available Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers. We show that this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov optimal noise filter. Using concepts from umbral calculus, we generalize the linear Wiener-Kolmogorov theory, originally introduced in the context of communication and control engineering, to take nonlinear signal transduction and discrete molecule populations into account. This allows us to derive rigorous constraints for efficient noise reduction in this biochemical system. Our mathematical formalism yields bounds on filter performance in cases important to cellular function—such as ultrasensitive response to stimuli. We highlight features of the system relevant for optimizing filter efficiency, encoded in a single, measurable, dimensionless parameter. Our theory, which describes noise control in a large class of signal transduction networks, is also useful both for the design of synthetic biochemical signaling pathways and the manipulation of pathways through experimental probes such as oscillatory input.
A Kolmogorov Complexity View of Analogy: From Logical Modeling to Experimentations
Bayoudh, Meriam; Prade, Henri; Richard, Gilles
Analogical reasoning is considered as one of the main mechanisms underlying human intelligence and creativity, allowing the paradigm shift essential to a creative process. More specific is the notion of analogical proportion like "2 is to 4 as 5 is to 10" or "read is to reader as lecture is to lecturer": such statements can be precisely described within an algebraic framework. When the proportion holds between concepts as in "engine is to car as heart is to human" or "wine is to France as beer is to England", applying an algebraic framework is less straightforward and a new way to understand analogical proportions on the basis of Kolmogorov complexity theory may seem more appropriate. This viewpoint has been used to develop a classifier detecting analogies in natural language. Despite their apparent difference, it is quite clear that the two viewpoints should be strongly related. In this paper, we investigate the link between a purely abstract view of analogical proportions and a definition based on Kolmogorov complexity theory. This theory is used as a backbone to experiment a classifier of natural language analogies whose results are consistent with the abstract setting.
An Experimental and Numerical Investigation of Bifurcations in a Kolmogorov-Like Flow
Tithof, Jeffrey; Pallantla, Ravi; Grigoriev, Roman O; Schatz, Michael F
2016-01-01
We present a combined experimental and numerical study of the primary and secondary bifurcations for a Kolmogorov-like flow. The experimental system is a quasi-two-dimensional incompressible fluid flow consisting of two immiscible layers of fluid for which electromagnetic forces drive a shear flow that approximates Kolmogorov flow. The two-dimensional (2D) direct numerical simulations (DNS) integrate a depth-averaged version of the full three-dimensional Navier-Stokes equations Suri ${\\it et}$ ${\\it al.}$ (2014), which contains a (non-unity) prefactor on the advection term, previously unaccounted for in all studies. Specifically, we present three separate 2D DNS: one that is doubly-periodic, one that is singly-periodic, and one that is non-periodic (i.e. no-slip is imposed at the lateral boundaries). All parameters are directly calculated or measured from experimental quantities. We show that inclusion of the advection term prefactor substantially improves agreement between experiment and numerics. However, g...
Hackl, J. F.; Yeung, P. K.; Sawford, B. L.
2009-11-01
Numerical simulations at up to (4096^3) grid resolution have been conducted on machines with very large processor counts to obtain the statistics of Lagrangian particle pairs and tetrads in turbulent relative dispersion. Richardson-Obukhov scaling for mean-square pair separation adjusted for initial conditions is observed for intermediate initial separations, in support of prior estimates of about 0.6 for Richardson's constant. Simulations at (Rλ 650) have also been conducted for sufficient duration to obtain fully converged exit time statistics for independently moving particles at very large scales. The fact that all particle pairs reach such large scales of separation means the inertial subrange of exit times is also captured accurately. The results show Kolmogorov scaling for positive moments of exit time, but a strong dependence on initial separations for inverse moments. Inertial-range estimates of tetrad shape factors are reinforced by simulations at Taylor-scale Reynolds numbers up to about 1100. Tetrad shape parameters conditioned on cluster size are also examined in order to understand geometric features of turbulent dispersion in more detail.
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
Incremental Bisimulation Abstraction Refinement
Godskesen, Jens Christian; Song, Lei; Zhang, Lijun
2013-01-01
an abstraction refinement approach for the probabilistic computation tree logic (PCTL), which is based on incrementally computing a sequence of may- and must-quotient automata. These are induced by depth-bounded bisimulation equivalences of increasing depth. The approach is both sound and complete, since...
Super-miniature multi-hot-film probe for sub-Kolmogorov resolution in high-Re turbulence
Borisenkov, Y.; Kholmyansky, M.; Krylov, S.; Liberzon, A.; Tsinober, A.
2011-12-01
The work reported here is motivated by the discovery of far more important role played by the sub-Kolmogorov scales than commonly believed. The first part is devoted to an overview of main results and issues that prompted the present developments. The emphasis is made on a number of manifestations of nonlocal nature of turbulence involving direct and bidirectional coupling of conventionally-defined inertial and dissipative ranges showing (a) that both concepts are ill-posed and (b) that further progress requires sub-Kolmogorov resolution. The second part contains a presentation on design, manufacturing and tests in laboratory of a micro-hot-film sensor using modern micro-fabrication technologies, as a basis for a probe of much smaller scale than available today with access to quantities like vorticity and strain at sub-Kolmogorov scales in high-Reynolds-number flows.
Zhang, Tao; Liu, Yi-Dong; Wang, Jiandong; Liu, Pusheng; Yang, Yuanjie
2016-09-01
It is generally true that the orbital angular momentum (OAM) mode persistently degenerate when a vortex beam propagates in the atmospheric turbulence. Here, however, we unveil an interesting self-recovery effect of OAM mode of the circular beam (CiB) in weak non-Kolmogorov turbulence. We show that the CiB displays the self-focusing effect and has clear focus in the weak non-Kolmogorov turbulence if we choose proper complex parameters, and the detection probability of the original OAM mode reaches the maximum at the focus. Our study proposes a method to alleviate the turbulent effects on OAM-based communication.
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...
Perspicuity and Granularity in Refinement
Boiten, Eerke
2011-01-01
This paper reconsiders refinements which introduce actions on the concrete level which were not present at the abstract level. It draws a distinction between concrete actions which are "perspicuous" at the abstract level, and changes of granularity of actions between different levels of abstraction. The main contribution of this paper is in exploring the relation between these different methods of "action refinement", and the basic refinement relation that is used. In particular, it shows how the "refining skip" method is incompatible with failures-based refinement relations, and consequently some decisions in designing Event-B refinement are entangled.
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.
Refinement for Administrative Policies
Dekker, MAC; Etalle, S Sandro
2007-01-01
Flexibility of management is an important requisite for access control systems as it allows users to adapt the access control system in accordance with practical requirements. This paper builds on earlier work where we defined administrative policies for a general class of RBAC models. We present a formal definition of administrative refinnement and we show that there is an ordering for administrative privileges which yields administrative refinements of policies. We argue (by giving an examp...
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.
Edward, Jimenez; Marco, Cortez; Jimenez, Esteban; Ayala, Carlos E; Gustavo, Lopez; Ullrich, Stahl
2016-01-01
In this work we show that the dynamics of chemical reactions of order zero, one and two have a representation through logistics probability. This probability is robust, stable and complies systemically with the differential equation of Fisher Kolmogorov (F K). It is robust, because in theorem 1 and theorem 3 differential equations of diffusion and heat transfer are obtained, where the temperature plays a key role. Also, the Eikonal equation of wave mechanics allows us to construct the heat equation. In Lemma 2, Fick diffusion equation is demonstrated. It is stable, because probability convergence when t converge infinitum, gives us new ways to analyze the kinetics of a reaction integrally, in Corollary 5. Finally, the theoretically and experimentally obtained algorithms and results support the convergence in probability of the quantum tunnel effect and chemical reactions for: hydrogen production at ultra low temperature and catalytic cracking of asphalt at high temperature.
Maximum Entropy Production vs. Kolmogorov-Sinai Entropy in a Constrained ASEP Model
Martin Mihelich
2014-02-01
Full Text Available The asymmetric simple exclusion process (ASEP has become a paradigmatic toy-model of a non-equilibrium system, and much effort has been made in the past decades to compute exactly its statistics for given dynamical rules. Here, a different approach is developed; analogously to the equilibrium situation, we consider that the dynamical rules are not exactly known. Allowing for the transition rate to vary, we show that the dynamical rules that maximize the entropy production and those that maximise the rate of variation of the dynamical entropy, known as the Kolmogorov-Sinai entropy coincide with good accuracy. We study the dependence of this agreement on the size of the system and the couplings with the reservoirs, for the original ASEP and a variant with Langmuir kinetics.
Pang, Hyunsoo; Shin, Young-Han; Ihm, Dongchul; Lee, Eok Kyun; Kum, Oyeon
2000-11-01
Molecular dynamics simulations were performed for soft- and hard-sphere systems, for number densities ranging from 0.5 to 1.0, and the Kolmogorov-Sinai entropy (KS entropy) and self-diffusion coefficients were calculated. It is found that the KS entropy, when expressed in terms of average collision frequency, is uniquely related to the self-diffusion coefficient by a simple scaling law. The dependence of the KS entropy on average collision frequency and number density was also explored. Numerical results show that the scaling laws proposed by Dzugutov, and by Beijeren, Dorfman, Posch, and Dellago, can be applied to both soft- and hard-sphere systems by changing to more generalized forms.
Velocity Profile in a Two-Layer Kolmogorov-Like Flow
Suri, Balachandra; Mitchell, Radford; Grigoriev, Roman O; Schatz, Michael F
2013-01-01
In this article we discuss flows in shallow, stratified horizontal layers of two immiscible fluids. The top layer is an electrolyte which is electromagnetically driven and the bottom layer is a dielectric fluid. Using a quasi-two-dimensional approximation, we derive the depth-averaged two-dimensional (2D) vorticity equation which includes a prefactor to the advection term, previously unaccounted for. In addition, we study how the horizontal components of velocity vary in the vertical direction. For a Kolmogorov-like flow, we evaluate analytical expressions for the coefficients in the generalized 2D vorticity equation, uncovering their dependence on experimental parameters. To test the accuracy of these estimates, we experimentally measure the horizontal velocity fields at the free-surface and at the electrolyte-dielectric interface using particle image velocimetry (PIV). We show that there is excellent agreement between the analytical predictions and the experimental measurements. Our analysis shows that by i...
Localised structures in 2D Kolmogorov flow in large domains: Kinks, Snakes and 'Kolmotons'
Lucas, Dan
2013-01-01
Kolmogorov flow in two dimensions - the 2D Navier-Stokes equations with a sinusoidal body force - is considered over extended periodic domains to reveal localised spatiotemporal complexity. The flow response mimicks the forcing at small forcing amplitudes but beyond a critical value, the vorticity of the flow localises into `kink' structures. These kinks act as building blocks for multiple localised attractors which emerge as the forcing further intensifies. Most notable of these is a temporally-periodic state which consists of two intertwined and wiggling kinks (resembling a snake) bordered by two steady chaperoning kinks. As the forcing is increased, this `snake' experiences a period doubling cascade to spatially-localised chaos before becoming a localised chaotic repeller through a boundary crisis. Further interesting dynamics arise when these kink and snake structures are confronted with each other. The most eye-catching example of this is the `particle-like' interaction of propagating kinks (christened `...
Calculating Kolmogorov complexity from the output frequency distributions of small Turing machines.
Soler-Toscano, Fernando; Zenil, Hector; Delahaye, Jean-Paul; Gauvrit, Nicolas
2014-01-01
Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The method is an alternative to the traditional lossless compression algorithms, which it may complement, the two being serviceable for different string lengths. We provide a thorough analysis for all Σ(n=1)(11) 2(n) binary strings of length nalgorithms, this work promises to deliver a range of applications, and to provide insight into the question of complexity calculation of finite (and short) strings. Additional material can be found at the Algorithmic Nature Group website at http://www.algorithmicnature.org. An Online Algorithmic Complexity Calculator implementing this technique and making the data available to the research community is accessible at http://www.complexitycalculator.com.
Kolmogorov's differential equations and positive semigroups on first moment sequence spaces.
Martcheva, Maia; Thieme, Horst R; Dhirasakdanon, Thanate
2006-10-01
Spatially implicit metapopulation models with discrete patch-size structure and host-macroparasite models which distinguish hosts by their parasite loads lead to infinite systems of ordinary differential equations. In several papers, a this-related theory will be developed in sufficient generality to cover these applications. In this paper the linear foundations are laid. They are of own interest as they apply to continuous-time population growth processes (Markov chains). Conditions are derived that the solutions of an infinite linear system of differential equations, known as Kolmogorov's differential equations, induce a C0-semigroup on an appropriate sequence space allowing for first moments. We derive estimates for the growth bound and the essential growth bound and study the asymptotic behavior. Our results will be illustrated for birth and death processes with immigration and catastrophes.
Rica, Sergio
2016-01-01
The recent observation of gravitational waves, stimulates the question of the longtime evolution of the space-time fluctuations. Gravitational waves interact themselves through the nonlinear character of Einstein's equations of general relativity. This nonlinear wave interaction allows the spectral energy transfer from mode to mode. According to the wave turbulence theory, the weakly nonlinear interaction of gravitational waves leads to the existence of an irreversible kinetic regime that dominates the longtime evolution. The resulting kinetic equation suggests the existence of an equilibrium wave spectrum and the existence of a non-equilibrium Kolmogorov-Zakharov spectrum for spatio-temporal fluctuations. Evidence of these solutions extracted in the fluctuating signal of the recent observations will be discussed in the paper. Probably, the present results would be pertinent in the new age of development of gravitational astronomy, as well as, in new tests of General Relativity.
The closed-form solution of the reduced Fokker-Planck-Kolmogorov equation for nonlinear systems
Chen, Lincong; Sun, Jian-Qiao
2016-12-01
In this paper, we propose a new method to obtain the closed-form solution of the reduced Fokker-Planck-Kolmogorov equation for single degree of freedom nonlinear systems under external and parametric Gaussian white noise excitations. The assumed stationary probability density function consists of an exponential polynomial with a logarithmic term to account for parametric excitations. The undetermined coefficients in the assumed solution are computed with the help of an iterative method of weighted residue. We have found that the iterative process generates a sequence of solutions that converge to the exact solutions if they exist. Three examples with known exact steady-state probability density functions are used to demonstrate the convergence of the proposed method.
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.
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.
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.
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.
Beijeren, H. van; Zon, R. van; Dorfman, J.R.
