Journal articles on the topic 'Lagrangian Statistical Method'
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Li, Jiaojiao, Shanzhou Niu, Jing Huang, Zhaoying Bian, Qianjin Feng, Gaohang Yu, Zhengrong Liang, Wufan Chen, and Jianhua Ma. "An Efficient Augmented Lagrangian Method for Statistical X-Ray CT Image Reconstruction." PLOS ONE 10, no. 10 (October 23, 2015): e0140579. http://dx.doi.org/10.1371/journal.pone.0140579.
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Grosshans, H., R. ‐Z Szász, and L. Fuchs. "Development of an efficient statistical volumes of fluid–Lagrangian particle tracking coupling method." International Journal for Numerical Methods in Fluids 74, no. 12 (February 4, 2014): 898–918. http://dx.doi.org/10.1002/fld.3879.
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WANG, Y. J., N. ZHAO, C. W. WANG, and D. H. WANG. "A SECOND-ORDER ADAPTIVE ARBITRARY LAGRANGIAN–EULERIAN METHOD FOR THE COMPRESSIBLE EULER EQUATIONS." Modern Physics Letters B 23, no. 04 (February 10, 2009): 583–601. http://dx.doi.org/10.1142/s0217984909017923.
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Most of finite volume schemes in the Arbitrary Lagrangian–Eulerian (ALE) method are constructed on the staggered mesh, where the momentum is defined at the nodes and the other variables (density, pressure and specific internal energy) are cell-centered. However, this kind of schemes must use a cell-centered remapping algorithm twice which is very inefficient. Furthermore, there is inconsistent treatment of the kinetic and internal energies.1 Recently, a new class of cell-centered Lagrangian scheme for two-dimensional compressible flow problems has been proposed in Ref. 2. The main new feature of the algorithm is the introduction of four pressures on each edge, two for each node on each side of the edge. This scheme is only first-order accurate. In this paper, a second-order cell-centered conservative ENO Lagrangian scheme is constructed by using an ENO-type approach to extend the spatial second-order accuracy. Time discretization is based on a second-order Runge–Kutta scheme. Combining a conservative interpolation (remapping) method3,4 with the second-order Lagrangian scheme, a kind of cell-centered second-order ALE methods can be obtained. Some numerical experiments are made with this method. All results show that our method is effective and have second-order accuracy. At last, in order to further increase the resolution of shock regions, we use an adaptive mesh generation based on the variational principle5 as a rezoned strategy for developing a class of adaptive ALE methods. Numerical experiments are also presented to valid the performance of the proposed method.
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CHEN, DI-JIA, KUN-HAO LIN, and CHAO-AN LIN. "IMMERSED BOUNDARY METHOD BASED LATTICE BOLTZMANN METHOD TO SIMULATE 2D AND 3D COMPLEX GEOMETRY FLOWS." International Journal of Modern Physics C 18, no. 04 (April 2007): 585–94. http://dx.doi.org/10.1142/s0129183107010826.
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In this paper, the lattice Boltzmann method is combined with the immersed boundary technique to simulate complex geometry flows. The complex geometry is represented by Lagrangian markers and forces are exerted at the Lagrangian markers in order to satisfy the prescribed velocity of the boundary. This force at the Lagrangian markers is then distributed to the Eulerian grid by a well-chosen discretized delta function. With the known force field in the Eulerian grid to mimic the boundary, the lattice Boltzmann method is used to compute the flow field where the complex geometry is immersed inside the Cartesian computational domain. Numerical experiments show that the second-order accuracy of the adopted numerical scheme is degraded to 1.8 order. The proposed method is examined by computing decaying vortex, lid driven cavity flow and 2D and 3D flows over asymmetrically placed cylinder. All the numerical results are compatible with the benchmark solutions.
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Fan, Xiaofeng, Jiangfeng Wang, Faming Zhao, Jiawei Li, and Tianpeng Yang. "Eulerian–Lagrangian method for liquid jet atomization in supersonic crossflow using statistical injection model." Advances in Mechanical Engineering 10, no. 2 (February 2018): 168781401876129. http://dx.doi.org/10.1177/1687814018761295.
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Sigmond, M., J. Meloen, and P. C. Siegmund. "Stratosphere-troposphere exchange in an extratropical cyclone, calculated with a Lagrangian method." Annales Geophysicae 18, no. 5 (May 31, 2000): 573–82. http://dx.doi.org/10.1007/s00585-000-0573-1.
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Abstract. A Lagrangian technique is developed and applied to calculate stratosphere-troposphere exchange in an extratropical cyclone. This exchange is computed from the potential vorticity or PV along trajectories, calculated from ECMWF circulation data. Special emphasis is put on the statistical significance of the results. The computed field of the cross-tropopause flux is dominated by elongated patterns of statistically significant large downward and small upward fluxes. The downward fluxes mainly occur in the lower part of the considered tropopause folds. The upward fluxes are found near the entrance of the folds, in the tropopause ridges. The ratio between the area averaged downward and upward cross-tropopause fluxes increases with increasing strength of the cyclone. Since the largest fluxes are shown to occur in the regions with the largest wind shear, where PV-mixing is thought to cause large cross-tropopause fluxes, the results are expected to be reliable, at least in a qualitative sense. The position of a tropopause fold along the northwest coast of Africa is confirmed by total ozone observations. The results indicate that the applied Lagrangian technique is an appropriate tool for diagnosing stratosphere-troposphere exchange.Key words: Meteorology and atmospheric dynamics (general circulation; mesoscale meteorology; middle atmosphere dynamics)
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Abarbanel, Henry D. I., Paul J. Rozdeba, and Sasha Shirman. "Machine Learning: Deepest Learning as Statistical Data Assimilation Problems." Neural Computation 30, no. 8 (August 2018): 2025–55. http://dx.doi.org/10.1162/neco_a_01094.
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We formulate an equivalence between machine learning and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in a feedforward artificial network setting is the analog of time in the data assimilation setting. This connection has been noted in the machine learning literature. We add a perspective that expands on how methods from statistical physics and aspects of Lagrangian and Hamiltonian dynamics play a role in how networks can be trained and designed. Within the discussion of this equivalence, we show that adding more layers (making the network deeper) is analogous to adding temporal resolution in a data assimilation framework. Extending this equivalence to recurrent networks is also discussed. We explore how one can find a candidate for the global minimum of the cost functions in the machine learning context using a method from data assimilation. Calculations on simple models from both sides of the equivalence are reported. Also discussed is a framework in which the time or layer label is taken to be continuous, providing a differential equation, the Euler-Lagrange equation and its boundary conditions, as a necessary condition for a minimum of the cost function. This shows that the problem being solved is a two-point boundary value problem familiar in the discussion of variational methods. The use of continuous layers is denoted “deepest learning.” These problems respect a symplectic symmetry in continuous layer phase space. Both Lagrangian versions and Hamiltonian versions of these problems are presented. Their well-studied implementation in a discrete time/layer, while respecting the symplectic structure, is addressed. The Hamiltonian version provides a direct rationale for backpropagation as a solution method for a certain two-point boundary value problem.
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Wang, Han, and Oliver Bühler. "Anisotropic Statistics of Lagrangian Structure Functions and Helmholtz Decomposition." Journal of Physical Oceanography 51, no. 5 (May 2021): 1375–93. http://dx.doi.org/10.1175/jpo-d-20-0199.1.