2000-01-01
The kinetic theory of gases provides methods for calculating Lyapunov exponents and other quantities, such as Kolmogorov-Sinai entropies, that characterize the chaotic behavior of hard-ball gases. Here we illustrate the use of these methods for calculating the Kolmogorov-Sinai entropy, and the
Capelli, Silvia C; Bürgi, Hans-Beat; Dittrich, Birger; Grabowsky, Simon; Jayatilaka, Dylan
2014-09-01
Hirshfeld atom refinement (HAR) is a method which determines structural parameters from single-crystal X-ray diffraction data by using an aspherical atom partitioning of tailor-made ab initio quantum mechanical molecular electron densities without any further approximation. Here the original HAR method is extended by implementing an iterative procedure of successive cycles of electron density calculations, Hirshfeld atom scattering factor calculations and structural least-squares refinements, repeated until convergence. The importance of this iterative procedure is illustrated via the example of crystalline ammonia. The new HAR method is then applied to X-ray diffraction data of the dipeptide Gly-l-Ala measured at 12, 50, 100, 150, 220 and 295 K, using Hartree-Fock and BLYP density functional theory electron densities and three different basis sets. All positions and anisotropic displacement parameters (ADPs) are freely refined without constraints or restraints - even those for hydrogen atoms. The results are systematically compared with those from neutron diffraction experiments at the temperatures 12, 50, 150 and 295 K. Although non-hydrogen-atom ADPs differ by up to three combined standard uncertainties (csu's), all other structural parameters agree within less than 2 csu's. Using our best calculations (BLYP/cc-pVTZ, recommended for organic molecules), the accuracy of determining bond lengths involving hydrogen atoms from HAR is better than 0.009 Å for temperatures of 150 K or below; for hydrogen-atom ADPs it is better than 0.006 Å(2) as judged from the mean absolute X-ray minus neutron differences. These results are among the best ever obtained. Remarkably, the precision of determining bond lengths and ADPs for the hydrogen atoms from the HAR procedure is comparable with that from the neutron measurements - an outcome which is obtained with a routinely achievable resolution of the X-ray data of 0.65 Å.
Benazzi, E.; Alario, F
2004-07-01
In 2003, refining margins showed a clear improvement that continued throughout the first three quarters of 2004. Oil companies posted significantly higher earnings in 2003 compared to 2002, with the results of first quarter 2004 confirming this trend. Due to higher feedstock prices, the implementation of new capacity and more intense competition, the petrochemicals industry was not able to boost margins in 2003. In such difficult business conditions, aggravated by soaring crude prices, the petrochemicals industry is not likely to see any improvement in profitability before the second half of 2004. (author)
Benazzi, E
2003-07-01
Down sharply in 2002, refining margins showed a clear improvement in the first half-year of 2003. As a result, the earnings reported by oil companies for financial year 2002 were significantly lower than in 2001, but the prospects are brighter for 2003. In the petrochemicals sector, slow demand and higher feedstock prices eroded margins in 2002, especially in Europe and the United States. The financial results for the first part of 2003 seem to indicate that sector profitability will not improve before 2004. (author)
Deng Peng; Yuan Xiuhua; Zeng Yanan; Zhao Ming; Luo Hanjun, E-mail: yuanxh@mail.hust.edu.cn [Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, Hubei (China)
2011-02-01
In free-space optical communication links, atmospheric turbulence causes fluctuations in both the intensity and the phase of the received signal, affecting link performance. Most theoretical treatments have been described by Kolmogorov's power spectral density model through weak turbulence with constant wind speed. However, several experiments showed that Kolmogorov theory is sometimes incomplete to describe atmospheric turbulence properly, especially through the strong turbulence with variable wind speed, which is known to contribute significantly to the turbulence in the atmosphere. We present an optical turbulence model that incorporates into variable wind speed instead of constant value, a non-Kolmogorov power spectrum that uses a generalized exponent instead of constant standard exponent value 11/3, and a generalized amplitude factor instead of constant value 0.033. The free space optical communication performance for a Gaussian beam wave of scintillation index, mean signal-to-noise ratio
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.
Macromolecular crystallographic estructure refinement
Afonine, Pavel V.
2015-04-01
Full Text Available Model refinement is a key step in crystallographic structure determination that ensures final atomic structure of macromolecule represents measured diffraction data as good as possible. Several decades have been put into developing methods and computational tools to streamline this step. In this manuscript we provide a brief overview of major milestones of crystallographic computing and methods development pertinent to structure refinement.El refinamiento es un paso clave en el proceso de determinación de una estructura cristalográfica al garantizar que la estructura atómica de la macromolécula final represente de la mejor manera posible los datos de difracción. Han hecho falta varias décadas para poder desarrollar nuevos métodos y herramientas computacionales dirigidas a dinamizar esta etapa. En este artículo ofrecemos un breve resumen de los principales hitos en la computación cristalográfica y de los nuevos métodos relevantes para el refinamiento de estructuras.
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.
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.
Refines Efficiency Improvement
WRI
2002-05-15
Refinery processes that convert heavy oils to lighter distillate fuels require heating for distillation, hydrogen addition or carbon rejection (coking). Efficiency is limited by the formation of insoluble carbon-rich coke deposits. Heat exchangers and other refinery units must be shut down for mechanical coke removal, resulting in a significant loss of output and revenue. When a residuum is heated above the temperature at which pyrolysis occurs (340 C, 650 F), there is typically an induction period before coke formation begins (Magaril and Aksenova 1968, Wiehe 1993). To avoid fouling, refiners often stop heating a residuum before coke formation begins, using arbitrary criteria. In many cases, this heating is stopped sooner than need be, resulting in less than maximum product yield. Western Research Institute (WRI) has developed innovative Coking Index concepts (patent pending) which can be used for process control by refiners to heat residua to the threshold, but not beyond the point at which coke formation begins when petroleum residua materials are heated at pyrolysis temperatures (Schabron et al. 2001). The development of this universal predictor solves a long standing problem in petroleum refining. These Coking Indexes have great potential value in improving the efficiency of distillation processes. The Coking Indexes were found to apply to residua in a universal manner, and the theoretical basis for the indexes has been established (Schabron et al. 2001a, 2001b, 2001c). For the first time, a few simple measurements indicates how close undesired coke formation is on the coke formation induction time line. The Coking Indexes can lead to new process controls that can improve refinery distillation efficiency by several percentage points. Petroleum residua consist of an ordered continuum of solvated polar materials usually referred to as asphaltenes dispersed in a lower polarity solvent phase held together by intermediate polarity materials usually referred to as
Silvia C. Capelli
2014-09-01
Full Text Available Hirshfeld atom refinement (HAR is a method which determines structural parameters from single-crystal X-ray diffraction data by using an aspherical atom partitioning of tailor-made ab initio quantum mechanical molecular electron densities without any further approximation. Here the original HAR method is extended by implementing an iterative procedure of successive cycles of electron density calculations, Hirshfeld atom scattering factor calculations and structural least-squares refinements, repeated until convergence. The importance of this iterative procedure is illustrated via the example of crystalline ammonia. The new HAR method is then applied to X-ray diffraction data of the dipeptide Gly–l-Ala measured at 12, 50, 100, 150, 220 and 295 K, using Hartree–Fock and BLYP density functional theory electron densities and three different basis sets. All positions and anisotropic displacement parameters (ADPs are freely refined without constraints or restraints – even those for hydrogen atoms. The results are systematically compared with those from neutron diffraction experiments at the temperatures 12, 50, 150 and 295 K. Although non-hydrogen-atom ADPs differ by up to three combined standard uncertainties (csu's, all other structural parameters agree within less than 2 csu's. Using our best calculations (BLYP/cc-pVTZ, recommended for organic molecules, the accuracy of determining bond lengths involving hydrogen atoms from HAR is better than 0.009 Å for temperatures of 150 K or below; for hydrogen-atom ADPs it is better than 0.006 Å2 as judged from the mean absolute X-ray minus neutron differences. These results are among the best ever obtained. Remarkably, the precision of determining bond lengths and ADPs for the hydrogen atoms from the HAR procedure is comparable with that from the neutron measurements – an outcome which is obtained with a routinely achievable resolution of the X-ray data of 0.65 Å.
Zhi, Dong; Tao, Rumao; Zhou, Pu; Ma, Yanxing; Wu, Wuming; Wang, Xiaolin; Si, Lei
2017-03-01
A new ring Airy Gaussian (RAiG) vortex beam generation method by coherent combination of Gaussian beam array has been proposed. To validate the feasibility of this method, the propagation properties of the RAiG vortex beam and the coherent combining beam in vacuum have been studied and analyzed. From the comparisons of the intensity distributions and phase patterns along the propagation path, we can conclude that the coherent combining beam has the same properties as those of the ideal RAiG vortex beam. So this method can be used to obtain RAiG vortex beam in practice. Then the general analytical expression of the root-mean-square (RMS) beam width of the RAiG vortex beam, which is appropriately generated by coherent combining method, through anisotropic non-Kolmogorov turbulence has been derived. The influence of anisotropic turbulence on RMS beam width of the generated RAiG vortex beam has been numerically calculated. This generation method has good appropriation to the ideal RAiG vortex beam and is very useful for deriving the analytical expression of propagation properties through a random media. The conclusions are useful in practical applications, such as laser communication and remote sensing systems.
A Kolmogorov-Smirnov Based Test for Comparing the Predictive Accuracy of Two Sets of Forecasts
Hossein Hassani
2015-08-01
Full Text Available This paper introduces a complement statistical test for distinguishing between the predictive accuracy of two sets of forecasts. We propose a non-parametric test founded upon the principles of the Kolmogorov-Smirnov (KS test, referred to as the KS Predictive Accuracy (KSPA test. The KSPA test is able to serve two distinct purposes. Initially, the test seeks to determine whether there exists a statistically significant difference between the distribution of forecast errors, and secondly it exploits the principles of stochastic dominance to determine whether the forecasts with the lower error also reports a stochastically smaller error than forecasts from a competing model, and thereby enables distinguishing between the predictive accuracy of forecasts. We perform a simulation study for the size and power of the proposed test and report the results for different noise distributions, sample sizes and forecasting horizons. The simulation results indicate that the KSPA test is correctly sized, and robust in the face of varying forecasting horizons and sample sizes along with significant accuracy gains reported especially in the case of small sample sizes. Real world applications are also considered to illustrate the applicability of the proposed KSPA test in practice.
Calculating Kolmogorov complexity from the output frequency distributions of small Turing machines.
Fernando Soler-Toscano
Full Text Available Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The method is an alternative to the traditional lossless compression algorithms, which it may complement, the two being serviceable for different string lengths. We provide a thorough analysis for all Σ(n=1(11 2(n binary strings of length n<12 and for most strings of length 12≤n≤16 by running all ~2.5 x 10(13 Turing machines with 5 states and 2 symbols (8 x 22(9 with reduction techniques using the most standard formalism of Turing machines, used in for example the Busy Beaver problem. We address the question of stability and error estimation, the sensitivity of the continued application of the method for wider coverage and better accuracy, and provide statistical evidence suggesting robustness. As with compression algorithms, this work promises to deliver a range of applications, and to provide insight into the question of complexity calculation of finite (and short strings. Additional material can be found at the Algorithmic Nature Group website at http://www.algorithmicnature.org. An Online Algorithmic Complexity Calculator implementing this technique and making the data available to the research community is accessible at http://www.complexitycalculator.com.
Kolmogorov-Sinai entropy in field line diffusion by anisotropic magnetic turbulence
Milovanov, Alexander V [Associazione Euratom-ENEA sulla Fusione, Centro Ricerche Frascati, Via E. Fermi 45, C.P. 65, I-00044 Frascati, Rome (Italy); Bitane, Rehab [Laboratoire Cassiopee, UNSA, CNRS, Observatoire de la Cote d' Azur, BP 4229, 06304 Nice Cedex 4 (France); Zimbardo, Gaetano [Dipartimento di Fisica, Universita degli Studi della Calabria, Ponte P. Bucci, Cubo 31C, I-87036 Arcavacata di Rende (Italy)
2009-07-15
The Kolmogorov-Sinai (KS) entropy in turbulent diffusion of magnetic field lines is analyzed on the basis of a numerical simulation model and theoretical investigations. In the parameter range of strongly anisotropic magnetic turbulence the KS entropy is shown to deviate considerably from the earlier predicted scaling relations (1992 Rev. Mod. Phys. 64 961). In particular, a slowing down logarithmic behavior versus the so-called Kubo number R >> 1 (R = ({delta}B/B{sub 0}) ({xi}{sub ||}/{xi}{sub perpendicular}), where {delta}B/B{sub 0} is the ratio of the rms magnetic fluctuation field to the magnetic field strength, and {xi}{sub perpendicular} and {xi}{sub ||} are the correlation lengths in respective dimensions) is found instead of a power-law dependence. These discrepancies are explained from general principles of Hamiltonian dynamics. We discuss the implication of Hamiltonian properties in governing the paradigmatic 'percolation' transport, characterized by R {yields} {infinity}, associating it with the concept of pseudochaos (random non-chaotic dynamics with zero Lyapunov exponents). Applications of this study pertain to both fusion and astrophysical plasma and by mathematical analogy to problems outside the plasma physics.
Extensivity and additivity of the Kolmogorov-Sinai entropy for simple fluids
Das, Moupriya; Costa, Anthony B.; Green, Jason R.
2017-02-01
According to the van der Waals picture, attractive and repulsive forces play distinct roles in the structure of simple fluids. Here, we examine their roles in dynamics; specifically, in the degree of deterministic chaos using the Kolmogorov-Sinai (KS) entropy rate and the spectra of Lyapunov exponents. With computer simulations of three-dimensional Lennard-Jones and Weeks-Chandler-Andersen fluids, we find repulsive forces dictate these dynamical properties, with attractive forces reducing the KS entropy at a given thermodynamic state. Regardless of interparticle forces, the maximal Lyapunov exponent is intensive for systems ranging from 200 to 2000 particles. Our finite-size scaling analysis also shows that the KS entropy is both extensive (a linear function of system-size) and additive. Both temperature and density control the "dynamical chemical potential," the rate of linear growth of the KS entropy with system size. At fixed system-size, both the KS entropy and the largest exponent exhibit a maximum as a function of density. We attribute the maxima to the competition between two effects: as particles are forced to be in closer proximity, there is an enhancement from the sharp curvature of the repulsive potential and a suppression from the diminishing free volume and particle mobility. The extensivity and additivity of the KS entropy and the intensivity of the largest Lyapunov exponent, however, hold over a range of temperatures and densities across the liquid and liquid-vapor coexistence regimes.
A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.
Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang
2013-01-01
We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.
Cheng, Mingjian; Zhang, Yixin; Gao, Jie; Wang, Fei; Zhao, Fengsheng
2014-06-20
We model the average channel capacity of optical wireless communication systems for cases of weak to strong turbulence channels, using the exponentiation Weibull distribution model. The joint effects of the beam wander and spread, pointing errors, atmospheric attenuation, and the spectral index of non-Kolmogorov turbulence on system performance are included. Our results show that the average capacity decreases steeply as the propagation length L changes from 0 to 200 m and decreases slowly down or tends to a stable value as the propagation length L is greater than 200 m. In the weak turbulence region, by increasing the detection aperture, we can improve the average channel capacity and the atmospheric visibility as an important issue affecting the average channel capacity. In the strong turbulence region, the increase of the radius of the detection aperture cannot reduce the effects of the atmospheric turbulence on the average channel capacity, and the effect of atmospheric visibility on the channel information capacity can be ignored. The effect of the spectral power exponent on the average channel capacity in the strong turbulence region is higher than weak turbulence region. Irrespective of the details determining the turbulent channel, we can say that pointing errors have a significant effect on the average channel capacity of optical wireless communication systems in turbulence channels.