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AbstractWe present a new method to estimate second-order horizontal velocity structure functions, as well as their Helmholtz decomposition into rotational and divergent components, from sparse data collected along Lagrangian observations. The novelty compared to existing methods is that we allow for anisotropic statistics in the velocity field and also in the collection of the Lagrangian data. Specifically, we assume only stationarity and spatial homogeneity of the data and that the cross covariance between the rotational and divergent flow components is either zero or a function of the separation distance only. No further assumptions are made and the anisotropy of the underlying flow components can be arbitrarily strong. We demonstrate our new method by testing it against synthetic data and applying it to the Lagrangian Submesoscale Experiment (LASER) dataset. We also identify an improved statistical angle-weighting technique that generally increases the accuracy of structure function estimations in the presence of anisotropy.
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WANG, DONGHONG, NING ZHAO, and YONGJIAN WANG. "A CELL-CENTERED LAGRANGIAN SCHEME FOR COMPRESSIBLE MULTI-MEDIUM FLOW." Modern Physics Letters B 24, no. 13 (May 30, 2010): 1283–86. http://dx.doi.org/10.1142/s0217984910023438.
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In this paper, a kind of Godunov-type Lagrangian scheme is developed in the one space dimension. The Riemann problems are constructed at the interface and the velocity and pressure are evaluated using an implicit characteristic method. Two different methods are used to solve for the equation of energy conservation. Four one-dimensional numerical examples are first presented to obtain the parameter through comparison of the L1 errors with the changing parameter values. The method having the minimal error is then extended to two dimensions and a cell-centered conservative Lagrangian scheme is proposed for the compressible multi-medium flow. The numerical results for some classical two dimensional hydrodynamic test cases show that the proposed numerical methods are effective and feasible.
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CHEN, HONGQUAN, and LING RAO. "THE TECHNIQUE OF THE IMMERSED BOUNDARY METHOD: APPLICATIONS TO THE NUMERICAL SOLUTIONS OF IMCOMPRESSIBLE FLOWS AND WAVE SCATTERING." Modern Physics Letters B 23, no. 03 (January 30, 2009): 437–40. http://dx.doi.org/10.1142/s021798490901859x.
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A fictitious domain method, in which the Dirichlet boundary conditions are treated using boundary supported Lagrangian multipliers, is considered. The technique of the immersed boundary method is incorporated into the framework of the fictitious domain method. Contrary to conventional methods, it does not make use of the finite element discretization. It has a simpler structure and is easily programmable. The numerical simulation of two-dimensional incompressible inviscid uniform flows over a circular cylinder validates the methodology and the numerical procedure. The numerical simulation of propagation phenomena for time harmonic electromagnetic waves by methods combining controllability and fictitious domain techniques is also presented. Using distributed Lagrangian multipliers, the propagation of the wave can be simulated on an obstacle free computational region with regular finite element meshes essentially independent of the geometry of the obstacle and by a controllability formulation which leads to algorithms with good convergence properties for time-periodic solutions. The numerical results presented are in good agreement with those in the literature using obstacle fitted meshes.
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ABECASIS, C., and O. S. ZANDRON. "DIAGRAMMATICS AND FEYNMAN RULES IN THE LAGRANGIAN THEORY BASED ON THE spl(2,1) GRADED ALGEBRA." International Journal of Modern Physics B 21, no. 01 (January 10, 2007): 97–115. http://dx.doi.org/10.1142/s0217979207035881.
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From the path-integral method, the diagrammatics and Feynman rules for the Lagrangian theory based on the spl(2,1) graded algebra are constructed. The first-order Lagrangian we have obtained is written in terms of the graded Hubbard operators. By using functional techniques, the correlation generating functional is given in terms of the proper effective Lagrangian of the model. Once the Feynman rules, propagators and vertices were found, a physical discussion about the free propagators is given. Finally, the expressions of the boson self-energy and the renormalized boson propagator are used to study the hole effects on the magnetic properties of the high-T c cuprates.
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Hillebrand, M., S. Zimper, A. Ngapasare, M. Katsanikas, S. Wiggins, and Ch Skokos. "Quantifying chaos using Lagrangian descriptors." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 12 (December 2022): 123122. http://dx.doi.org/10.1063/5.0120889.
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We present and validate simple and efficient methods to estimate the chaoticity of orbits in low-dimensional conservative dynamical systems, namely, autonomous Hamiltonian systems and area-preserving symplectic maps, from computations of Lagrangian descriptors (LDs) on short time scales. Two quantities are proposed for determining the chaotic or regular nature of orbits in a system’s phase space, which are based on the values of the LDs of these orbits and of nearby ones: The difference and ratio of neighboring orbits’ LDs. Using as generic test models the prototypical two degree of freedom Hénon–Heiles system and the two-dimensional standard map, we find that these indicators are able to correctly characterize the chaotic or regular nature of orbits to better than 90% agreement with results obtained by implementing the Smaller Alignment Index (SALI) method, which is a well-established chaos detection technique. Further investigating the performance of the two introduced quantities, we discuss the effects of the total integration time and of the spacing between the used neighboring orbits on the accuracy of the methods, finding that even typical short time, coarse-grid LD computations are sufficient to provide reliable quantification of the systems’ chaotic component, using less CPU time than the SALI. In addition to quantifying chaos, the introduced indicators have the ability to reveal details about the systems’ local and global chaotic phase space structure. Our findings clearly suggest that LDs can also be used to quantify and investigate chaos in continuous and discrete low-dimensional conservative dynamical systems.
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Lee, T. W. "Lagrangian transport equations and an iterative solution method for turbulent jet flows." Physica D: Nonlinear Phenomena 403 (February 2020): 132333. http://dx.doi.org/10.1016/j.physd.2020.132333.
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Gambár, Katalin, and Ferenc Márkus. "Hamilton's Principle for a Set of Nonlinear Heat Conduction." Open Systems & Information Dynamics 12, no. 03 (September 2005): 239–48. http://dx.doi.org/10.1007/s11080-005-0921-4.
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We calculate the Lagrangian for certain type of differential equations of nonlinear heat conduction, applying potential function method introduced previously. On the other hand, we point out that these kind of nonlinear parabolic differential equations describe Markovian processes in a new phase space.
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Li, Jiahua, Xiang Qiu, Yu Shao, Haoxuan Liu, Yuan Fu, Yizhou Tao, and Yulu Liu. "Turbulent coherent structures in channel flow with a wall-mounted hemisphere." AIP Advances 12, no. 3 (March 1, 2022): 035006. http://dx.doi.org/10.1063/5.0079605.
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Turbulent channel flows around a wall-mounted hemisphere numerically are investigated by large eddy simulation, and the Reynolds number based on the hemisphere’s diameter is 3 × 104. The statistical characteristics and turbulent structure evolution are revealed in the Eulerian frameworks and Lagrangian frameworks. The vortex identification and Dynamic Mode Decomposition (DMD) are used to study the evolution of turbulent structure in the Eulerian frameworks, and the finite-time Lyapunov exponents are applied to identify Lagrangian coherent structures (LCS) in the Lagrangian framework. It is found that the developing angle of the hairpin vortex is ∼7° at two frameworks. What is more, there are some hairpin vortices formed behind the hemisphere and some turbulent structures formed near the wall by DMD method. The correlation analysis is applied to investigate the angle variation and scale variation of turbulent structures, and it is observed that the angle of turbulent structures is negative at Y/ d ≥ 1.2 and the spanwise length scales of turbulent structures increase as it moves downstream. By studying the LCS behind a wall-mounted hemisphere, there is formation of “kink” caused by viscous interaction between some hairpin vortex legs, which is the characteristic of hairpin vortex deformation. The comparisons of statistical characteristics between Eulerian frameworks and Lagrangian frameworks are conducted by the correlation analysis, the spectrum analysis, and the structure functions.
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Boso, F., and D. M. Tartakovsky. "Learning on dynamic statistical manifolds." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2239 (July 2020): 20200213. http://dx.doi.org/10.1098/rspa.2020.0213.
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Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data assimilation, remain an open challenge. That is due to nonlinearity of governing equations, whose solutions are highly non-Gaussian and often discontinuous. To ameliorate these issues in a computationally efficient way, we use the method of distributions, which here takes the form of a deterministic equation for spatio-temporal evolution of the cumulative distribution function (CDF) of the random system state, as a means of forward uncertainty propagation. Uncertainty reduction is achieved by recasting the standard loss function, i.e. discrepancy between observations and model predictions, in distributional terms. This step exploits the equivalence between minimization of the square error discrepancy and the Kullback–Leibler divergence. The loss function is regularized by adding a Lagrangian constraint enforcing fulfilment of the CDF equation. Minimization is performed sequentially, progressively updating the parameters of the CDF equation as more measurements are assimilated.
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Sirignano, W. A. "The Formulation of Spray Combustion Models: Resolution Compared to Droplet Spacing." Journal of Heat Transfer 108, no. 3 (August 1, 1986): 633–39. http://dx.doi.org/10.1115/1.3246983.
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Formulations of the governing equations for burning air/fuel spray mixtures are discussed. The subsystem of equations describing liquid properties is formulated in three ways: Eulerian description, Lagrangian description, and probabilistic or distribution function description. The relationships among these approaches and the relative advantages and disadvantages are discussed. The reduction of numerical error, the ability to resolve multivalued solutions, and the ability to achieve resolution a scale smaller than droplet spacing lead to a preference of the Lagrangian method over the Eulerian method. However, when resolution is desired on a scale smaller than the average droplet spacing, the location of each droplet is known only in a statistical manner. The advantages of a probabilistic formulation in this case are evaluated.
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Durand, Fabien, and Gilles Reverdin. "A Statistical Method for Correcting Salinity Observations from Autonomous Profiling Floats: An ARGO Perspective." Journal of Atmospheric and Oceanic Technology 22, no. 3 (March 1, 2005): 292–301. http://dx.doi.org/10.1175/jtech1693.1.
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Abstract The Profiling Autonomous Lagrangian Circulation Explorer (PALACE) float is used to implement the Array for Real-Time Geostrophic Oceanography (ARGO). This study presents a statistical approach to correct salinity measurement errors of an ARGO-type fleet of PALACE floats. The focus is on slowly evolving drifts (typically with time scales longer than a few weeks). Considered for this case study is an ensemble of about 80 floats in the Irminger and Labrador Seas, during the 1996–97 period. Two different algorithms were implemented and validated based on float-to-float data comparison at depth, where the water masses are relatively stable over the time scales of interest. The first algorithm is based upon objective analysis of the float data, while the second consists of a least squares adjustment of the data of the various floats. The authors’ method exhibits good skills to retrieve the proper hydrological structure of the case study area. It significantly improves the consistency of the PALACE dataset with in situ data as well as with satellite altimetric data. As such, the method is readily usable on a near-real-time basis, as required by the ARGO project.
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Irshad, Muhammed Rasheed, Christophe Chesneau, Damodaran Santhamani Shibu, Mohanan Monisha, and Radhakumari Maya. "Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications." Symmetry 14, no. 9 (August 25, 2022): 1775. http://dx.doi.org/10.3390/sym14091775.
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In this paper, we construct a new Lagrangian discrete distribution, named the Lagrangian zero truncated Poisson distribution (LZTPD). It can be presented as a generalization of the zero truncated Poissson distribution (ZTPD) and an alternative to the intervened Poisson distribution (IPD), which was elaborated for modelling both over-dispersed and under-dispersed count datasets. The mathematical aspects of the LZTPD are thoroughly investigated, and its connection to other discrete distributions is crucially observed. Further, we define a finite mixture of LZTPDs and establish its identifiability condition along with some distributional aspects. Statistical work is then performed. The maximum likelihood and method of moment approaches are used to estimate the unknown parameters of the LZTPD. Simulation studies are also undertaken as an assessment of the long-term performance of the estimates. The significance of one additional parameter in the LZTPD is tested using a generalized likelihood ratio test. Moreover, we propose a new count regression model named the Lagrangian zero truncated Poisson regression model (LZTPRM) and its parameters are estimated by the maximum likelihood estimation method. Two real-world datasets are considered to demonstrate the LZTPD’s real-world applicability, and healthcare data are analyzed to demonstrate the LZTPRM’s superiority.
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Irshad, Muhammed Rasheed, Mohanan Monisha, Christophe Chesneau, Radhakumari Maya, and Damodaran Santhamani Shibu. "A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach." Stats 6, no. 1 (January 15, 2023): 150–68. http://dx.doi.org/10.3390/stats6010010.
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The zero-truncated Poisson distribution (ZTPD) generates a statistical model that could be appropriate when observations begin once at least one event occurs. The intervened Poisson distribution (IPD) is a substitute for the ZTPD, in which some intervention processes may change the mean of the rare events. These two zero-truncated distributions exhibit underdispersion (i.e., their variance is less than their mean). In this research, we offer an alternative solution for dealing with intervention problems by proposing a generalization of the IPD by a Lagrangian approach called the Lagrangian intervened Poisson distribution (LIPD), which in fact generalizes both the ZTPD and the IPD. As a notable feature, it has the ability to analyze both overdispersed and underdispersed datasets. In addition, the LIPD has a closed-form expression of all of its statistical characteristics, as well as an increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rate function. A consequent part is devoted to its statistical application. The maximum likelihood estimation method is considered, and the effectiveness of the estimates is demonstrated through a simulated study. To evaluate the significance of the new parameter in the LIPD, a generalized likelihood ratio test is performed. Subsequently, we present a new count regression model that is suitable for both overdispersed and underdispersed datasets using the mean-parametrized form of the LIPD. Additionally, the LIPD’s relevance and application are shown using real-world datasets.
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Carinena, J. F., and M. F. Ranada. "Lagrangian systems with constraints: a geometric approach to the method of Lagrange multipliers." Journal of Physics A: Mathematical and General 26, no. 6 (March 21, 1993): 1335–51. http://dx.doi.org/10.1088/0305-4470/26/6/016.
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YANG, YUE, D. I. PULLIN, and IVÁN BERMEJO-MORENO. "Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence." Journal of Fluid Mechanics 654 (May 17, 2010): 233–70. http://dx.doi.org/10.1017/s0022112010000571.