Structure refinement of astrophyllite
MA; Zhesheng
2001-01-01
［1］Abdel-Fattah M. Abdel-Rahman., Mineral chemistry and paragenesis of astrophyllite from Egypt, Mineralogical Magazine, 1992, 56: 17-26.［2］Liu Yan, Ma Zhesheng, Han Xiuling et al, Astrophyllite from the Namjabarwa Area, Eastern Tibet, Acta Petrologica et Mineralogica, 1997,16(4): 338-340.［3］Peng Zhizhong, Ma Zhesheng, The crystal structure of astrophyllite (in Russian), Scientia Sinica, 1963, 12(2): 272-276.［4］Pen Zhizhong, Ma Zhesheng, The crystal structure of Tricinic Mangano-astrophyllite (in Russian), Scientia Sinica (Scien-ce in China), 1964, 13(7): 1180-1183.［5］Shi Nicheng, Ma Zhesheng, Li Guowu et al., Stucyure Refinement of Monoclinic astrophyllite, Acta Crystallographica, Section B, 1998, B54: 109-114.［6］Woodrow, P. J., The Crystal structure of astrophyllite, Acta Crystallographica, 1967, 22: 673-678.［7］СеменовЕ. И., Куплетскит-Новый Минерал Группы Астрофиллита, ДАН, 1956, 108(5), 933-936.［8］Nickel, E. H., Rowland, J. E., Charette, D. J., Niobophyllite the niobium analogue of astrophyllite: A new mineral from Sead Laxe Labrador, Canad. Mine., 1964, 8(1): 40.［9］X-Ray Laboratory of Hubei Geologic College, The crystal chemistry of astrophyllite group minerals (in Chinese), Scientia Geologica Sinica, 1974, (1): 18-30.［10］Sheldrick, G. M., Program for the solution of crystal structures, SHELX86, University of G?ttingen, 1985, Germany.［11］Sheldrick, G. M., Program for the refinement of crystal structures, SHELXL93, University of G?ttingen, 1993, Germany.［12］Liebau, F., Structural Chemistry of Silicates Structure, Bonding, and Classification, Heidelberg: Springer-Verlag QD181, S6L614, 1985.［13］Ferraris, G., Ivaldi, G., Khomyakov, A. P. et al., Nafertisite, a layer titanosilicate member of a polysomatic series including mica, Eur. J. Mineral.,1996, 8: 241-249.［14］Ferraris, G., Polysomatism as a tool for correlating properties and structure, in EMU Notes in
Durato, M. V.; Albano, A. M.; Rapp, P. E.; Nawang, S. A.
2015-06-01
The validity of ERPs as indices of stable neurophysiological traits is partially dependent on their stability over time. Previous studies on ERP stability, however, have reported diverse stability estimates despite using the same component scoring methods. This present study explores a novel approach in investigating the longitudinal stability of average ERPs—that is, by treating the ERP waveform as a time series and then applying Euclidean Distance and Kolmogorov-Smirnov analyses to evaluate the similarity or dissimilarity between the ERP time series of different sessions or run pairs. Nonlinear dynamical analysis show that in the absence of a change in medical condition, the average ERPs of healthy human adults are highly longitudinally stable—as evaluated by both the Euclidean distance and the Kolmogorov-Smirnov test.
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.
Risultati di regolarità per il problema dell'ostacolo relativo ad equazioni di Kolmogorov degeneri
Sergio Polidoro
2010-12-01
Full Text Available We prove optimal regularity for solutions to the obstacle problem for a class of second order differential operators of Kolmogorov type. We treat smooth obstacles as well as non-smooth obstacles. All our proofs follow the same line of thought and are based on blow-ups, compactness, barriers and arguments by contradiction. This problem arises in nancial mathematics, when considering path-dependent derivative contracts with the early exercise feature.
Poje, Andrew C.; Ã-zgökmen, Tamay M.; Bogucki, Darek J.; Kirwan, A. D.
2017-02-01
Using two-point velocity and position data from the near-simultaneous release of O(100) GPS-tracked surface drifters in the northern Gulf of Mexico, we examine the applicability of classical turbulent scaling laws to upper ocean velocity fields. The dataset allows direct estimates of both velocity structure functions and the temporal evolution of the distribution of particle pair separations. On 100 m-10 km spatial scales, and time scales of order 1-10 days, all metrics of the observed surface fluctuations are consistent with standard Kolmogorov turbulence theory in an energy cascade inertial-range regime. The sign of the third-order structure function is negative and proportional to the separation distance for scales ≲10 km where local, fluctuating Rossby numbers are found to be larger than 0.1. The scale-independent energy dissipation rate, or downscale spectral flux, estimated from Kolmogorov's 4/5th law in this regime closely matches nearby microscale dissipation measurements in the near-surface. In contrast, similar statistics derived from a like-sized set of synthetic drifters advected by purely geostrophic altimetric AVISO data agree well with Kolmogorov-Kraichnan scaling for 2D turbulence in the forward enstrophy cascade range.
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...
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).
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.
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.
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.
Crystal structure refinement with SHELXL
Sheldrick, George M., E-mail: gsheldr@shelx.uni-ac.gwdg.de [Department of Structural Chemistry, Georg-August Universität Göttingen, Tammannstraße 4, Göttingen 37077 (Germany)
2015-01-01
New features added to the refinement program SHELXL since 2008 are described and explained. The improvements in the crystal structure refinement program SHELXL have been closely coupled with the development and increasing importance of the CIF (Crystallographic Information Framework) format for validating and archiving crystal structures. An important simplification is that now only one file in CIF format (for convenience, referred to simply as ‘a CIF’) containing embedded reflection data and SHELXL instructions is needed for a complete structure archive; the program SHREDCIF can be used to extract the .hkl and .ins files required for further refinement with SHELXL. Recent developments in SHELXL facilitate refinement against neutron diffraction data, the treatment of H atoms, the determination of absolute structure, the input of partial structure factors and the refinement of twinned and disordered structures. SHELXL is available free to academics for the Windows, Linux and Mac OS X operating systems, and is particularly suitable for multiple-core processors.
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...
Parallel Adaptive Mesh Refinement
Diachin, L; Hornung, R; Plassmann, P; WIssink, A
2005-03-04
As large-scale, parallel computers have become more widely available and numerical models and algorithms have advanced, the range of physical phenomena that can be simulated has expanded dramatically. Many important science and engineering problems exhibit solutions with localized behavior where highly-detailed salient features or large gradients appear in certain regions which are separated by much larger regions where the solution is smooth. Examples include chemically-reacting flows with radiative heat transfer, high Reynolds number flows interacting with solid objects, and combustion problems where the flame front is essentially a two-dimensional sheet occupying a small part of a three-dimensional domain. Modeling such problems numerically requires approximating the governing partial differential equations on a discrete domain, or grid. Grid spacing is an important factor in determining the accuracy and cost of a computation. A fine grid may be needed to resolve key local features while a much coarser grid may suffice elsewhere. Employing a fine grid everywhere may be inefficient at best and, at worst, may make an adequately resolved simulation impractical. Moreover, the location and resolution of fine grid required for an accurate solution is a dynamic property of a problem's transient features and may not be known a priori. Adaptive mesh refinement (AMR) is a technique that can be used with both structured and unstructured meshes to adjust local grid spacing dynamically to capture solution features with an appropriate degree of resolution. Thus, computational resources can be focused where and when they are needed most to efficiently achieve an accurate solution without incurring the cost of a globally-fine grid. Figure 1.1 shows two example computations using AMR; on the left is a structured mesh calculation of a impulsively-sheared contact surface and on the right is the fuselage and volume discretization of an RAH-66 Comanche helicopter [35]. Note the
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.
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
Refining and classifying finite-time Lyapunov exponent ridges
Allshouse, Michael R
2015-01-01
While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of an FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by an FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model.
Crystal structure refinement with SHELXL.
Sheldrick, George M
2015-01-01
The improvements in the crystal structure refinement program SHELXL have been closely coupled with the development and increasing importance of the CIF (Crystallographic Information Framework) format for validating and archiving crystal structures. An important simplification is that now only one file in CIF format (for convenience, referred to simply as `a CIF') containing embedded reflection data and SHELXL instructions is needed for a complete structure archive; the program SHREDCIF can be used to extract the .hkl and .ins files required for further refinement with SHELXL. Recent developments in SHELXL facilitate refinement against neutron diffraction data, the treatment of H atoms, the determination of absolute structure, the input of partial structure factors and the refinement of twinned and disordered structures. SHELXL is available free to academics for the Windows, Linux and Mac OS X operating systems, and is particularly suitable for multiple-core processors.
On Modal Refinement and Consistency
Nyman, Ulrik; Larsen, Kim Guldstrand; Wasowski, Andrzej
2007-01-01
Almost 20 years after the original conception, we revisit several fundamental question about modal transition systems. First, we demonstrate the incompleteness of the standard modal refinement using a counterexample due to Hüttel. Deciding any refinement, complete with respect to the standard...... notions of implementation, is shown to be computationally hard (co-NP hard). Second, we consider four forms of consistency (existence of implementations) for modal specifications. We characterize each operationally, giving algorithms for deciding, and for synthesizing implementations, together...
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.
Maslova, T. V.
2006-12-01
The results obtained in V. P. Maslov’s article [1] can automatically be carried over to arbitrary semiotic systems if the string of signs is sufficiently long. We shall show in this article, by using arguments based on the ideas of Kolmogorov complexity and by applying the theorem of V. P. Maslov from [2], that one can obtain similar formulas for the distribution of various semiotic objects. In order to do this, we must introduce notions generalizing the occurrence frequency of words in corpora of texts. We also interpret a formula due to Maslov (appearing in [3]) from the point of view of the general semiotic notions introduced here.
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 ...
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.
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.
Zone refining of plutonium metal
Blau, Michael S. [Univ. of Idaho, Moscow, ID (United States)
1994-08-01
The zone refining process was applied to Pu metal containing known amounts of impurities. Rod specimens of plutonium metal were melted into and contained in tantalum boats, each of which was passed horizontally through a three-turn, high-frequency coil in such a manner as to cause a narrow molten zone to pass through the Pu metal rod 10 times. The impurity elements Co, Cr, Fe, Ni, Np, U were found to move in the same direction as the molten zone as predicted by binary phase diagrams. The elements Al, Am, and Ga moved in the opposite direction of the molten zone as predicted by binary phase diagrams. As the impurity alloy was zone refined, {delta}-phase plutonium metal crystals were produced. The first few zone refining passes were more effective than each later pass because an oxide layer formed on the rod surface. There was no clear evidence of better impurity movement at the slower zone refining speed. Also, constant or variable coil power appeared to have no effect on impurity movement during a single run (10 passes). This experiment was the first step to developing a zone refining process for plutonium metal.
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.
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.
A truly noninterpolating semi-Lagrangian Lax-Wendroff method
Olim, M.
1994-06-01
A truly noninterpolating semi-Lagrangian method has been developed. It is based upon a modification of a standard Lax-Wendroff scheme and is unconditionally stable on a regular rectangular grid. The method is explicit and second-order accurate in both time and space. It is suggested that the computational cost and memory allocation required by this method are the least possible for a semi-Lagrangian algorithm of this order of accuracy. The numerical experiments presented indicate that the algorithm is very accurate indeed.
The anomalous chiral Lagrangian of order $p^6$
Bijnens, J; Talavera, P
2002-01-01
We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$. The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavors, 23 terms for three and five for two flavors. In the two flavor case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well.
Experimental investigation of Lagrangian structure functions in turbulence
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...
Kurtz, S.E.; Fields, D.E.
1983-10-01
The KSTEST code presented here is designed to perform the Kolmogorov-Smirnov one-sample test. The code may be used as a stand-alone program or the principal subroutines may be excerpted and used to service other programs. The Kolmogorov-Smirnov one-sample test is a nonparametric goodness-of-fit test. A number of codes to perform this test are in existence, but they suffer from the inability to provide meaningful results in the case of small sample sizes (number of values less than or equal to 80). The KSTEST code overcomes this inadequacy by using two distinct algorithms. If the sample size is greater than 80, an asymptotic series developed by Smirnov is evaluated. If the sample size is 80 or less, a table of values generated by Birnbaum is referenced. Valid results can be obtained from KSTEST when the sample contains from 3 to 300 data points. The program was developed on a Digital Equipment Corporation PDP-10 computer using the FORTRAN-10 language. The code size is approximately 450 card images and the typical CPU execution time is 0.19 s.
Pg Haji Mohd Ariffin, Ak Muhamad Amirul Irfan
2015-01-01
This paper presents the project that I have been tasked while attending a three-month Summer Programme at CERN. The Project specification is to analyse the result of a weekly data produced by Compact Muon Solenoid (CMS) in the form of histograms. CMS is a detector which is a multi-purpose apparatus use to operate at the Large Hadron Collider (LHC) at CERN. It will yield head-on collisions of two proton (ion) beams of 7 TeV (2.75 TeV per nucleon) each, with a design luminosity of 10 34 cm -2s-1. A comparison of the results is then made using two methods namely Kolmogorov Smirnov Statistic Test and Chi-Squared Test. These tests will be further elaborated in the subsequent paragraphs. To execute this project, I have to firstly study the entire basic computer programming in particular C++ and the ROOT Basic Programmes. This is important to ensure the tasks given can be resolved within the given time. A program is subsequently written to provide output of histogram and calculation of Kolmogorov-Smirnov Test and Ch...
Bauxite Mining and Alumina Refining
Frisch, Neale; Olney, David
2014-01-01
Objective: To describe bauxite mining and alumina refining processes and to outline the relevant physical, chemical, biological, ergonomic, and psychosocial health risks. Methods: Review article. Results: The most important risks relate to noise, ergonomics, trauma, and caustic soda splashes of the skin/eyes. Other risks of note relate to fatigue, heat, and solar ultraviolet and for some operations tropical diseases, venomous/dangerous animals, and remote locations. Exposures to bauxite dust, alumina dust, and caustic mist in contemporary best-practice bauxite mining and alumina refining operations have not been demonstrated to be associated with clinically significant decrements in lung function. Exposures to bauxite dust and alumina dust at such operations are also not associated with the incidence of cancer. Conclusions: A range of occupational health risks in bauxite mining and alumina refining require the maintenance of effective control measures. PMID:24806720
Data refinement for true concurrency
Brijesh Dongol
2013-05-01
Full Text Available The majority of modern systems exhibit sophisticated concurrent behaviour, where several system components modify and observe the system state with fine-grained atomicity. Many systems (e.g., multi-core processors, real-time controllers also exhibit truly concurrent behaviour, where multiple events can occur simultaneously. This paper presents data refinement defined in terms of an interval-based framework, which includes high-level operators that capture non-deterministic expression evaluation. By modifying the type of an interval, our theory may be specialised to cover data refinement of both discrete and continuous systems. We present an interval-based encoding of forward simulation, then prove that our forward simulation rule is sound with respect to our data refinement definition. A number of rules for decomposing forward simulation proofs over both sequential and parallel composition are developed.