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We report the multi-scale geometric analysis of Lagrangian structures in forced isotropic turbulence and also with a frozen turbulent field. A particle backward-tracking method, which is stable and topology preserving, was applied to obtain the Lagrangian scalar field φ governed by the pure advection equation in the Eulerian form ∂tφ + u · ∇φ = 0. The temporal evolution of Lagrangian structures was first obtained by extracting iso-surfaces of φ with resolution 10243 at different times, from t = 0 to t = Te, where Te is the eddy turnover time. The surface area growth rate of the Lagrangian structure was quantified and the formation of stretched and rolled-up structures was observed in straining regions and stretched vortex tubes, respectively. The multi-scale geometric analysis of Bermejo-Moreno & Pullin (J. Fluid Mech., vol. 603, 2008, p. 101) has been applied to the evolution of φ to extract structures at different length scales and to characterize their non-local geometry in a space of reduced geometrical parameters. In this multi-scale sense, we observe, for the evolving turbulent velocity field, an evolutionary breakdown of initially large-scale Lagrangian structures that first distort and then either themselves are broken down or stretched laterally into sheets. Moreover, after a finite time, this progression appears to be insensible to the form of the initially smooth Lagrangian field. In comparison with the statistical geometry of instantaneous passive scalar and enstrophy fields in turbulence obtained by Bermejo-Moreno & Pullin (2008) and Bermejo-Moreno et al. (J. Fluid Mech., vol. 620, 2009, p. 121), Lagrangian structures tend to exhibit more prevalent sheet-like shapes at intermediate and small scales. For the frozen flow, the Lagrangian field appears to be attracted onto a stream-surface field and it develops less complex multi-scale geometry than found for the turbulent velocity field. In the latter case, there appears to be a tendency for the Lagrangian field to move towards a vortex-surface field of the evolving turbulent flow but this is mitigated by cumulative viscous effects.
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Wang, Zi-Qiang, Qin Liu, and Jun-Ying Cao. "A Higher-Order Numerical Scheme for Two-Dimensional Nonlinear Fractional Volterra Integral Equations with Uniform Accuracy." Fractal and Fractional 6, no. 6 (June 2, 2022): 314. http://dx.doi.org/10.3390/fractalfract6060314.
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In this paper, based on the modified block-by-block method, we propose a higher-order numerical scheme for two-dimensional nonlinear fractional Volterra integral equations with uniform accuracy. This approach involves discretizing the domain into a large number of subdomains and using biquadratic Lagrangian interpolation on each subdomain. The convergence of the high-order numerical scheme is rigorously established. We prove that the numerical solution converges to the exact solution with the optimal convergence order O(hx4−α+hy4−β) for 0<α,β<1. Finally, experiments with four numerical examples are shown, to support the theoretical findings and to illustrate the efficiency of our proposed method.
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Cheng, Huan, and Fabao Gao. "Periodic Orbits of the Restricted Three-Body Problem Based on the Mass Distribution of Saturn’s Regular Moons." Universe 8, no. 2 (January 20, 2022): 63. http://dx.doi.org/10.3390/universe8020063.
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This paper uses the Kolmogorov–Smirnov test to perform a fitting analysis on the mass data of Saturn’s regular moons and found that the lognormal distribution is its best-fitting distribution with an extremely high p-value of 0.9889. Moreover, novel dynamic equations for the variable-mass restricted three-body problem are established based on the newly discovered distribution of mass data, rather than the empirical Jeans’ law, and the Lindstedt–Poincaré perturbation method was used to give the approximate analytical periodic orbits near the Lagrangian point L3. Furthermore, this paper also discusses the influence of the three-body gravitational interaction parameter, the variable-mass parameter of the third body, and the scale parameter in the statistical results on the periodic orbits and the position of the Lagrangian point L3 through numerical simulation.
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Ekhlakov, Roman, Ekaterina Romanova, Elena Dogadina, Sergey Korchagin, Sergey Gataullin, Józef Mosiej, Timur Gataullin, and Petr Nikitin. "Modeling the Chemical Pollution of the Area by the Random-Addition Method." Fractal and Fractional 6, no. 4 (March 31, 2022): 193. http://dx.doi.org/10.3390/fractalfract6040193.
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Currently, a significant group of industrial facilities can be classified as chemically hazardous facilities (CHFs). To predict the spread of harmful impurities in the programs being developed, Gaussian and Lagrangian models are actively used, on the basis of which the complexes used both in the EMERCOM of Russia and in research organizations are being implemented. These complexes require the introduction of a large amount of information, including the characteristics of the wind field in the distribution of an emergency chemically hazardous substance, which limits their use. In systems, the formation of which is influenced by a large number of different random factors, spatial scaling (similarity) is often found, and one or another parameter can be described using the methods of fractal geometry, which in the past few decades has been actively and successfully applied to the description of various physical objects. The purpose of this study is to analyze the possibility of using the random-addition method for early prediction of the distribution of harmful impurities in the surface air layer during the short-term release of a substance on the surface as a result of an emergency.
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Luque, Alejandro, and Jordi Villanueva. "A numerical method for computing initial conditions of Lagrangian invariant tori using the frequency map." Physica D: Nonlinear Phenomena 325 (June 2016): 63–73. http://dx.doi.org/10.1016/j.physd.2016.02.014.
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Rampal, Pierre, Sylvain Bouillon, Einar Ólason, and Mathieu Morlighem. "neXtSIM: a new Lagrangian sea ice model." Cryosphere 10, no. 3 (May 20, 2016): 1055–73. http://dx.doi.org/10.5194/tc-10-1055-2016.
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Abstract. The Arctic sea ice cover has changed drastically over the last decades. Associated with these changes is a shift in dynamical regime seen by an increase of extreme fracturing events and an acceleration of sea ice drift. The highly non-linear dynamical response of sea ice to external forcing makes modelling these changes and the future evolution of Arctic sea ice a challenge for current models. It is, however, increasingly important that this challenge be better met, both because of the important role of sea ice in the climate system and because of the steady increase of industrial operations in the Arctic. In this paper we present a new dynamical/thermodynamical sea ice model called neXtSIM that is designed to address this challenge. neXtSIM is a continuous and fully Lagrangian model, whose momentum equation is discretised with the finite-element method. In this model, sea ice physics are driven by the combination of two core components: a model for sea ice dynamics built on a mechanical framework using an elasto-brittle rheology, and a model for sea ice thermodynamics providing damage healing for the mechanical framework. The evaluation of the model performance for the Arctic is presented for the period September 2007 to October 2008 and shows that observed multi-scale statistical properties of sea ice drift and deformation are well captured as well as the seasonal cycles of ice volume, area, and extent. These results show that neXtSIM is an appropriate tool for simulating sea ice over a wide range of spatial and temporal scales.
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Rampal, P., S. Bouillon, E. Ólason, and M. Morlighem. "neXtSIM: a new Lagrangian sea ice model." Cryosphere Discussions 9, no. 5 (October 30, 2015): 5885–941. http://dx.doi.org/10.5194/tcd-9-5885-2015.