Pointing Refinement of SIRTF Images
Masci, F; Moshir, M; Shupe, D; Fowler, J W; Fowler, John W.
2002-01-01
The soon-to-be-launched Space Infrared Telescope Facility (SIRTF) shall produce image data with an a-posteriori pointing knowledge of 1.4 arcsec (1 sigma radial) with a goal of 1.2 arcsec in the International Celestial Reference System (ICRS). To perform robust image coaddition, mosaic generation, extraction and position determination of faint sources, the pointing will need to be refined to better than a few-tenths of an arcsecond. We use a linear-sparse matrix solver to find a "global-minimization" of all relative image offsets in a mosaic from which refined pointings and orientations can be computed. This paper summarizes the pointing-refinement algorithm and presents the results of testing on simulated data.
DSm Vector Spaces of Refined Labels
Kandasamy, W B Vasantha
2011-01-01
In this book the authors introduce the notion of DSm vector spaces of refined labels. They also realize the refined labels as a plane and a n-dimensional space. Further, using these refined labels, several algebraic structures are defined. Finally DSm semivector space or refined labels is described. Authors also propose some research problems.
Refining Nodes and Edges of State Machines
Hallerstede, Stefan; Snook, Colin
2011-01-01
State machines are hierarchical automata that are widely used to structure complex behavioural specifications. We develop two notions of refinement of state machines, node refinement and edge refinement. We compare the two notions by means of examples and argue that, by adopting simple convention...... refinement theory and UML-B state machine refinement influences the style of node refinement. Hence we propose a method with direct proof of state machine refinement avoiding the detour via Event-B that is needed by UML-B....
Conformal refinement of unstructured quadrilateral meshes
Garmella, Rao [Los Alamos National Laboratory
2009-01-01
We present a multilevel adaptive refinement technique for unstructured quadrilateral meshes in which the mesh is kept conformal at all times. This means that the refined mesh, like the original, is formed of only quadrilateral elements that intersect strictly along edges or at vertices, i.e., vertices of one quadrilateral element do not lie in an edge of another quadrilateral. Elements are refined using templates based on 1:3 refinement of edges. We demonstrate that by careful design of the refinement and coarsening strategy, we can maintain high quality elements in the refined mesh. We demonstrate the method on a number of examples with dynamically changing refinement regions.
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...
Refining analgesia strategies using lasers.
Hampshire, Victoria
2015-08-01
Sound programs for the humane care and use of animals within research facilities incorporate experimental refinements such as multimodal approaches for pain management. These approaches can include non-traditional strategies along with more established ones. The use of lasers for pain relief is growing in popularity among companion animal veterinary practitioners and technologists. Therefore, its application in the research sector warrants closer consideration.
On Interaction Refinement in Middleware
Truyen, Eddy; Jørgensen, Bo Nørregaard; Joosen, Wouter;
2000-01-01
components together. We have examined a reflective technique that improve the dynamics of this gluing process such that interaction between components can be refined at run-time. In this paper, we show how we have used this reflective technique to dynamically integrate into the architecture of middleware...
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
U. Karstens
2012-01-01
Full Text Available We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM. The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian on models' spatial resolution is further investigated. A case study using airborne measurements during which both models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km. Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data. Thus suggests that it is reasonable to use STILT as an adjoint model of WRF atmospheric transport.
U. Karstens
2012-10-01
Full Text Available We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM. The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian on models' spatial resolution is further investigated. A case study using airborne measurements during which two models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km. Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data.
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.
D. Lekomtcev
2015-06-01
Full Text Available The cognitive radio technology allows solving one of the main issues of current wireless communication technologies, namely a deficit of vacant spectrum. A dynamic spectrum access used in the cognitive radio networks (CRN gives an ability to access an unused spectrum in real time. Cooperative spectrum sensing is the most effective method for spectrum holes detecting. It combines sensing information of multiple cognitive radio users. In this paper, an experimental evaluation of spectrum sensing methods based on the Kolmogorov - Smirnov statistical test and Energy Detector using the Universal Software Radio Peripheral (USRP devices synchronized through a MIMO cable and with further processing in the GNU Radio and Matlab software are presented. Three hard decision fusion schemes are analyzed. Simulation comparison between these rules is presented via Receiver Operating Characteristic (ROC curves. The influence of real channel with interferences is compared in contrast to commonly assumed AWGN channel model of vacant channel noise.
Li, Jinhong; Zeng, Jun; Duan, Meiling
2015-05-04
The analytical expressions for the cross-spectral density function of partially coherent sinh-Gaussian (ShG) vortex beams propagating through free space and non-Kolmogorov atmospheric turbulence are derived, and used to study the classification of coherent vortices creation and distance of topological charge conservation. With the increment of the general structure constant and the waist width, as well as the decrement of the general exponent, the inner scale of turbulence and spatial correlation length, the distance of topological charge conservation will decrease, whereas the outer scale of turbulence and the Sh-part parameter have no effect on the distance of topological charge conservation. According to the creation, the coherent vortices are grouped into three classes: the first is the inherent coherent vortices of the vortex beams, the second is created by the vortex beams when propagating through free space, and the third is created by the atmospheric turbulence inducing the vortex beams.
Trifonov, A. Yu.; Shapovalov, A. V.
2011-05-01
The two-dimensional Kolmogorov-Petrovskii-Piskunov-Fisher equation with nonlocal nonlinearity and axially symmetric coefficients in polar coordinates is considered. The method of separation of variables in polar coordinates and the nonlinear superposition principle proposed by the authors are used to construct the asymptotic solution of a Cauchy problem in a special class of smooth functions. The functions of this class arbitrarily depend on the angular variable and are semiclassically concentrated in the radial variable. The angular dependence of the function has been exactly taken into account in the solution. For the radial equation, the formalism of semiclassical asymptotics has been developed for the class of functions which singularly depend on an asymptotic small parameter, whose part is played by the diffusion coefficient. A dynamic system of Einstein-Ehrenfest equations (a system of equations in mean and central moments) has been derived. The evolution operator for the class of functions under consideration has been constructed in explicit form.
Tomellini, Massimo
2017-03-01
On the basis of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) method for space tessellation the kinetics of Voronoi cell filling, by central grain growth, has been studied as a function of the cell size. This is done by solving an integral equation for which a class of solutions is obtained in closed form, where the cell-size probability density is the Gamma distribution function. The computation gives the time evolution of the mean grain size, as a function of cell volume, which is further employed for describing the grain-size probability density function. The present approach is applied to determine, analytically, the exact grain-size distribution function in 1D and the size distributions in 2D and 3D through approximation.
Refining Visually Detected Object poses
Holm, Preben; Petersen, Henrik Gordon
2010-01-01
Automated industrial assembly today require that the 3D position and orientation (hereafter ''pose`) of the objects to be assembled are known precisely. Today this precision is mostly established by a dedicated mechanical object alignment system. However, such systems are often dedicated...... that enables direct assembly. Conventional vision systems and laser triangulation systems can locate randomly placed known objects (with 3D CAD models available) with some accuracy, but not necessarily a good enough accuracy. In this paper, we present a novel method for refining the pose accuracy of an object...... that has been located based on the appearance as detected by a monocular camera. We illustrate the quality of our refinement method experimentally....
Iterative Goal Refinement for Robotics
2014-06-01
Iterative Goal Refinement for Robotics Mark Roberts1, Swaroop Vattam1, Ronald Alford2, Bryan Auslander3, Justin Karneeb3, Matthew Molineaux3... robotics researchers and practitioners. We present a goal lifecycle and define a formal model for GR that (1) relates distinct disciplines concerning...researchers to collaborate in exploring this exciting frontier. 1. Introduction Robotic systems often act using incomplete models in environments
Ames, Thomas L.; Farnsworth, Grant V.; Ketcheson, David Isaac; Robinson, Allen Conrad
2009-09-01
The modeling of solids is most naturally placed within a Lagrangian framework because it requires constitutive models which depend on knowledge of the original material orientations and subsequent deformations. Detailed kinematic information is needed to ensure material frame indifference which is captured through the deformation gradient F. Such information can be tracked easily in a Lagrangian code. Unfortunately, not all problems can be easily modeled using Lagrangian concepts due to severe distortions in the underlying motion. Either a Lagrangian/Eulerian or a pure Eulerian modeling framework must be introduced. We discuss and contrast several Lagrangian/Eulerian approaches for keeping track of the details of material kinematics.
Li, Linmin; Li, Baokuan
2016-08-01
In ladle metallurgy, bubble-liquid interaction leads to complex phase structures. Gas bubble behavior, as well as the induced slag layer behavior, plays a significant role in the refining process and the steel quality. In the present work, a mathematical model using the large eddy simulation (LES) is developed to investigate the bubble transport and slag layer behavior in a water model of an argon-stirred ladle. The Eulerian volume of fluid model is adopted to track the liquid steel-slag-air free surfaces while the Lagrangian discrete phase model is used for tracking and handling the dynamics of discrete bubbles. The bubble coalescence is considered using O'Rourke's algorithm to solve the bubble diameter redistribution and bubbles are removed after leaving the air-liquid interface. The turbulent liquid flow that is induced by bubble-liquid interaction is solved by LES. The slag layer fluactuation, slag droplet entrainment and spout eye open-close phenomenon are well revealed. The bubble diameter distribution and the spout eye size are compared with the experiment. The results show that the hybrid Eulerian-Lagrangian-LES model provides a valid modeling framework to predict the unsteady gas bubble-slag layer coupled behaviors.
The existence of Hamiltonian stationary Lagrangian tori in Kahler manifolds of any dimension
Lee, Yng-Ing
2010-01-01
Hamiltonian stationary Lagrangians are Lagrangian submanifolds that are critical points of the volume functional under Hamiltonian deformations. They can be considered as a generalization of special Lagrangians or Lagrangian and minimal submanifolds. Joyce, Schoen and the author show that given any compact rigid Hamiltonian stationary Lagrangian in $\\C^n$, one can always find a family of Hamiltonian stationary Lagrangians of the same type in any compact symplectic manifolds with a compatible metric. The advantage of this result is that it holds in very general classes. But the disadvantage is that we do not know where these examples locate and examples in this family might be far apart. In this paper, we derive a local condition on Kahler manifolds which ensures the existence of one family of Hamiltonian stationary Lagrangian tori near a point with given frame satisfying the criterion. Butscher and Corvino ever proposed a condition in n=2. But our condition appears to be different from theirs. The condition d...
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.
Lagrangian tools to monitor transport and mixing in the ocean
Prants, S V; Uleysky, M Yu
2012-01-01
We apply the Lagrangian approach to study surface transport and mixing in the ocean. New tools have been developed to track the motion of water masses, their origin and fate and to quantify transport and mixing. To illustrate the methods used we compute the Lagrangian synoptic maps a comparatively small marine bay, the Peter the Great Bay in the Japan Sea near Vladivostok city (Russia), and in a comparatively large region in the North Pacific, the Kuroshio Extension system. In the first case we use velocity data from a Japan Sea circulation numerical model and in the second one the velocity data are derived from satellite altimeter measurements of anomalies of the sea height distributed by AVISO.
Finite Spectral Semi-Lagrangian Method for Incompressible Flows
LI Shao-Wu; WANG Jian-Ping
2012-01-01
A new semi-Lagrangian (SL) scheme is proposed by using finite spectral regional interpolation and adequate numerical dissipation to control the nonlinear instability. The finite spectrai basis function is C1 continuous at the boundary and is easy to construct. Comparison between numerical and experimental results indicates that the present method works well in solving incompressible Navier-Stokes equations for unsteady Sows around airfoil with different angles of attack.%A new semi-Lagrangian (SL) scheme is proposed by using finite spectral regional interpolation and adequate numerical dissipation to control the nonlinear instability.The finite spectral basis function is C1 continuous at the boundary and is easy to construct.Comparison between numerical and experimental results indicates that the present method works well in solving incompressible Navier-Stokes equations for unsteady flows around airfoil with different angles of attack.
Acoustic Streaming: An Arbitrary Lagrangian-Eulerian Perspective
Nama, Nitesh; Costanzo, Francesco
2016-01-01
We analyze acoustic streaming flows using an ALE perspective. The formulation stems from an explicit separation of time-scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacosutofluidic devices. After the formulation's exposition, we present numerical re...
Unambiguous formalism for higher order Lagrangian field theories
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain); Vankerschaver, Joris [Control and Dynamical Systems, California Institute of Technology, CA (United States)], E-mail: cedricmc@imaff.cfmac.csic.es, E-mail: mdeleon@imaff.cfmac.csic.es, E-mail: d.martin@imaff.cfmac.csic.es, E-mail: jv@caltech.edu
2009-11-27
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
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......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...
Chiral lagrangian approach to exchange vector currents in nuclei
Park, T S; Rho, M; Park, Tae Sun; Min, Dong Pil; Rho, Mannque
1995-01-01
Exchange vector currents are calculated up to one-loop order (corresponding to next-to-next-to-leading order) in chiral perturbation theory. As an illustration of the power of the approach, we apply the formalism to the classic nuclear process n+p\\rightarrow d +\\gamma at thermal energy. The exchange current correction comes out to be (4.5 \\pm 0.3) \\% in amplitude giving a predicted cross section \\sigma= (334\\pm 3)\\ {\\mbox mb} in excellent agreement with the experimental value (334.2\\pm 0.5)\\ {\\mbox mb}. Together with the axial charge transitions computed previously, this result provides a strong support for the power of chiral Lagrangians in nuclear physics. As a by-product of our results, we suggest an open problem in the application of chiral Lagrangian approach to nuclear processes that has to do with giving a physical meaning to the short-range correlations that play an important role in nuclei.
Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics.
Busse, Angela; Müller, Wolf-Christian; Gogoberidze, Grigol
2010-12-01
For the phenomenological description of magnetohydrodynamic turbulence competing models exist, e.g., Boldyrev [Phys. Rev. Lett. 96, 115002 (2006)] and Gogoberidze [Phys. Plasmas 14, 022304 (2007)], which predict the same Eulerian inertial-range scaling of the turbulent energy spectrum although they employ fundamentally different basic interaction mechanisms. A relation is found that links the Lagrangian frequency spectrum with the autocorrelation time scale of the turbulent fluctuations τ(ac) and the associated cascade time scale τ(cas). Thus, the Lagrangian energy spectrum can serve to identify weak (τ(ac) ≪ τ(cas)) and strong (τ(ac) ∼ τ(cas)) interaction mechanisms providing insight into the turbulent energy cascade. The new approach is illustrated by results from direct numerical simulations of two- and three-dimensional incompressible MHD turbulence.