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Abstract. The Arctic sea ice cover has changed drastically over the last decades. Associated with these changes is a shift in dynamical regime seen by an increase of extreme fracturing events and an acceleration of sea ice drift. The highly non-linear dynamical response of sea ice to external forcing makes modelling these changes, and the future evolution of Arctic sea ice a challenge for current models. It is, however, increasingly important that this challenge be better met, both because of the important role of sea ice in the climate system and because of the steady increase of industrial operations in the Arctic. In this paper we present a new dynamical/thermodynamical sea ice model, called neXtSIM in order to address this. neXtSIM is a continuous and fully Lagrangian model, and the equations are discretised with the finite-element method. In this model, sea ice physics are driven by a synergic combination of two core components: a model for sea ice dynamics built on a new mechanical framework using an elasto-brittle rheology, and a model for sea ice thermodynamics providing damage healing for the mechanical framework. The results of a thorough evaluation of the model performance for the Arctic are presented for the period September 2007 to October 2008. They show that observed multi-scale statistical properties of sea ice drift and deformation are well captured as well as the seasonal cycles of ice volume, area, and extent. These results show that neXtSIM is a very promising tool for simulating the sea ice over a wide range of spatial and temporal scales.
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ZHANG, DALIN, and WEIJIAN CHEN. "NUMERICAL INVESTIGATION OF SUPERCOOLED DROPLETS IMPINGEMENT ON COMPLICATED ICING SURFACE." Modern Physics Letters B 23, no. 03 (January 30, 2009): 469–72. http://dx.doi.org/10.1142/s0217984909018679.
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The supercooled droplet impingement on complicated icing surface has been investigated with the Eulerian method. A simplified air/droplet two-phase model is established, and an effective algorithm is proposed to deal with the dilute, weakly coupled air/droplet flows for aircraft icing problem. An Eulerian droplets computation code has been developed and validated with the iced NACA23012, and the results agree well with the experimental data. Meanwhile, compared with the results from the traditional Lagrangian method, it indicates that the Eulerian method gives a better prediction when the multiple impingement zones occur on complicated icing surface.
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Hu, Y., and E. Gutheil. "Transported Joint Probability Density Function Modeling of Turbulent Dilute Spray Flows." Eurasian Chemico-Technological Journal 16, no. 2-3 (April 8, 2014): 227. http://dx.doi.org/10.18321/ectj186.
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A transported joint probability density function (PDF) model for turbulent spray flows is presented, where a one-point one-time statistical description of the gas-phase mixture fraction and the gas velocity is used. This approach requires the closure of the molecular mixing, which is achieved through use of the extended interaction-by-exchange-with-the-mean (IEM) model and a simplified Langevin model for the closure of the gas velocity both of which are extended through additional terms accounting for spray evaporation. These equations require the solution of the turbulent time scales and the mean pressure field through a Eulerian description. The numerical approach includes a Lagrangian Monte Carlo method for the solution of modeled joint PDF equation with a Eulerian finite-volume algorithm to determine the turbulent time scale and the mean pressure field. For the dispersed liquid phase, Lagrangian equations are used to describe the droplet heating, evaporation, and motion in the framework of a discrete droplet model. The convective droplet evaporation model is employed, and the infinite conductivity model with consideration of non-equilibrium effects based on the Langmuir-Knudsen law is used. The droplet turbulent dispersion is modeled with two different Lagrangian stochastic models. The resulting spray evolution equations are solved by a Lagrangian discrete droplet method using the point source approximation for a dilute spray. The numerical results are compared with experimental data of Gounder et al. [1], where the experimental set B of the acetone spray flows SP2 and SP6 are simulated. Comparison of numerical and experimental results includes droplet size, liquid volume flux as well as the mean and fluctuating velocities. Generally, good agreement is achieved, although the radial droplet dispersion is somewhat under-predicted by the computations. The droplet fluctuating velocities show sensitivity to the different dispersion models.
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Lilly, Jonathan M., and Paula Pérez-Brunius. "Extracting statistically significant eddy signals from large Lagrangian datasets using wavelet ridge analysis, with application to the Gulf of Mexico." Nonlinear Processes in Geophysics 28, no. 2 (April 20, 2021): 181–212. http://dx.doi.org/10.5194/npg-28-181-2021.
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Abstract. A method for objectively extracting the displacement signals associated with coherent eddies from Lagrangian trajectories is presented, refined, and applied to a large dataset of 3770 surface drifters from the Gulf of Mexico. The method, wavelet ridge analysis, is a general method for the analysis of modulated oscillations, here modified to be more suitable to the eddy-detection problem. A means for formally assessing statistical significance is introduced, addressing the issue of false positives arising by chance from an unstructured turbulent background and opening the door to confident application of the method to very large datasets. Significance is measured through a frequency-dependent comparison with a stochastic dataset having statistical and spectral properties that match the original, but lacking organized oscillations due to eddies or waves. The application to the Gulf of Mexico reveals major asymmetries between cyclones and anticyclones, with anticyclones dominating at radii larger than about 50 km, but an unexpectedly rich population of highly nonlinear cyclones dominating at smaller radii. Both the method and the Gulf of Mexico eddy dataset are made freely available to the community for noncommercial use in future research.
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NASSIF, CLÁUDIO, and P. R. SILVA. "UNIFIED TREATMENT OF THE SCALAR FIELD THEORIES-Φn THROUGH THOMPSON'S RENORMALIZATION GROUP METHOD." International Journal of Modern Physics B 17, no. 26 (October 20, 2003): 4645–60. http://dx.doi.org/10.1142/s0217979203022751.
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In this work we apply Thompson's scaling approach (of dimensions) to study the scalar field theories Φn. This method can be considered as a simple and alternative way to the renormalization group (RG) approach and when applied to the Φn Lagrangian is able to obtain the coupling constant behavior g(μ), namely the dependence of g on the energy scale μ. The calculations are evaluated just at [Formula: see text], where the dimension dc is similar to a kind of upper critical dimension of the problem, or in other words the dimension where the Φn theory becomes renormalizable, so that we obtain logarithmic behavior of the coupling g at dc. Due to the universal logharithmic behavior of the coupling g at dc for any value of n in the Φn theory, we are able to estimate a certain βn function given in a closed form, which is a novelty obtained by the present method.
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Park, Sungsu, Conway B. Leovy, and Margaret A. Rozendaal. "A New Heuristic Lagrangian Marine Boundary Layer Cloud Model." Journal of the Atmospheric Sciences 61, no. 24 (December 1, 2004): 3002–24. http://dx.doi.org/10.1175/jas-3344.1.
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Abstract A new heuristic model of stratocumulus cloudiness in the inversion-capped marine boundary layer is developed and tested. The essential ingredient is a new method for predicting the statistical distribution of temperature and specific humidity at the inversion base under partially decoupled conditions along steady-state marine boundary layer (MBL) trajectories. MBL decoupling is parameterized as an increasing function of the height difference between the inversion base and lifting condensation level (LCL) of the mixed-layer air. Required inputs are sea surface temperature (SST), free air (above inversion) temperature and humidity, subsidence velocity, and mean boundary layer wind speed. Upstream boundary conditions must also be specified but have little influence at sufficient downstream distances (>2000 km). The model is applied to the cold advection regime of the northeastern subtropical Pacific and to both warm and cold advection regimes of the eastern equatorial Pacific Ocean. The model is conceptually simple and avoids explicit calculation of several important physical processes. Nevertheless, it is at least qualitatively successful in predicting both the climatological mean properties and climate anomaly variations of MBL stratocumulus in both regions. These results suggest that, regardless of other properties, successful MBL stratocumulus models will need to accurately predict inversion base height and the LCL and they will have to account for downstream memory effects.