An algorithm for discovering Lagrangians automatically from data
Daniel J.A. Hills
2015-11-01
Full Text Available An activity fundamental to science is building mathematical models. These models are used to both predict the results of future experiments and gain insight into the structure of the system under study. We present an algorithm that automates the model building process in a scientifically principled way. The algorithm can take observed trajectories from a wide variety of mechanical systems and, without any other prior knowledge or tuning of parameters, predict the future evolution of the system. It does this by applying the principle of least action and searching for the simplest Lagrangian that describes the system’s behaviour. By generating this Lagrangian in a human interpretable form, it can also provide insight into the workings of the system.
Statistical Decoupling of Lagrangian Fluid Parcel in Newtonian Cosmology
Wang, Xin
2016-01-01
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the non-linear evolution of various cosmic objects, e.g. dark matter halos, in the context of Lagrangian fluid dynamics, since a fluid parcel with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the probability distribution evolution equation of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (PDF). Consequently it is guaranteed that the one-point PDF would be preserved by evolving these...
Lagrangian intersection Floer theory anomaly and obstruction, part I
Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru
2009-01-01
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A_\\infty-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A_\\infty algebras and A_\\infty bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-co...
Lagrangian intersection Floer theory anomaly and obstruction, part II
Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru
2009-01-01
This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A_\\infty-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A_\\infty algebras and A_\\infty bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-co...
Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
Ruiz, D E
2015-01-01
Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Both phenomena are governed by an effective gauge Hamiltonian, which vanishes in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of $N$ resonant modes, where $N$ is arbitrary, and lead to equations for the wave spin, which happens to be a $(N^2-1)$-dimensional spin vector. As a special case, classical equations for a Dirac particle $(N=2)$ are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangi...
Singular Lorentz-Violating Lagrangians and Associated Finsler Structures
Colladay, Don
2015-01-01
Several lagrangians associated to classical limits of lorenz-violating fermions in the Standard Model extension (SME) have been shown to yield Finsler functions when the theory is expressed in Euclidean space. When spin-couplings are present, the lagrangian can develop singularities that obstruct the construction of a globally defined Legendre transformation, leading to singular Finsler spaces. A specific sector of the SME where such problems arise is studied. It is found that the singular behavior can be eliminated by an appropriate lifting of the problem to an associated algebraic variety. This provides a smooth classical model for the singular problem. In Euclidean space, the procedure involves combining two related singular Finsler functions into a single smooth function with a semi-positive definite quadratic form defined on a desingularized variety.
Yasutake, Nobutoshi; Fujisawa, Kotaro; Yamada, Shoichi
2016-12-01
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.
Inertial-particle accelerations in turbulence: a Lagrangian closure
Vajedi, S; Mehlig, B; Biferale, L
2016-01-01
The distribution of particle accelerations in turbulence is intermittent, with non-Gaussian tails that are quite different for light and heavy particles. In this article we analyse a closure scheme for the acceleration fluctuations of light and heavy inertial particles in turbulence, formulated in terms of Lagrangian correlation functions of fluid tracers. We compute the variance and the flatness of inertial particle accelerations and we discuss their dependency on the Stokes number. The closure incorporates effects induced by the Lagrangian correlations along the trajectories of fluid tracers, and its predictions agree well with results of direct numerical simulations of inertial particles in turbulence, provided that the effects induced by the inertial preferential sampling of heavy/light particles outside/inside vortices are negligible. In particular, the scheme predicts the correct functional behaviour of the acceleration variance, as a function of Stokes, as well as the presence of a minimum/maximum for ...
Chiral Lagrangian and chiral quark model from confinement in QCD
Simonov, Yu A
2015-01-01
The effective chiral Lagrangian in both nonlocal form $L_{ECCL}$ and standard local form $L_{ECL}$ are derived in QCD using the confining kernel, obtained in the vacuum correlator formalism. As a result all coefficients of $L_{ECL}$ can be computed via $q\\bar q$ Green's functions. In the $p^2$ order of $L_{ECL}$ one obtains GOR relations and quark decay constants $f_a$ are calculated $a=1,...8$, while in the $p^4$ order the coefficients $L_1, L_2, L_3,L_4, L_5, L_6$ are obtained in good agreement with the values given by data. The chiral quark model is shown to be a simple consequence of $L_{ECCL}$ with defined coefficients. It is demonstrated that $L_{ECCL}$ gives an extension of the limiting low-energy Lagrangian $L_{ECL}$ to arbitrary momenta.
Low-spin models for higher-spin Lagrangians
Francia, Dario
2011-01-01
Higher-spin theories are most commonly modelled on the example of spin 2. While this is appropriate for the description of free irreducible spin-s particles, alternative options could be equally interesting. In particular Maxwell's equations provide the effective model for maximally reducible theories of higher spins inspired by the tensionless limit of the open string. For both options, as well as for their fermionic counterparts, one can extend the analogy beyond the equations for the gauge potentials, formulating the corresponding Lagrangians in terms of higher-spin curvatures. The associated non-localities are effectively due to the elimination of auxiliary fields and do not modify the spectrum. Massive deformations of these theories are also possible, and in particular in this contribution we propose a generalisation of the Proca Lagrangian for the Maxwell-inspired geometric theories.
The Lagrangian Deformation Structure of Three-Dimensional Steady Flow
Lester, Daniel R; Borgne, Tanguy Le; de Barros, Felipe P J
2016-01-01
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures (LCSs). To understand and model these processes it is necessary to quantify Lagrangian deformation in terms of Eulerian flow properties, currently an open problem. To elucidate this link we develop a Protean (streamline) coordinate transform for steady three-dimensional (3D) flows which renders both the velocity gradient and deformation gradient upper triangular. This frame not only simplifies computation of fluid deformation metrics such as fi?nite-time Lyapunov exponents (FTLEs) and elucidates the deformation structure of the flow, but moreover explicitly recovers kinematic and topological constraints upon deformation such as those related to helicity density and the Poincar\\'{e}-Bendixson theorem. We apply this transform to several classes of steady 3D flow, including helical ...
A non-conventional discontinuous Lagrangian for viscous flow
Scholle, M.; Marner, F.
2017-02-01
Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier-Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier-Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.
Proof of the equivalence theorem in the chiral lagrangian formalism
He, H J; Li, X; Hong-Jian He; He, Hong-Jian; Kuang, Yu-Ping; Li, Xiaoyuan; Xiaoyuan Li
1994-01-01
A general proof of the equivalence theorem in electroweak theories with the symmetry breaking sector described by the chiral Lagrangian is given in the $R_{\\xi}$ gauge by means of the Ward-Takahashi identities. The precise form of the theorem contains a modification factor $C_{mod}$ associated with each external Goldstone boson similar to that in the standard model. $C_{mod}$ is exactly unity in our previously proposed renormalization scheme, {\\it Scheme-II}.
Lagrangian model for oil spill diffusion at sea
Lonin, Serguei A. [Centro de Investigaciones Oceanograficas e Hidrograficas, Escuela Naval, Cartagena de Indias (Colombia)
1999-07-01
The Eulerian and Lagrangian methods for oil spill simulations are discussed. A mathematical description of the vertical movement of an oil droplet in the ocean is proposed based on the Langeven equation and the analytical test results are presented to compare the results. The results are that the buoyant effect and the vertical turbulent variations are very important mechanisms for vertical movement of oil in the water column. (Author)
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 Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
Torrieri, Giorgio
2016-01-01
We rederive relativistic hydrodynamics as a Lagrangian effective theory using the doubled coordinates technique, allowing us to include dissipative terms. We include Navier-Stokes shear and bulk terms, as well as Israel-Stewart relaxation time terms, within this formalism. We show how the inclusion of shear viscosity, and the requirement of a bounded energy-momentum "vacuum", forces the inclusion of the Israel-Stewart term into the theory, thereby providing a justification for the origin and uniqueness of these terms.
Lagrangian Data Analysis in Mesoscale Prediction and Model Validation Studies
2016-06-21
Department Rosenstiel School of Marine and Atmospheric Science 4600 Rickenbacker Causeway, Miami, Florida 33149 phone: (305) 361 4892, fax: (305) 361...of Marine and Atmospheric Science ,4600 Rickenbacker Causeway,Miami,FL,33149 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY...stratification and direct wind forcing. Second, a stochastic Lagrangian model of transport has been implemented, and tested with positive results against
Lagrangian formulation of relativistic Israel-Stewart hydrodynamics
Montenegro, David; Torrieri, Giorgio
2016-09-01
We rederive relativistic hydrodynamics as a Lagrangian effective theory using the doubled coordinates technique, allowing us to include dissipative terms. We include Navier-Stokes shear and bulk terms, as well as Israel-Stewart relaxation time terms, within this formalism. We show how the inclusion of shear dissipation forces the inclusion of the Israel-Stewart term into the theory, thereby providing an additional justification for the form of this term.
Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds
Yau, S-T
2002-01-01
The collection of articles in this volume are based on lectures presented during the Winter School on Mirror Symmetry held at Harvard University. There are many new directions suggested by mirror symmetry which could potentially have very rich connections in physics and mathematics. This book brings together the latest research in a major area of mathematical physics, including the recent progress in mirror manifolds and Lagrangian submanifolds. In particular, several articles describing homological approach and related topics are included.
The hybrid Eulerian Lagrangian numerical scheme tested with Chemistry
A. B. Hansen
2012-11-01
Full Text Available A newly developed advection scheme, the Hybrid Eulerian Lagrangian (HEL scheme, has been tested, including a module for atmospheric chemistry, including 58 chemical species, and compared to two other traditional advection schemes; a classical pseudospectral Eulerian method the Accurate Space Derivative (ASD scheme and the bi-cubic semi-Lagrangian (SL scheme using classical rotation tests. The rotation tests have been designed to test and compare the advection schemes for different spatial and temporal resolutions in different chemical conditions (rural and urban and for different shapes (cone and slotted cylinder giving the advection schemes different challenges with respect to relatively slow or fast chemistry and smooth or sharp gradients, respectively. In every test, error measures have been calculated and used for ranking of the advection schemes with respect to performance, i.e. lowest overall errors for all chemical species. Furthermore, the HEL and SL schemes have been compared in a shallow water model, demonstrating the performance in a more realistic non-linear deformation flow.
The results in this paper show that the new advection scheme, HEL, by far outperforms both the Eulerian and semi-Lagrangian schemes with very low error estimates compared to the two other schemes. Although no analytic solution can be obtained for the performance in the non-linear shallow water model flow, the tracer distribution appears realistic as compared to LMCSL when a mixing between local parcel concentrations is introduced in HEL.
Geometric Time and Causal Time in Relativistic Lagrangian Mechanics
Brunet, Olivier
2016-01-01
In this article, we argue that two distinct types of time should be taken into account in relativistic physics: a geometric time, which emanates from the structure of spacetime and its metrics, and a causal time, indicating the flow from the past to the future. A particularity of causal times is that its values have no intrinsic meaning, as their evolution alone is meaningful. In the context of relativistic Lagrangian mechanics, causal times corresponds to admissible parameterizations of paths, and we show that in order for a langragian to not depend on any particular causal time (as its values have no intrinsic meaning), it has to be homogeneous in its velocity argument. We illustrate this property with the example of a free particle in a potential. Then, using a geometric Lagrangian (i.e. a parameterization independent Lagrangian which is also manifestly covariant), we introduce the notion of ageodesicity of a path which measures to what extent a path is far from being a geodesic, and show how the notion ca...
Bounded fractional diffusion in geological media: Definition and Lagrangian approximation
Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang
2016-11-01
Spatiotemporal fractional-derivative models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and nonzero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing nonzero-value spatial-nonlocal boundary conditions with directional superdiffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eulerian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the nonlocal and nonsymmetric fractional diffusion. For a nonzero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite domains to those with any size and boundary conditions.
Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices
Huhn, F.; van Rees, W. M.; Gazzola, M.; Rossinelli, D.; Haller, G.; Koumoutsakos, P.
2015-08-01
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
Connections between chiral Lagrangians and QCD sum-rules
Fariborz, Amir H; Steele, T G
2016-01-01
It is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g., quark-antiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that are particularly effective in studies of the substructure of light scalar mesons with multiple complicated resonance shapes and substantial underlying mixings. The validity of these connections is demonstrated for the example of the isotriplet $a_0(980)$-$a_0(1450)$ system, resulting in an unambiguous determination of the scale factors from the combined inputs of QCD sum-rules and chiral Lagrangians. These scale factors ...
Currents in the Dead Sea: Lagrangian and Eulerian observations
Ozer, Tal; Gertman, Isaac; Katsenelson, Boris; Bodzin, Raanan; Lensly, Nadav
2015-04-01
The Dead Sea is a terminal hypersaline lake located in the lowest surface on Earth (currently -429 m bsl). The physical properties of the brine are significantly different than in common marine systems: the DS brine density is ~1.24 gr/cc and its viscosity ~3 times higher than marine systems. We present observational data on wind and currents in the Dead Sea. The observation setup includes a few fixed (Eulerian) stations which are equipped with wind meter and current meter profiler that covers the entire water column (ADCP). Thermal stratification is continuously measured in some of the stations using a thermistor chain. Lagrangian drifters that record the shallow water currents were released in liner array of single drifters between the fixed stations, and also in triplets (15 m triangle). The results include the measured time series data of wind (atmospheric forcing) and the measured current profiles from the fixed stations. Data of the Lagrangian drifters is presented as trajectories along with vector time series. Quality control check included comparison of drifter data and ADCP data whenever the drifters passed by the fixed stations; a very good agreement was found between the different measuring approaches. We discuss the following issues : (i) the relation between the wind and current data, (ii) the Lagrangian trajectories and transport aspects.
The effective Lagrangian of dark energy from observations
Jimenez, Raul; Verde, Licia [ICREA and ICC, Institut de Ciencies del Cosmos, Universitat de Barcelona (IEEC-UB), Marti i Franques 1, Barcelona 08028 (Spain); Talavera, P. [DFEN and ICC, Universitat Politècnica de Catalunya, Comte Urgell 187, Barcelona (Spain); Moresco, Michele; Cimatti, Andrea [Dipartimento di Astronomia, Università di Bologna, via Ranzani 1, 40127 Bologna (Italy); Pozzetti, Lucia, E-mail: raul.jimenez@icc.ub.edu, E-mail: pere.talavera@icc.ub.edu, E-mail: liciaverde@icc.ub.edu, E-mail: michele.moresco@unibo.it, E-mail: a.cimatti@unibo.it, E-mail: lucia.pozzetti@oabo.inaf.it [INAF — Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna (Italy)
2012-03-01
Using observational data on the expansion rate of the universe (H(z)) we constrain the effective Lagrangian of the current accelerated expansion. Our results show that the effective potential is consistent with being flat i.e., a cosmological constant; it is also consistent with the field moving along an almost flat potential like a pseudo-Goldstone boson. We show that the potential of dark energy does not deviate from a constant at more than 6% over the redshift range 0 < z < 1. The data can be described by just a constant term in the Lagrangian and do not require any extra parameters; therefore there is no evidence for augmenting the number of parameters of the LCDM paradigm. We also find that the data justify the effective theory approach to describe accelerated expansion and that the allowed parameters range satisfy the expected hierarchy. Future data, both from cosmic chronometers and baryonic acoustic oscillations, that can measure H(z) at the % level, could greatly improve constraints on the flatness of the potential or shed some light on possible mechanisms driving the accelerated expansion. Besides the above result, it is shown that the effective Lagrangian of accelerated expansion can be constrained from cosmological observations in a model-independent way and that direct measurements of the expansion rate H(z) are most useful to do so.