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Sizykh, Grigory. "New Lagrangian view of vorticity evolution in two-dimensional flows of liquid and gas." Izvestiya VUZ. Applied Nonlinear Dynamics 30, no. 1 (January 31, 2022): 30–36. http://dx.doi.org/10.18500/0869-6632-2022-30-1-30-36.
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Purpose of the study is to obtain formulas for such a speed of imaginary particles that the circulation of the speed of a (real) fluid along any circuit consisting of these imaginary particles changes (in the process of motion of imaginary particles) according to a given time law. (Until now, only those speeds of imaginary particles were known, at which the mentioned circulation during the motion remained unchanged). Method. Without implementation of asymptotic, numerical and other approximate methods, a rigorous analysis of the dynamic equation of motion (flow) of any continuous fluid medium, from an ideal liquid to a viscous gas, is carried out. Plane-parallel and nonswirling axisymmetric flows are considered. The concept of motion of imaginary particles is used, based on the K. Zoravsky criterion (which is also called A. A. Fridman’s theorem). Results. Formulas for the speed of imaginary particles are proposed. These formulas include the parameters of the (real) flow, their spatial derivatives and the function of time, which determines the law of the change in time of the (real fluid) velocity circulation along the contours moving together with the imaginary particles. In addition, it turned out that for a given function of time (and, as a consequence, for a given law of change in circulation with respect to time), the speed of imaginary particles is determined ambiguously. As a result, a method is proposed to change the speed and direction of motion of imaginary particles in a certain range (while maintaining the selected law of changes in circulation in time). For a viscous incompressible fluid, formulas are proposed that do not include pressure and its derivatives. Conclusion. A new Lagrangian point of view on the vorticity evolution in two-dimensional flows of fluids of all types is proposed. Formulas are obtained for the velocity of such movement of contours, at which the real fluid velocity circulation along any contour changes according to a given time law. This theoretical result can be used in computational fluid dynamics to limit the number of domains when using a gridless method for calculating flows of a viscous incompressible fluid (the method of viscous vortex domains).
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Ankiewicz, Adrian, and Nail Akhmediev. "Comparison of Lagrangian approach and method of moments for reducing dimensionality of soliton dynamical systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 18, no. 3 (September 2008): 033129. http://dx.doi.org/10.1063/1.2976628.
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Huilier, Daniel G. F. "An Overview of the Lagrangian Dispersion Modeling of Heavy Particles in Homogeneous Isotropic Turbulence and Considerations on Related LES Simulations." Fluids 6, no. 4 (April 8, 2021): 145. http://dx.doi.org/10.3390/fluids6040145.
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Particle tracking is a competitive technique widely used in two-phase flows and best suited to simulate the dispersion of heavy particles in the atmosphere. Most Lagrangian models in the statistical approach to turbulence are based either on the eddy interaction model (EIM) and the Monte-Carlo method or on random walk models (RWMs) making use of Markov chains and a Langevin equation. In the present work, both discontinuous and continuous random walk techniques are used to model the dispersion of heavy spherical particles in homogeneous isotropic stationary turbulence (HIST). Their efficiency to predict particle long time dispersion, mean-square velocity and Lagrangian integral time scales are discussed. Computation results with zero and no-zero mean drift velocity are reported; they are intended to quantify the inertia, gravity, crossing-trajectory and continuity effects controlling the dispersion. The calculations concern dense monodisperse spheres in air, the particle Stokes number ranging from 0.007 to 4. Due to the weaknesses of such models, a more sophisticated matrix method will also be explored, able to simulate the true fluid turbulence experienced by the particle for long time dispersion studies. Computer evolution and performance since allowed to develop, instead of Reynold-Averaged Navier-Stokes (RANS)-based studies, large eddy simulation (LES) and direct numerical simulation (DNS) of turbulence coupled to Generalized Langevin Models. A short review on the progress of the Lagrangian simulations based on large eddy simulation (LES) will therefore be provided too, highlighting preferential concentration. The theoretical framework for the fluid time correlation functions along the heavy particle path is that suggested by Wang and Stock.
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QU, KUN, CHANG SHU, and YONG TIAN CHEW. "SIMULATION OF SHOCK-WAVE PROPAGATION WITH FINITE VOLUME LATTICE BOLTZMANN METHOD." International Journal of Modern Physics C 18, no. 04 (April 2007): 447–54. http://dx.doi.org/10.1142/s012918310701067x.
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A new approach was recently proposed to construct equilibrium distribution functions [Formula: see text] of the lattice Boltzmann method for simulation of compressible flows. In this approach, the Maxwellian function is replaced by a simple function which satisfies all needed relations to recover compressible Euler equations. With Lagrangian interpolation polynomials, the simple function is discretized onto a fixed velocity pattern to construct [Formula: see text]. In this paper, the finite volume method is combined with the new lattice Boltzmann models to simulate 1D and 2D shock-wave propagation. The numerical results agree well with available data in the literatures.
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Wang, Yichen, and Wenwen Xu. "Statistical Delay QoS Provisioning for Energy-Efficient Spectrum-Sharing Based Wireless Ad Hoc Sensor Networks." Journal of Sensors 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/6545791.
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In this paper, we develop the statistical delay quality-of-service (QoS) provisioning framework for the energy-efficient spectrum-sharing based wireless ad hoc sensor network (WAHSN), which is characterized by thedelay-bound violation probability. Based on the established delay QoS provisioning framework, we formulate the nonconvex optimization problem which aims at maximizing the average energy efficiency of the sensor node in the WAHSN while meeting PU’s statistical delay QoS requirement as well as satisfying sensor node’s average transmission rate, average transmitting power, and peak transmitting power constraints. By employing the theories offractional programming,convex hull, andprobabilistic transmission, we convert the original fractional-structured nonconvex problem to theadditively structured parametric convex problemand obtain the optimal power allocation strategy under the given parameter via Lagrangian method. Finally, we derive the optimal average energy efficiency and corresponding optimal power allocation scheme by employing theDinkelbach method. Simulation results show that our derived optimal power allocation strategy can be dynamically adjusted based on PU’s delay QoS requirement as well as the channel conditions. The impact of PU’s delay QoS requirement on sensor node’s energy efficiency is also illustrated.
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Oscroft, Sarah, Adam M. Sykulski, and Jeffrey J. Early. "Separating Mesoscale and Submesoscale Flows from Clustered Drifter Trajectories." Fluids 6, no. 1 (December 31, 2020): 14. http://dx.doi.org/10.3390/fluids6010014.
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Drifters deployed in close proximity collectively provide a unique observational data set with which to separate mesoscale and submesoscale flows. In this paper we provide a principled approach for doing so by fitting observed velocities to a local Taylor expansion of the velocity flow field. We demonstrate how to estimate mesoscale and submesoscale quantities that evolve slowly over time, as well as their associated statistical uncertainty. We show that in practice the mesoscale component of our model can explain much first and second-moment variability in drifter velocities, especially at low frequencies. This results in much lower and more meaningful measures of submesoscale diffusivity, which would otherwise be contaminated by unresolved mesoscale flow. We quantify these effects theoretically via computing Lagrangian frequency spectra, and demonstrate the usefulness of our methodology through simulations as well as with real observations from the LatMix deployment of drifters. The outcome of this method is a full Lagrangian decomposition of each drifter trajectory into three components that represent the background, mesoscale, and submesoscale flow.