On the Lagrangian Biduality of Sparsity Minimization Problems
Singaraju, Dheeraj; Tron, Roberto; Yang, Allen Y; Sastry, S Shankar
2012-01-01
Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of the original problem. In this work, we present a novel primal-dual analysis on a class of sparsity minimization problems. We show that the Lagrangian bidual (i.e., the Lagrangian dual of the Lagrangian dual) of the sparsity minimization problems can be used to derive interesting convex relaxations: the bidual of the $\\ell_0$-minimization problem is the $\\ell_1$-minimization problem; and the bidual of the $\\ell_{0,1}$-minimization problem for enforcing group sparsity on structured data is the $\\ell_{1,\\infty}$-minimization problem. The analysis provides a means to compute per-instance non-trivial lower bounds on the (group) sparsity of the desired solutions. In a real-world application, the bidual relaxation improves the performance of a sparsity-based classification framewor...
Lagrangian chaos in three- dimensional steady buoyancy-driven flows
Contreras, Sebastian; Speetjens, Michel; Clercx, Herman
2016-11-01
Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside a cubic cavity differentially-heated from the side. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. The Lagrangian dynamics are controlled by the Péclet number (Pe) and the Prandtl number (Pr). Pe controls the behaviour qualitatively in that growing Pe progressively perturbs the integable state (Pe =0), thus paving the way to chaotic dynamics. Pr plays an entirely quantitative role in that Pr1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).
Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices.
Huhn, F; van Rees, W M; Gazzola, M; Rossinelli, D; Haller, G; Koumoutsakos, P
2015-08-01
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
Parallel octree-based hexahedral mesh generation for eulerian to lagrangian conversion.
Staten, Matthew L.; Owen, Steven James
2010-09-01
Computational simulation must often be performed on domains where materials are represented as scalar quantities or volume fractions at cell centers of an octree-based grid. Common examples include bio-medical, geotechnical or shock physics calculations where interface boundaries are represented only as discrete statistical approximations. In this work, we introduce new methods for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to ASC codes such as CTH and Alegra. New procedures for generating all-hexahedral finite element meshes from volume fraction data are introduced. A new primal-contouring approach is introduced for defining a geometric domain. New methods for refinement, node smoothing, resolving non-manifold conditions and defining geometry are also introduced as well as an extension of the algorithm to handle tetrahedral meshes. We also describe new scalable MPI-based implementations of these procedures. We describe a new software module, Sculptor, which has been developed for use as an embedded component of CTH. We also describe its interface and its use within the mesh generation code, CUBIT. Several examples are shown to illustrate the capabilities of Sculptor.
The Refined Function-Behaviour-Structure Framework
Diertens, B.
2013-01-01
We refine the function-behaviour-structure framework for design introduced by John Gero in order to deal with complexity. We do this by connecting the frameworks for the desing of two models, one the refinement of the other. The result is a refined framework for the design of an object on two levels
Grain Refinement of Deoxidized Copper
Balart, María José; Patel, Jayesh B.; Gao, Feng; Fan, Zhongyun
2016-10-01
This study reports the current status of grain refinement of copper accompanied in particular by a critical appraisal of grain refinement of phosphorus-deoxidized, high residual P (DHP) copper microalloyed with 150 ppm Ag. Some deviations exist in terms of the growth restriction factor ( Q) framework, on the basis of empirical evidence reported in the literature for grain size measurements of copper with individual additions of 0.05, 0.1, and 0.5 wt pct of Mo, In, Sn, Bi, Sb, Pb, and Se, cast under a protective atmosphere of pure Ar and water quenching. The columnar-to-equiaxed transition (CET) has been observed in copper, with an individual addition of 0.4B and with combined additions of 0.4Zr-0.04P and 0.4Zr-0.04P-0.015Ag and, in a previous study, with combined additions of 0.1Ag-0.069P (in wt pct). CETs in these B- and Zr-treated casts have been ascribed to changes in the morphology and chemistry of particles, concurrently in association with free solute type and availability. No further grain-refining action was observed due to microalloying additions of B, Mg, Ca, Zr, Ti, Mn, In, Fe, and Zn (~0.1 wt pct) with respect to DHP-Cu microalloyed with Ag, and therefore are no longer relevant for the casting conditions studied. The critical microalloying element for grain size control in deoxidized copper and in particular DHP-Cu is Ag.
Inflation in a refined racetrack
Wen, Wen-Yu
2007-01-01
In this note, we refine the racetrack inflation model constructed in arXiv:hep-th/0406230 by including the open string modulus. This modulus encodes the embedding of our braneworld inside some Calabi-Yau throat. We argue that in generic this open string modulus dynamically runs with the inflaton field thanks to its nonlinear coupling. A full analysis becomes difficult because the scalar potential changes progressively during the inflation epoch. Nevertheless, by explicit construction we are still able to build a realistic model through appropriate choices of the initial conditions.
Rotary impeller refinement of 7075Al alloy
WANG Liping; GUO Erjun; HUANG Yongchang; LU Bin
2009-01-01
The effects of four parameters, gas flow, rotational speed, refining time, and stewing time, on the rotary impeller refinement of 7075 Al were studied. The effects of C2Cl6refining, rotary impeller refuting, and composite refining of 7075 AI alloy were compared with each other. The results showed that the greatest impact parameter of rotary impeller refinement was rotational speed, followed by gas flow, refining time, and stewing time. The optimum purification parameters obtained by orthogonal analysis were as follows: rotor speed of 400 r/min, inert gas flow of 0.4 mL/h, refining time of 15 min, and stewing time of 6 min. The best degassing effect can be obtained by the composite refuting of C2Cl6 and rotary impeller. The degassing rate of C2Cl6 rotary impeller, and composite refining was 34.5%, 69.2%, and 78%, respectively. The mechanical properties of the specimen refined by rotary impeller were higher than those by C2C16 refining, but lower than those by composite refining.
Zone refining of plutonium metal
NONE
1997-05-01
The purpose of this study was to investigate zone refining techniques for the purification of plutonium metal. The redistribution of 10 impurity elements from zone melting was examined. Four tantalum boats were loaded with plutonium impurity alloy, placed in a vacuum furnace, heated to 700{degrees}C, and held at temperature for one hour. Ten passes were made with each boat. Metallographic and chemical analyses performed on the plutonium rods showed that, after 10 passes, moderate movement of certain elements were achieved. Molten zone speeds of 1 or 2 inches per hour had no effect on impurity element movement. Likewise, the application of constant or variable power had no effect on impurity movement. The study implies that development of a zone refining process to purify plutonium is feasible. Development of a process will be hampered by two factors: (1) the effect on impurity element redistribution of the oxide layer formed on the exposed surface of the material is not understood, and (2) the tantalum container material is not inert in the presence of plutonium. Cold boat studies are planned, with higher temperature and vacuum levels, to determine the effect on these factors. 5 refs., 1 tab., 5 figs.
Di Bernardino, Annalisa; Monti, Paolo; Leuzzi, Giovanni; Querzoli, Giorgio
2017-07-01
Lagrangian and Eulerian statistics are obtained from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. The objective is to quantify the Eulerian (TE) and Lagrangian (TL) time scales of the turbulence above the canopy layer as well as to investigate their dependence on the aspect ratio of the canopy, AR, as the latter is the ratio of the width (W) to the height (H) of the canyon. Experiments are also conducted for the case of flat terrain, which can be thought of as equivalent to a classical one-directional shear flow. The values found for the Eulerian time scales on flat terrain are in agreement with previous numerical results found in the literature. It is found that both the streamwise and vertical components of the Lagrangian time scale, T_u^L and T_w^L , follow Raupach's linear law within the constant-flux layer. The same holds true for T_w^L in both the canopies analyzed (AR= 1 and AR= 2 ) and also for T_u^L when AR = 1 . In contrast, for AR = 2 , T_u^L follows Raupach's law only above z=2H . Below that level, T_u^L is nearly constant with height, showing at z=H a value approximately one order of magnitude greater than that found for AR = 1 . It is shown that the assumption usually adopted for flat terrain, that β =TL/TE is proportional to the inverse of the turbulence intensity, also holds true even for the canopy flow in the constant-flux layer. In particular, γ /i_u fits well β _u =T_u^L /T_u^E in both the configurations by choosing γ to be 0.35 (here, i_u =σ _u / \\bar{u} , where \\bar{u} and σ _u are the mean and the root-mean-square of the streamwise velocity component, respectively). On the other hand, β _w =T_w^L /T_w^E follows approximately γ /i_w =0.65/( {σ _w /\\bar{u} } ) for z > 2H , irrespective of the AR value. The second main objective is to estimate other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum (KT) and the Kolmogorov constant (C_0) . It
Sumbekova, Sholpan; Aliseda, Alberto; Bourgoin, Mickael
2016-01-01
Turbulent flows laden with inertial particles present multiple open questions and are a subject of great interest in current research. Due to their higher density compared to the carrier fluid, inertial particles tend to form high concentration regions, i.e. clusters, and low concentration regions, i.e. voids, due to the interaction with the turbulence. In this work, we present an experimental investigation of the clustering phenomenon of heavy sub-Kolmogorov particles in homogeneous isotropic turbulent flows. Three control parameters have been varied over significant ranges: $Re_{\\lambda} \\in [170 - 450]$, $St\\in [0.1 - 5]$ and volume fraction $\\phi_v\\in [2\\times 10^{-6} - 2\\times 10^{-5}]$. The scaling of clustering characteristics, such as the distribution of Vorono\\"i areas and the dimensions of cluster and void regions, with the three parameters are discussed. In particular, for the polydispersed size distributions considered here, clustering is found to be enhanced strongly (quasi-linearly) by $Re_{\\lam...
Ermann, Leonardo; Vergini, Eduardo; Shepelyansky, Dima L.
2017-08-01
We study the dynamics of a Bose-Einstein condensate in a Sinai-oscillator trap under a monochromatic driving force. Such a trap is formed by a harmonic potential and a repulsive disk located in the center vicinity corresponding to the first experiments of condensate formation by Ketterle and co-workers in 1995. We allow that the external driving allows us to model the regime of weak wave turbulence with the Kolmogorov energy flow from low to high energies. We show that in a certain regime of weak driving and weak nonlinearity such a turbulent energy flow is defeated by the Anderson localization that leads to localization of energy on low energy modes. This is in a drastic contrast to the random phase approximation leading to energy flow to high modes. A critical threshold is determined above which the turbulent flow to high energies becomes possible. We argue that this phenomenon can be studied with ultracold atoms in magneto-optical traps.
A lagrangian dynamical theory for the mass function of cosmic structures; 1, dynamics
Monaco, P
1996-01-01
A new theory for determining the mass function of cosmic structures is presented. It relies on a realistic treatment of collapse dynamics. Gravitational collapse is analyzed in the Lagrangian perturbative framework. Lagrangian perturbations provide an approximation of truncated type, i.e. small-scale structure is filtered out. The collapse time is suitably defined as the instant at which orbit crossing takes place. The convergence of the Lagrangian series in predicting the collapse time of a homogeneous ellipsoid is demonstrated; it is also shown that third-order calculations are necessary in predicting collapse. Then, the Lagrangian prediction, with a correction for quasi-spherical perturbations, can be used to determine the collapse time of a homogeneous ellipsoid in a very fast and precise way. Furthermore, ellipsoidal collapse can be considered as a particular truncation of the Lagrangian series. Gaussian fields with scale-free power spectra are then considered. The Lagrangian series for the collapse time...
Differential geometry based solvation model II: Lagrangian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2011-12-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of
Adaptive mesh refinement in titanium
Colella, Phillip; Wen, Tong
2005-01-21
In this paper, we evaluate Titanium's usability as a high-level parallel programming language through a case study, where we implement a subset of Chombo's functionality in Titanium. Chombo is a software package applying the Adaptive Mesh Refinement methodology to numerical Partial Differential Equations at the production level. In Chombo, the library approach is used to parallel programming (C++ and Fortran, with MPI), whereas Titanium is a Java dialect designed for high-performance scientific computing. The performance of our implementation is studied and compared with that of Chombo in solving Poisson's equation based on two grid configurations from a real application. Also provided are the counts of lines of code from both sides.
Algorithm refinement for fluctuating hydrodynamics
Williams, Sarah A.; Bell, John B.; Garcia, Alejandro L.
2007-07-03
This paper introduces an adaptive mesh and algorithmrefinement method for fluctuating hydrodynamics. This particle-continuumhybrid simulates the dynamics of a compressible fluid with thermalfluctuations. The particle algorithm is direct simulation Monte Carlo(DSMC), a molecular-level scheme based on the Boltzmann equation. Thecontinuum algorithm is based on the Landau-Lifshitz Navier-Stokes (LLNS)equations, which incorporate thermal fluctuations into macroscopichydrodynamics by using stochastic fluxes. It uses a recently-developedsolver for LLNS, based on third-order Runge-Kutta. We present numericaltests of systems in and out of equilibrium, including time-dependentsystems, and demonstrate dynamic adaptive refinement by the computationof a moving shock wave. Mean system behavior and second moment statisticsof our simulations match theoretical values and benchmarks well. We findthat particular attention should be paid to the spectrum of the flux atthe interface between the particle and continuum methods, specificallyfor the non-hydrodynamic (kinetic) time scales.
SILICON REFINING BY VACUUM TREATMENT
André Alexandrino Lotto
2014-12-01
Full Text Available This work aims to investigate the phosphorus removal by vacuum from metallurgical grade silicon (MGSi (98.5% to 99% Si. Melting experiments were carried out in a vacuum induction furnace, varying parameters such as temperature, time and relation area exposed to the vacuum / volume of molten silicon. The results of chemical analysis were obtained by inductively coupled plasma (ICP, and evaluated based on thermodynamic and kinetic aspects of the reaction of vaporization of the phosphorus in the silicon. The phosphorus was decreased from 33 to approximately 1.5 ppm after three hours of vacuum treatment, concluding that the evaporation step is the controlling step of the process for parameters of temperature, pressure and agitation used and refining by this process is technically feasible.
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.
Comparing High-latitude Ionospheric and Thermospheric Lagrangian Coherent Structures
Wang, N.; Ramirez, U.; Flores, F.; Okic, D.; Datta-Barua, S.