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Pinsky, M. B., A. P. Khain, B. Grits, and M. Shapiro. "Collisions of Small Drops in a Turbulent Flow. Part III: Relative Droplet Fluxes and Swept Volumes." Journal of the Atmospheric Sciences 63, no. 8 (August 1, 2006): 2123–39. http://dx.doi.org/10.1175/jas3730.1.
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Abstract Swept volumes of cloud droplets with radii below 20 μm are calculated under conditions typical of atmospheric cloud turbulence characterized by enormous values of Reynolds numbers, high turbulent intermittency, and characteristic values of the dissipation rate. To perform the calculations, the motion equation for small droplets proposed by Maxey is generalized for Stokes numbers St > 0.1, which allows one to simulate relative droplet motion even for very high turbulence intensities typical of deep cumulus clouds. Analytical considerations show that droplet motion is fully determined by turbulent shears and the Lagrangian accelerations. A new statistical representation of a turbulent flow has been proposed based on the results of the scale analysis of turbulence characteristics and those related to the droplet motion. According to the method proposed, statistical properties of turbulent flow are represented by a set of noncorrelated samples of turbulent shears and Lagrangian accelerations. Each sample can be assigned to a certain point of the turbulent flow. Each such point can be surrounded by a small “elementary” volume with linear length scales of the Kolmogorov length scale, in which the Lagrangian acceleration and turbulent shears can be considered as uniform in space and invariable in time. This present study (Part III) investigates the droplet collisions in a turbulent flow when hydrodynamic droplet interaction (HDI) is disregarded. Using a statistical model, long series of turbulent shears and accelerations were generated, reproducing probability distribution functions (PDF) at high Reynolds numbers, as they were obtained in recent laboratory and theoretical studies. Swept volumes of droplets are calculated for each sample of an acceleration–shear pair, and the PDF of swept volumes is calculated for turbulent parameters typical of cloud turbulence. The effect of turbulent flow intermittency manifests itself in two aspects: 1) an increase of swept volume variance with increasing Reynolds number, and 2) formation of the swept volume PDF that has a sharp maximum and an elongated tail. In spite of the fact that the magnitude of the mean swept volume increases significantly with Reynolds number and the dissipation rate, this increase does not exceed ∼60% of pure gravity values even under turbulent conditions typical of strong cumulus clouds. A comparison with the classical results of Saffman and Turner is presented and discussed.
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Ding, Yu, Haifei Liu, and Yujun Yi. "A Lagrangian model for the age of tracer in surface water." International Journal of Modern Physics C 29, no. 02 (February 2018): 1850013. http://dx.doi.org/10.1142/s0129183118500134.
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The age of tracer is a spatio-temporal scale, indicating the transition time of solute particles, which is helpful to monitor and manage the pollutant leakage accidents. In this study, an effective Lagrangian model for the age of tracer is developed based on the lattice Boltzmann method in [Formula: see text]5 lattices. A tracer age problem in an asymmetrical circular reservoir is then employed as a benchmark test to verify this method. Then it is applied to computing the age of tracers under two different reservoir operation schemes in the Danjiangkou Reservoir, the drinking water source for the Middle Route of South-to-North Water Transfer Project.
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BEL'KOV, A. A., D. EBERT, A. V. LANYOV, and A. SCHAALE. "HEAT-KERNEL CALCULATION OF QUARK DETERMINANT AND COMPUTER ALGEBRA." International Journal of Modern Physics C 04, no. 04 (August 1993): 775–86. http://dx.doi.org/10.1142/s0129183193000641.
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In this paper we describe the calculational background of deriving a strong meson Lagrangian from the Nambu–Jona-Lasinio quark model using the computer algebra systems FORM and REDUCE in recursive algorithms, based on the heat-kernel method for the calculation of the quark determinant.
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Souhar, Otmane, Alexis Marceau, and Benjamin Loubet. "Modelling and inference of maize pollen emission rate with a Lagrangian dispersal model using Monte Carlo method." Journal of Agricultural Science 158, no. 5 (July 2020): 383–95. http://dx.doi.org/10.1017/s0021859620000763.
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AbstractThis work explores the uncertainty of the inferred maize pollen emission rate using measurements and simulations of pollen dispersion at Grignon in France. Measurements were obtained via deposition of pollen on the ground in a canopy gap; simulations were conducted using the two-dimensional Lagrangian Stochastic Mechanistic mOdel for Pollen dispersion and deposition (SMOP). First, a quantitative evaluation of the model's performance was conducted using a global sensitivity analysis to analyse the convergence behaviour of the results and scatter diagrams. Then, a qualitative study was conducted to infer the pollen emission rate and calibrate the methodology against experimental data for several sets of variable values. The analysis showed that predicted and observed values were in good agreement and the calculated statistical indices were mostly within the range of acceptable model performance. Furthermore, it was revealed that the mean settling velocity and vertical leaf area index are the main variables affecting pollen deposition in the canopy gap. Finally, an estimated pollen emission rate was obtained according to a restricted setting, where the model studied includes no deposition on leaves, no resuspension and with horizontal pollen fluctuations either taken into account or not. The estimated pollen emission rate obtained was nearly identical to the measured quantity. In conclusion, the findings of the current study show that the described methodology could be an interesting approach for accurate prediction of maize pollen deposition and emission rates and may be appropriate for other pollen types.
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Sukhov, E. A., and E. V. Volkov. "Numerical Orbital Stability Analysis of Nonresonant Periodic Motions in the Planar Restricted Four-Body Problem." Nelineinaya Dinamika 18, no. 4 (2022): 0. http://dx.doi.org/10.20537/nd221201.
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We address the planar restricted four-body problem with a small body of negligible mass moving in the Newtonian gravitational field of three primary bodies with nonnegligible masses. We assume that two of the primaries have equal masses and that all primary bodies move in circular orbits forming a Lagrangian equilateral triangular configuration. This configuration admits relative equilibria for the small body analogous to the libration points in the three-body problem. We consider the equilibrium points located on the perpendicular bisector of the Lagrangian triangle in which case the bodies constitute the so-called central configurations. Using the method of normal forms, we analytically obtain families of periodic motions emanating from the stable relative equilibria in a nonresonant case and continue them numerically to the borders of their existence domains. Using a numerical method, we investigate the orbital stability of the aforementioned periodic motions and represent the conclusions as stability diagrams in the problem’s parameter space.
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Vojta, Martin, Andreas Plach, Rona L. Thompson, and Andreas Stohl. "A comprehensive evaluation of the use of Lagrangian particle dispersion models for inverse modeling of greenhouse gas emissions." Geoscientific Model Development 15, no. 22 (November 18, 2022): 8295–323. http://dx.doi.org/10.5194/gmd-15-8295-2022.
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Abstract. Using the example of sulfur hexafluoride (SF6), we investigate the use of Lagrangian particle dispersion models (LPDMs) for inverse modeling of greenhouse gas (GHG) emissions and explore the limitations of this approach. We put the main focus on the impacts of baseline methods and the LPDM backward simulation period on the a posteriori emissions determined by the inversion. We consider baseline methods that are based on a statistical selection of observations at individual measurement sites and a global-distribution-based (GDB) approach, where global mixing ratio fields are coupled to the LPDM back-trajectories at their termination points. We show that purely statistical baseline methods can cause large systematic errors, which lead to inversion results that are sensitive to the LPDM backward simulation period and can generate unrealistic global total a posteriori emissions. The GDB method produces a posteriori emissions that are far less sensitive to the backward simulation period and that show a better agreement with recognized global total emissions. Our results show that longer backward simulation periods, beyond the often used 5 to 10 d, reduce the mean squared error and increase the correlation between a priori modeled and observed mixing ratios. Also, the inversion becomes less sensitive to biases in the a priori emissions and the global mixing ratio fields for longer backward simulation periods. Further, longer periods might help to better constrain emissions in regions poorly covered by the global SF6 monitoring network. We find that the inclusion of existing flask measurements in the inversion helps to further close these gaps and suggest that a few additional and well-placed flask sampling sites would have great value for improving global a posteriori emission fields.
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Hu, Jianyu, Xiaoli Chen, and Jinqiao Duan. "An Onsager–Machlup approach to the most probable transition pathway for a genetic regulatory network." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 4 (April 2022): 041103. http://dx.doi.org/10.1063/5.0088397.
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We investigate a quantitative network of gene expression dynamics describing the competence development in Bacillus subtilis. First, we introduce an Onsager–Machlup approach to quantify the most probable transition pathway for both excitable and bistable dynamics. Then, we apply a machine learning method to calculate the most probable transition pathway via the Euler–Lagrangian equation. Finally, we analyze how the noise intensity affects the transition phenomena.
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Rigby, M., A. J. Manning, and R. G. Prinn. "Inversion of long-lived trace gas emissions using combined Eulerian and Lagrangian chemical transport models." Atmospheric Chemistry and Physics Discussions 11, no. 5 (May 13, 2011): 14689–717. http://dx.doi.org/10.5194/acpd-11-14689-2011.
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Abstract. We present a method for estimating emissions of long-lived trace gases from a sparse global network of high-frequency observatories, using both a global Eulerian chemical transport model and Lagrangian particle dispersion model. Emissions are derived in a single step after determining sensitivities of the observations to initial conditions, the high-resolution emissions field close to observation points, and larger regions further from the measurements. This method has the several advantages over inversions using one type of model alone, in that: high-resolution simulations can be carried out in limited domains close to the measurement sites, with lower resolution being used further from them; the influence of errors due to aggregation of emissions close to the measurement sites can be minimized; assumptions about boundary conditions to the Lagrangian model do not need to be made, since the entire emissions field is estimated; any combination of appropriate models can be used, with no code modification. Because the sensitivity to the entire emissions field is derived, the estimation can be carried out using traditional statistical methods without the need for multiple steps in the inversion. We demonstrate the utility of this approach by determining global SF6 emissions using measurements from the Advanced Global Atmospheric Gases Experiment (AGAGE) between 2007 and 2009. The global total and large-scale patterns of the derived emissions agree well with previous studies, whilst allowing emissions to be determined at higher resolution than has previously been possible, and improving the agreement between the modeled and observed mole fractions at some sites.
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Rigby, M., A. J. Manning, and R. G. Prinn. "Inversion of long-lived trace gas emissions using combined Eulerian and Lagrangian chemical transport models." Atmospheric Chemistry and Physics 11, no. 18 (September 26, 2011): 9887–98. http://dx.doi.org/10.5194/acp-11-9887-2011.
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Abstract. We present a method for estimating emissions of long-lived trace gases from a sparse global network of high-frequency observatories, using both a global Eulerian chemical transport model and Lagrangian particle dispersion model. Emissions are derived in a single step after determining sensitivities of the observations to initial conditions, the high-resolution emissions field close to observation points, and larger regions further from the measurements. This method has the several advantages over inversions using one type of model alone, in that: high-resolution simulations can be carried out in limited domains close to the measurement sites, with lower resolution being used further from them; the influence of errors due to aggregation of emissions close to the measurement sites can be minimized; assumptions about boundary conditions to the Lagrangian model do not need to be made, since the entire emissions field is estimated; any combination of appropriate models can be used, with no code modification. Because the sensitivity to the entire emissions field is derived, the estimation can be carried out using traditional statistical methods without the need for multiple steps in the inversion. We demonstrate the utility of this approach by determining global SF6 emissions using measurements from the Advanced Global Atmospheric Gases Experiment (AGAGE) between 2007 and 2009. The global total and large-scale patterns of the derived emissions agree well with previous studies, whilst allowing emissions to be determined at higher resolution than has previously been possible, and improving the agreement between the modeled and observed mole fractions at some sites.
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Liu, Xiao, Wei Tan, Yu Bu, Yu Jin Liu, and Ze Jun Wang. "Numerical Simulation of Instantaneous Flashing LPG Release." Advanced Materials Research 236-238 (May 2011): 2660–63. http://dx.doi.org/10.4028/www.scientific.net/amr.236-238.2660.
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An accident instantaneous release of LPG can results in a rapidly expanding two-phase flammable cloud, which is the medium of potentially disastrous consequences. In this paper, CFD (Computational Fluid Dynamics) method was applied for instantaneous LPG release in an open environment in order to analysis the expansion process of two-phase cloud. The results from simulation are compared with the published experimental data to validate the model. Statistical analysis of experimental data is used to set the initial conditions and computational inlet in the model. The mass and heat transfer is calculated in eulerian-lagrangian method. The features in expansion process are studied by the analyses of the variation of size, temperature, volume averaged rate of evaporation of the cloud and entropy of the whole flow field.
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Malik, N. A., and J. C. Vassilicos. "Eulerian and Lagrangian scaling properties of randomly advected vortex tubes." Journal of Fluid Mechanics 326 (November 10, 1996): 417–36. http://dx.doi.org/10.1017/s0022112096008385.
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We investigate the Eulerian and Lagrangian spectral scaling properties of vortex tubes, and the consistency of these properties with Tennekes’ (1975) statistical advection analysis and universal equilibrium arguments. We consider three different vortex tubes with power-law wavenumber spectra: a Burgers vortex tube, an inviscid Lundgren single spiral vortex sheet, and a vortex tube solution of the Euler equation. While the Burgers vortex is a steady solution of the Navier–Stokes equation, the other two are unsteady solutions of, respectively, the Navier–Stokes and the Euler equations. In our numerical experiments we study the vortex tubes by subjecting each of them to external ‘large-scale’ sinusoidal advection of characteristic frequency f and length scale ρ.Not only do we find that the Eulerian frequency spectrum ϕE(ω) can be derived from the wavenumber spectrum E(k) using the simple Tennekes advection relation ω ∼ k for all finite advection frequencies f when the vortex is steady, but also when the vortex is unsteady, and in the Lundgren case even when f = 0 owing to the self-advection of the Lundgren vortex by its own differential rotation.An analytical calculation using the method of stationary phases for f = 0 shows that for large enough Reynolds numbers the combination of strain with differential rotation implies that ϕL(ω) ∼ ω−2+Const for large values of ω. We verify numerically that ϕL(ω) does not change when f ≠ 0. With the Burgers vortex tube we are in a position to investigate the spectral broadening of the Eulerian frequency spectrum with respect to the Lagrangian frequency spectrum. A spectral broadening does exist but is different from the spectral broadening predicted by Tennekes (1975).