2015-12-01
Lagrangian Coherent Structures (LCSs) are invisible boundaries in time varying flow fields that may be subject to mixing and turbulence. The LCS is defined by the local maxima of the finite time Lyapunov exponent (FTLE), a scalar field quantifying the degree of stretching of fluid elements over the flow domain. Although the thermosphere is dominated by neutral wind processes and the ionosphere is governed by plasma electrodynamics, we can compare the LCS in the two modeled flow fields to yield insight into transport and interaction processes in the high-latitude IT system. For obtaining thermospheric LCS, we use the Horizontal Wind Model 2014 (HWM14) [1] at a single altitude to generate the two-dimensional velocity field. The FTLE computation is applied to study the flow field of the neutral wind, and to visualize the forward-time Lagrangian Coherent Structures in the flow domain. The time-varying structures indicate a possible thermospheric LCS ridge in the auroral oval area. The results of a two-day run during a geomagnetically quiet period show that the structures are diurnally quasi-periodic, thus that solar radiation influences the neutral wind flow field. To find the LCS in the high-latitude ionospheric drifts, the Weimer 2001 [2] polar electric potential model and the International Geomagnetic Reference Field 11 [3] are used to compute the ExB drift flow field in ionosphere. As with the neutral winds, the Lagrangian Coherent Structures are obtained by applying the FTLE computation. The relationship between the thermospheric and ionospheric LCS is analyzed by comparing overlapping FTLE maps. Both a publicly available FTLE solver [4] and a custom-built FTLE computation are used and compared for validation [5]. Comparing the modeled IT LCSs on a quiet day with the modeled IT LCSs on a storm day indicates important factors on the structure and time evolution of the LCS.
Bounded fractional diffusion in geological media: Definition and Lagrangian approximation
Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang
2016-01-01
Spatiotemporal Fractional-Derivative Models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and non-zero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing non-zero-value spatial-nonlocal boundary conditions with directional super-diffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eularian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the non-local and non-symmetric fractional diffusion. For a non-zero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite do mains to those with any size and boundary conditions.
Zhang, Y.; Dioos, B.; Hu, Z.; Vrancken, L.; Wang, X.
2016-10-01
In this paper, we study the Lagrangian submanifolds in the homogeneous nearly Kähler S3 ×S3 with parallel second fundamental form. We first prove that every Lagrangian submanifold with parallel second fundamental form in any 6-dimensional strict nearly Kähler manifold is totally geodesic. Then we give a complete classification of the totally geodesic Lagrangian submanifolds in the homogeneous nearly Kähler S3 ×S3.
Comment on Pauli-Villars Lagrangian on the Lattice
Haga, K; Okuyama, K; Suzuki, H; Haga, Kazunobu; Igarashi, Hiroshi; Okuyama, Kiyoshi; Suzuki, Hiroshi
1997-01-01
It is interesting to superimpose the Pauli--Villars regularization on the lattice regularization. We illustrate how this scheme works by evaluating the axial anomaly in a simple lattice fermion model, the Pauli--Villars Lagrangian with a gauge non-invariant Wilson term. The gauge non-invariance of the axial anomaly, caused by the Wilson term, is remedied by a compensation between Pauli--Villars regulators in the continuum limit. A subtlety in Frolov--Slavnov's scheme for an {\\it odd\\/} number of chiral fermions in an anomaly free complex gauge representation, which requires an infinite number of regulators, is briefly mentioned.
Inflation, bifurcations of nonlinear curvature Lagrangians and dark energy
Mielke, Eckehard W; Schunck, Franz E
2008-01-01
A possible equivalence of scalar dark matter, the inflaton, and modified gravity is analyzed. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einsteinian spaces, distinguished only by a different effective gravitational strength and cosmological constant. A swallow tail catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This `triple unification' may shed new light on the nature and large scale distribution not only of dark matter but also on `dark energy', regarded as an effective cosmological constant, and inflation.
Attraction-Based Computation of Hyperbolic Lagrangian Coherent Structures
Karrasch, Daniel; Haller, George
2014-01-01
Recent advances enable the simultaneous computation of both attracting and repelling families of Lagrangian Coherent Structures (LCS) at the same initial or final time of interest. Obtaining LCS positions at intermediate times, however, has been problematic, because either the repelling or the attracting family is unstable with respect to numerical advection in a given time direction. Here we develop a new approach to compute arbitrary positions of hyperbolic LCS in a numerically robust fashion. Our approach only involves the advection of attracting material surfaces, thereby providing accurate LCS tracking at low computational cost. We illustrate the advantages of this approach on a simple model and on a turbulent velocity data set.
Radiative neutron-proton capture in effective chiral lagrangians
Park, T S; Rho, M; Park, Tae Sun; Min, Dong Pil; Rho, Mannque
1994-01-01
We calculate the cross-section for the thermal n+p\\rightarrow d+\\gamma process in chiral perturbation theory to next-to-next-to-leading order using heavy-fermion formalism. The exchange current correction is found to be (4.5\\pm 0.3)~\\% in amplitude and the chiral perturbation at one-loop order gives the cross section \\sigma_{th}^{np}=(334\\pm 2)\\ {\\mbox mb} which is in agreement with the experimental value (334.2\\pm 0.5)\\ {\\mbox mb}. Together with the axial charge transitions, this provides a strong support for the power of chiral Lagrangians for nuclear physics.
Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics.
Ilinskii, Yurii A; Hamilton, Mark F; Zabolotskaya, Evgenia A
2007-02-01
Two models of interacting bubble dynamics are presented, a coupled system of second-order differential equations based on Lagrangian mechanics, and a first-order system based on Hamiltonian mechanics. Both account for pulsation and translation of an arbitrary number of spherical bubbles. For large numbers of interacting bubbles, numerical solution of the Hamiltonian equations provides greater stability. The presence of external acoustic sources is taken into account explicitly in the derivation of both sets of equations. In addition to the acoustic pressure and its gradient, it is found that the particle velocity associated with external sources appears in the dynamical equations.
On Problems of the Lagrangian Quantization of W3-gravity
Geyer, B; Lavrov, P M; Moshin, P Y
2003-01-01
We consider the two-dimensional model of W3-gravity within Lagrangian quantization methods for general gauge theories. We use the Batalin-Vilkovisky formalism to study the arbitrariness in the realization of the gauge algebra. We obtain a one-parametric non-analytic extension of the gauge algebra, and a corresponding solution of the classical master equation, related via an anticanonical transformation to a solution corresponding to an analytic realization. We investigate the possibility of closed solutions of the classical master equation in the Sp(2)-covariant formalism and show that such solutions do not exist in the approximation up to the third order in ghost and auxiliary fields.
Lagrangian chaos and small scale structure of passive scalars
Vulpiani, Angelo
1989-09-01
We revise the classical theory of Batchelor, which gives a k-1 law for the power spectrum of a passive scalar at wavenumbers k, for which the molecular diffusion is unimportant and much smaller than the fluid viscosity. Using some ideas borrowed from the theory of dynamical systems, we show that this power law is related to the chaotic motion of marker particles (Lagrangian chaos) and to the incompressibility constraint. Moreover our approach permits showing that the k-1 regime is present in fluids which are not turbulent and it is valid for all dimensionalities d⩾2.
k Spectrum of Passive Scalars in Lagrangian Chaotic Fluid Flows
Antonsen, Thomas M., Jr.; Fan, Zhencan Frank; Ott, Edward
1995-08-01
An eikonal-type description for the evolution of k spectra of passive scalars convected in a Lagrangian chaotic fluid flow is shown to accurately reproduce results from orders of magnitude more time consuming computations based on the full passive scalar partial differential equation. Furthermore, the validity of the reduced description, combined with concepts from chaotic dynamics, allows new theoretical results on passive scalar k spectra to be obtained. Illustrative applications are presented to long-time passive scalar decay, and to Batchelor's law k spectrum and its diffusive cutoff.
Hilbert series for constructing Lagrangians: Expanding the phenomenologist's toolbox
Lehman, Landon; Martin, Adam
2015-05-01
This paper presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a given field content and is a useful cross-check on more well-known group theoretical methods. In addition, at least when restricted to invariants without derivatives, the Hilbert series technique supplies a robust way of counting invariants in scenarios which, due to the large number of fields involved or to high-dimensional group representations, are intractable by traditional methods. We work out several practical examples.
Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
Lehman, Landon
2015-01-01
This note presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a given field content, and is a useful cross check on more well-known group theoretical methods. In addition, at least when restricted to invariants without derivatives, the Hilbert series technique supplies a robust way of counting invariants in scenarios which, due to the large number of fields involved or to high dimensional group representations, are intractable by traditional methods. We work out several practical examples.
A hybrid Eulerian Lagrangian numerical scheme for solving prognostic equations in fluid dynamics
E. Kaas
2013-07-01
Full Text Available A new hybrid Eulerian Lagrangian numerical scheme (HEL for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place, i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.
A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
Li, Wenliang
2015-01-01
We develop a general framework for Lorentz-invariant Lagrangian field theories that leads to second order equations of motion. The key ingredient is the antisymmetric Kronecker delta. Then we reformulate the general ghost-free Lagrangians in the language of differential forms. The absence of higher order equations of motion stems from the basic fact that every exact form is closed. All known ghost-free Lagrangian theories for spin-0, spin-1, spin-2 fields have natural formulations in this framework. We propose new ghost-free Lagrangians, for example, novel nonlinear kinetic terms for graviton.
宋丽娜; 王维国
2012-01-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Zone refining of cadmium and related characterization
N R Munirathnam; D S Prasad; Ch Sudheer; J V Rao; T L Prakash
2005-06-01
We present the zone refining results of cadmium using horizontal resistive zone refiner under constant flow of moisture free hydrogen gas. The boron impurity in cadmium can be avoided using quartz (GE 214 grade) boat in lieu of high pure graphite boat. The analytical results using inductively coupled plasma optical emission spectrometry (ICPOES) show that majority of the impurities are less than the detection limits. Comparatively, zinc is the most difficult impurity element to remove in cadmium matrix by zone refining.
Refined curve counting on complex surfaces
Göttsche, Lothar; Shende, Vivek
2012-01-01
We define refined invariants which "count" nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces. We also give a refinement of the Caporaso-Harris recursion, and conjecture that it produces the same invariants in the sufficiently ample setting. The refined recursion specializes at y = -1 to the Itenberg-Kharlamov-Shustin recursion for Welschinger invari...
Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions
Yale, Alexandre
2010-01-01
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 co-variance, 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 $D = 2m$ 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 $D = 2m$. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In parti...
Lagrangian Floer Superpotentials and Crepant Resolutions for Toric Orbifolds
Chan, Kwokwai; Cho, Cheol-Hyun; Lau, Siu-Cheong; Tseng, Hsian-Hua
2014-05-01
We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold and that of its toric crepant resolution Y coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we find that the change of variable formula which appears in closed CRC can be explained by relations between open (orbifold) Gromov-Witten invariants. We also discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appears in Ruan's original CRC (Gromov-Witten theory of spin curves and orbifolds, contemp math, Amer. Math. Soc., Providence, RI, pp 117-126, 2006). We prove the open CRC for the weighted projective spaces using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.
The initial value problem in Lagrangian drift kinetic theory
Burby, J. W.
2016-06-01
> Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low orders. These unphysical modes, which may be rapidly oscillating, damped or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model's initial value problem. In short, the (infinite dimensional) system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, `renormalized' variational approach to drift kinetic theory that manifestly respects the parent model's initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase-space Lagrangian instead of the usual `field particle' Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dimensional toy model of high-order variational drift kinetics; the analogous full-on drift kinetic story is discussed subsequently. The renormalized drift kinetic system, while variational and just as formally accurate as conventional formulations, does not support the troublesome rapidly varying modes.
The initial value problem in Lagrangian drift kinetic theory
Burby, J W
2015-01-01
Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low-orders. These unphysical modes, which may be rapidly oscillating, damped, or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model's initial value problem (Vlasov-Poisson for electrostatics, Vlasov-Darwin or Vlasov-Maxwell for electromagnetics.) In short, the system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, "renormalized" variational approach to drift kinetic theory that manifestly respects the parent model's initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase space Lagrangian instead of the usual "field+particle" Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dime...
Linear wave equations and effective lagrangians for Wigner supermultiplets
Dahm, R
1995-01-01
The relevance of the contracted SU(4) group as a symmetry group of the pion nucleon scattering amplitudes in the large N_c limit of QCD raises the problem on the construction of effective Lagrangians for SU(4) supermultiplets. In the present study we suggest effective Lagrangians for selfconjugate representations of SU(4) in exploiting isomorphism between so(6) and ist universal covering su(4). The model can be viewed as an extension of the linear \\sigma model with SO(6) symmetry in place of SO(4) and generalizes the concept of the linear wave equations for particles with arbitrary spin. We show that the vector representation of SU(4) reduces on the SO(4) level to a complexified quaternion. Its real part gives rise to the standard linear \\sigma model with a hedgehog configuration for the pion field, whereas the imaginary part describes vector meson degrees of freedom via purely transversal \\rho mesons for which a helical field configuration is predicted. As a minimal model, baryonic states are suggested to ap...
The effective Lagrangian of dark energy from observations
Jimenez, Raul; Verde, Licia; Moresco, Michele; Cimatti, Andrea; Pozzetti, Lucia
2012-01-01
Using observational data on the expansion rate of the universe (H(z)) we constrain the effective Lagrangian of the current accelerated expansion. Our results show that the effective potential is consistent with being flat i.e., a cosmological constant; it is also consistent with the field moving along an almost flat potential like a pseudo-Goldstone boson. We show that the potential of dark energy does not deviate from a constant at more than 6% over the redshift range 0 < z < 1. The data can be described by just a constant term in the Lagrangian and do not require any extra parameters; therefore there is no evidence for augmenting the number of parameters of the LCDM paradigm. We also find that the data justify the effective theory approach to describe accelerated expansion and that the allowed parameters range satisfy the expected hierarchy. Future data, both from cosmic chronometers and baryonic acoustic oscillations, that can measure H(z) at the % level, could greatly improve constraints on the flat...
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).
The Gaussian streaming model and Lagrangian effective field theory
Vlah, Zvonimir; White, Martin
2016-01-01
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of int...
The Gaussian streaming model and convolution Lagrangian effective field theory
Vlah, Zvonimir; Castorina, Emanuele; White, Martin
2016-12-01
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.
Hamiltonian and Lagrangian Dynamical Matrix Approaches Applied to Magnetic Nanostructures
Roberto Zivieri
2012-01-01
Full Text Available Two micromagnetic tools to study the spin dynamics are reviewed. Both approaches are based upon the so-called dynamical matrix method, a hybrid micromagnetic framework used to investigate the spin-wave normal modes of confined magnetic systems. The approach which was formulated first is the Hamiltonian-based dynamical matrix method. This method, used to investigate dynamic magnetic properties of conservative systems, was originally developed for studying spin excitations in isolated magnetic nanoparticles and it has been recently generalized to study the dynamics of periodic magnetic nanoparticles. The other one, the Lagrangian-based dynamical matrix method, was formulated as an extension of the previous one in order to include also dissipative effects. Such dissipative phenomena are associated not only to intrinsic but also to extrinsic damping caused by injection of a spin current in the form of spin-transfer torque. This method is very accurate in identifying spin modes that become unstable under the action of a spin current. The analytical development of the system of the linearized equations of motion leads to a complex generalized Hermitian eigenvalue problem in the Hamiltonian dynamical matrix method and to a non-Hermitian one in the Lagrangian approach. In both cases, such systems have to be solved numerically.
Fingerprints of heavy scales in electroweak effective Lagrangians
Pich, Antonio; Santos, Joaquin; Sanz-Cillero, Juan Jose
2016-01-01
The couplings of the electroweak effective theory contain information on the heavy-mass scales which are no-longer present in the low-energy Lagrangian. We build a general effective Lagrangian, implementing the electroweak chiral symmetry breaking $SU(2)_L\\otimes SU(2)_R\\to SU(2)_{L+R}$, which couples the known particle fields to heavier states with bosonic quantum numbers $J^P=0^\\pm$ and $1^\\pm$. We consider colour-singlet heavy fields that are in singlet or triplet representations of the electroweak group. Integrating out these heavy scales, we analyze the pattern of low-energy couplings among the light fields which are generated by the massive states. We adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs, without making any assumption about its possible doublet structure. Special attention is given to the different possible descriptions of massive spin-1 fields and the differences arising from naive implementations of these formalisms, showing their full equiva...
Lagrangian structures, integrability and chaos for 3D dynamical equations
Bustamante, M D; Bustamante, Miguel D.; Hojman, Sergio A.
2003-01-01
In this paper we consider the general setting for constructing Action Principles for three-dimensional first order autonomous equations. We present the results for some integrable and non-integrable cases of the Lotka-Volterra equation, and we show Lagrangian descriptions which are valid for systems satisfying Shil'nikov criteria on the existence of strange attractors, though chaotic behavior or homoclinic orbits have not been verified up to now. The Euler-Lagrange equations we get for these systems usually present "time reparameterization" symmetry, though other kinds of invariance may be found according to the kernel of the associated symplectic 2-form. The formulation of a Hamiltonian structure (Poisson brackets and Hamiltonians) for these systems from the Lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones, which is applied to some systems found in the literature known to possess a constant of the motion, to find the other and thus showing their integrabi...
A few words about resonances in the electroweak effective Lagrangian
Rosell, Ignasi [Departamento de Ciencias Físicas, Matemáticas y de la Computación, Universidad CEU Cardenal Herrera, c/ Sant Bartomeu 55, 46115 Alfara del Patriarca, València (Spain); Pich, Antonio; Santos, Joaquín [Departament de Física Teòrica, IFIC, Universitat de València – CSIC, Apt. Correus 22085, 46071 València (Spain); Sanz-Cillero, Juan José [Departamento de Física Teórica and Instituto Física Teórica, IFT-UAM/CSIC, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain)
2016-01-22
Contrary to a widely spread believe, we have demonstrated that strongly coupled electroweak models including both a light Higgs-like boson and massive spin-1 resonances are not in conflict with experimental constraints on the oblique S and T parameters. We use an effective Lagrangian implementing the chiral symmetry breaking SU (2){sub L} ⊗ SU (2){sub R} → SU (2){sub L+R} that contains the Standard Model gauge bosons coupled to the electroweak Goldstones, one Higgs-like scalar state h with mass m{sub h} = 126 GeV and the lightest vector and axial-vector resonance multiplets V and A. We have considered the one-loop calculation of S and T in order to study the viability of these strongly-coupled scenarios, being short-distance constraints and dispersive relations the main ingredients of the calculation. Once we have constrained the resonance parameters, we do a first approach to the determination of the low energy constants of the electroweak effective theory at low energies (without resonances). We show this determination in the case of the purely Higgsless bosonic Lagrangian.
Chen, H. X.; Chua, Patrick S. K.; Lim, G. H.
2008-10-01
The machinery fault diagnosis is important for improving reliability and performance of systems. Many methods such as Time Synchronous Average (TSA), Fast Fourier Transform (FFT)-based spectrum analysis and short-time Fourier transform (STFT) have been applied in fault diagnosis and condition monitoring of mechanical system. The above methods analyze the signal in frequency domain with low resolution, which is not suitable for non-stationary vibration signal. The Kolmogorov-Smirnov (KS) test is a simple and precise technique in vibration signal analysis for machinery fault diagnosis. It has limited use and advantage to analyze the vibration signal with higher noise directly. In this paper, a new method for the fault degradation assessment of the water hydraulic motor is proposed based on Wavelet Packet Analysis (WPA) and KS test to analyze the impulsive energy of the vibration signal, which is used to detect the piston condition of water hydraulic motor. WPA is used to analyze the impulsive vibration signal from the casing of the water hydraulic motor to obtain the impulsive energy. The impulsive energy of the vibration signal can be obtained by the multi-decomposition based on Wavelet Packet Transform (WPT) and used as feature values to assess the fault degradation of the pistons. The kurtosis of the impulsive energy in the reconstructed signal from the Wavelet Packet coefficients is used to extract the feature values of the impulse energy by calculating the coefficients of the WPT multi-decomposition. The KS test is used to compare the kurtosis of the impulse energy of the vibration signal statistically under the different piston conditions. The results show the applicability and effectiveness of the proposed method to assess the fault degradation of the pistons in the water hydraulic motor.
Zhan, Yimin; Mechefske, Chris K.
2007-07-01
Optimal maintenance decision analysis is heavily dependent on the accuracy of condition indicators. A condition indicator that is subject to such varying operating conditions as load is unable to provide precise condition information of the monitored object for making optimal operational maintenance decisions even if the maintenance program is established within a rigorous theoretical framework. For this reason, the performance of condition monitoring techniques applied to rotating machinery under varying load conditions has been a long-term concern and has attracted intensive research interest. Part I of this study proposed a novel technique based on adaptive autoregressive modeling and hypothesis tests. The method is able to automatically search for the optimal time-series model order and establish a compromised autoregressive model fitting based on the healthy gear motion residual signals under varying load conditions. The condition of the monitored gearbox is numerically represented by a modified Kolmogorov-Smirnov test statistic. Part II of this study is devoted to applications of the proposed technique to entire lifetime condition detection of three gearboxes with distinct physical specifications, distinct load conditions, and distinct failure modes. A comprehensive and thorough comparative study is conducted between the proposed technique and several counterparts. The detection technique is further enhanced by a proposed method to automatically identify and generate fault alerts with the aid of the Wilcoxon rank-sum test and thus requires no supervision from maintenance personnel. Experimental analysis demonstrated that the proposed technique applied to automatic identification and generation of fault alerts also features two highly desirable properties, i.e. few false alerts and early alert for incipient faults. Furthermore, it is found that the proposed technique is able to identify two types of abnormalities, i.e. strong ghost components abruptly
High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model.
Graham, J Pietarila; Mininni, P D; Pouquet, A
2011-07-01
With the help of a model of magnetohydrodynamic (MHD) turbulence tested previously, we explore high Reynolds number regimes up to equivalent resolutions of 6000(3) grid points in the absence of forcing and with no imposed uniform magnetic field. For the given initial condition chosen here, with equal kinetic and magnetic energy, the flow ends up being dominated by the magnetic field, and the dynamics leads to an isotropic Iroshnikov-Kraichnan energy spectrum. However, the locally anisotropic magnetic field fluctuations perpendicular to the local mean field follow a Kolmogorov law. We find that the ratio of the eddy turnover time to the Alfvén time increases with wave number, contrary to the so-called critical balance hypothesis. Residual energy and helicity spectra are also considered; the role played by the conservation of magnetic helicity is studied, and scaling laws are found for the magnetic helicity and residual helicity spectra. We put these results in the context of the dynamics of a globally isotropic MHD flow that is locally anisotropic because of the influence of the strong large-scale magnetic field, leading to a partial equilibration between kinetic and magnetic modes for the energy and the helicity.
沈伯骞; 刘德明
2000-01-01
This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system may possess limit cycles.
Protein structure refinement by optimization.
Carlsen, Martin; Røgen, Peter
2015-09-01
Knowledge-based protein potentials are simplified potentials designed to improve the quality of protein models, which is important as more accurate models are more useful for biological and pharmaceutical studies. Consequently, knowledge-based potentials often are designed to be efficient in ordering a given set of deformed structures denoted decoys according to how close they are to the relevant native protein structure. This, however, does not necessarily imply that energy minimization of this potential will bring the decoys closer to the native structure. In this study, we introduce an iterative strategy to improve the convergence of decoy structures. It works by adding energy optimized decoys to the pool of decoys used to construct the next and improved knowledge-based potential. We demonstrate that this strategy results in significantly improved decoy convergence on Titan high resolution decoys and refinement targets from Critical Assessment of protein Structure Prediction competitions. Our potential is formulated in Cartesian coordinates and has a fixed backbone potential to restricts motions to be close to those of a dihedral model, a fixed hydrogen-bonding potential and a variable coarse grained carbon alpha potential consisting of a pair potential and a novel solvent potential that are b-spline based as we use explicit gradient and Hessian for efficient energy optimization.
Model Checking Linearizability via Refinement
Liu, Yang; Chen, Wei; Liu, Yanhong A.; Sun, Jun
Linearizability is an important correctness criterion for implementations of concurrent objects. Automatic checking of linearizability is challenging because it requires checking that 1) all executions of concurrent operations be serializable, and 2) the serialized executions be correct with respect to the sequential semantics. This paper describes a new method to automatically check linearizability based on refinement relations from abstract specifications to concrete implementations. Our method avoids the often difficult task of determining linearization points in implementations, but can also take advantage of linearization points if they are given. The method exploits model checking of finite state systems specified as concurrent processes with shared variables. Partial order reduction is used to effectively reduce the search space. The approach is built into a toolset that supports a rich set of concurrent operators. The tool has been used to automatically check a variety of implementations of concurrent objects, including the first algorithms for the mailbox problem and scalable NonZero indicators. Our system was able to find all known and injected bugs in these implementations.
Finite Element Based Lagrangian Vortex Dynamics Model for Wind Turbine Aerodynamics
McWilliam, Michael K.; Crawford, Curran
2014-06-01
This paper presents a novel aerodynamic model based on Lagrangian Vortex Dynamics (LVD) formulated using a Finite Element (FE) approach. The advantage of LVD is improved fidelity over Blade Element Momentum Theory (BEMT) while being faster than Numerical Navier-Stokes Models (NNSM) in either primitive or velocity-vorticity formulations. The model improves on conventional LVD in three ways. First, the model is based on an error minimization formulation that can be solved with fast root finding algorithms. In addition to improving accuracy, this eliminates the intrinsic numerical instability of conventional relaxed wake simulations. The method has further advantages in optimization and aero-elastic simulations for two reasons. The root finding algorithm can solve the aerodynamic and structural equations simultaneously, avoiding Gauss-Seidel iteration for compatibility constraints. The second is that the formulation allows for an analytical definition for sensitivity calculations. The second improvement comes from a new discretization scheme based on an FE formulation and numerical quadrature that decouples the spatial, influencing and temporal meshes. The shape for each trailing filament uses basis functions (interpolating splines) that allow for both local polynomial order and element size refinement. A completely independent scheme distributes the influencing (vorticity) elements along the basis functions. This allows for concentrated elements in the near wake for accuracy and progressively less in the far-wake for efficiency. Finally the third improvement is the use of a far-wake model based on semi-infinite vortex cylinders where the radius and strength are related to the wake state. The error-based FE formulation allows the transition to the far wake to occur across a fixed plane.
Refinement Checking on Parametric Modal Transition Systems
Benes, Nikola; Kretínsky, Jan; Larsen, Kim Guldstrand
2015-01-01
Modal transition systems (MTS) is a well-studied specification formalism of reactive systems supporting a step-wise refinement methodology. Despite its many advantages, the formalism as well as its currently known extensions are incapable of expressing some practically needed aspects in the refin...
Refined large N duality for torus knots
Nawata, Satoshi; Kameyama, Masaya
We formulate large N duality of U(N) refined Chern-Simons theory with a torus knot/link in S³. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate...
Refinement Checking on Parametric Modal Transition Systems
Benes, Nikola; Kretínsky, Jan; Larsen, Kim Guldstrand
2015-01-01
Modal transition systems (MTS) is a well-studied specification formalism of reactive systems supporting a step-wise refinement methodology. Despite its many advantages, the formalism as well as its currently known extensions are incapable of expressing some practically needed aspects in the refin...
Refined Black Hole Ensembles and Topological Strings
Aganagic, Mina
2012-01-01
We formulate a refined version of the Ooguri-Strominger-Vafa (OSV) conjecture. The OSV conjecture that Z_{BH} = |Z_{top}|^2 relates the BPS black hole partition function to the topological string partition function Z_{top}. In the refined conjecture, Z_{BH} is the partition function of BPS black holes counted with spin, or more precisely the protected spin character. Z_{top} becomes the partition function of the refined topological string, which is itself an index. Both the original and the refined conjecture are examples of large N duality in the 't Hooft sense. The refined conjecture applies to non-compact Calabi-Yau manifolds only, so the black holes are really BPS particles with large entropy, of order N^2. The refined OSV conjecture states that the refined BPS partition function has a large N dual which is captured by the refined topological string. We provide evidence that the conjecture holds by studying local Calabi-Yau threefolds consisting of line bundles over a genus g Riemann surface. We show that...
Refined large N duality for torus knots
Nawata, Satoshi; Kameyama, Masaya
We formulate large N duality of U(N) refined Chern-Simons theory with a torus knot/link in S³. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the Ω-background. This form enables us to relate...
China Becomes Globe's Second Largest Oil Refiner
Zhang Weijun
2010-01-01
@@ China's refining capacity of crude oil reached 477 million tons by the end of last year,ranking the second in the world.CNPC and Sinopec now own 27 percent of the country's oil refineries with a combined refining capacity amounting to 76 percent of the country's total.As the country's biggest oil refiner,Sinopec's refining ability has increased 72.8 percent in the past ten years with a growth rate of 6.3 percent per year,ranking the third in the world,according to statistics released by Sinopec.Meanwhile,China's local oil refining enterprises' total capacity has reached 88 million tons per year.According to Sinopec,China has built 17 ten-million-ton-oil refineries which amount to half of the country's total capacity.
Wang, Dake
2011-01-01
We construct singular solutions to special Lagrangian equa- tions with subcritical phases and minimal surface systems. A priori estimate breaking families of smooth solutions are also produced cor- respondingly. A priori estimates for special Lagrangian equations with certain convexity are largely known by now.
On nonlinear controllability and series expansions for Lagrangian systems with dissipative forces
Cortes, J.; Martinez, S.; Bullo, F.
2002-01-01
This paper presents series expansions and nonlinear controllability results for Lagrangian systems subject to dissipative forces. The treatment relies on the assumption of dissipative forces of linear isotropic nature. The approach is based on the affine connection formalism for Lagrangian control s
Modified Lagrangian and Least Root Approaches for General Nonlinear Optimization Problems
W. Oettli; X.Q. Yang
2002-01-01
In this paper we study nonlinear Lagrangian methods for optimization problems with side constraints.Nonlinear Lagrangian dual problems are introduced and their relations with the original problem are established.Moreover, a least root approach is investigated for these optimization problems.