Lagrangian description of nonlinear dust-ion acoustic waves in dusty plasmas

An analytical model is presented for the description of nonlinear dust-ion-acoustic waves propagating in an unmagnetized, collisionless, three component plasma composed of electrons, ions and inertial dust grains. The formulation relies on a Lagrangian approach of the plasma fluid model. The modulational stability of the wave amplitude is investigated. Different types of localized envelope electrostatic excitations are shown to exist.

Nonlinear Lagrangian theory of envelope electrostatic plasma waves in a two-electron-temperature plasma

An analytical model based on Lagrangian variables is presented for the description of ion-acoustic waves propagating in an unmagnetized, collisionless, three-component plasma composed of inertial positive ions and two thermalized electron populations, characterized by different temperatures. The wave's amplitude is shown to be modulationally unstable. Different types of localized envelope electrostatic excitations are shown to exist, and their forms are analytically and numerically investigated in terms of the plasma dispersion and nonlinearity laws. These results are in qualitative agreement with satellite observations in the magnetosphere. (C) 2004 American Institute of Physics.

Comparison of lagrangian and eulerian simulations of slurry flows in a sudden expansion

From a review of technical literature, it was not apparent if the Lagrangian or the Eulerian dispersed phase modeling approach was more valid to simulate dilute erosive slurry flow. In this study, both modeling approaches were employed and a comparative analysis of performances and accuracy between the two models was carried out. Due to an impossibility to define, for the Eulerian model already implemented in FLUENT, a set of boundary conditions consistent with the Lagrangian impulsive equations, an Eulerian dispersed phase model was integrated in the FLUENT code using subroutines and user-defined scalar equations. Numerical predictions obtained from the two different approaches for two-phase flow in a sudden expansion were compared with the measured data. Excellent agreement was attained between the predicted and observed fluid and particle velocity in the axial direction and for the kinetic energy. Erosion profiles in a sudden expansion computed using the Lagrangian scheme yielded good qualitative agreement with measured data and predicted a maximum impact angle of 29 deg at the fluid reattachment point. The Eulerian model was adversely affected by the reattachment of the fluid phase to the wall and the simulated erosion profiles were not in agreement with the Lagrangian or measured data. Furthermore, the Eulerian model under-predicted the Lagrangian impact angle at all locations except the reattachment point. © 2010 American Society of Mechanical Engineers.

A Lagrangian approach for modeling road collisions using second-order models of traffic flow

In [M. Herty, A. Klein, S. Moutari, V. Schleper, and G. Steinaur, IMA J. Appl. Math., 78(5), 1087–1108, 2013] and [M. Herty and V. Schleper, ZAMM J. Appl. Math. Mech., 91, 763–776, 2011], a macroscopic approach, derived from fluid-dynamics models, has been introduced to infer traffic conditions prone to road traffic collisions along highways’ sections. In these studies, the governing equations are coupled within an Eulerian framework, which assumes fixed interfaces between the models. A coupling in Lagrangian coordinates would enable us to get rid of this (not very realistic) assumption. In this paper, we investigate the well-posedness and the suitability of the coupling of the governing equations within the Lagrangian framework. Further, we illustrate some features of the proposed approach through some numerical simulations.

Lagrangian transport of particles in Ria de Aveiro lagoon, Portugal

A two-dimensional vertically integrated hydrodynamic model coupled to a particle tracking model is applied to study the dispersion processes and residence time in Ria de Aveiro lagoon (Portugal). The only dispersion process that is considered in this study is the advection, according to the main characteristics of the local hydrodynamic. The particle tracking model computes the particles position at each time step, using a fourth-order Runge-Kutta integration method. The dispersion of passive particles released along the lagoon and in critical areas are studied in this work. The residence time is also determined for the entire lagoon. The results show that the mixture between particles coming from different channels of the lagoon is negligible in a time scale higher than 2 tidal cycles. The residence time for the lagoon central area is about 2 days, revealing a strong marine influence in this area. At the upper reaches of the channels were found values higher than 2 weeks.

Determination of Alternaria spp. Habitats Using 7-Day Volumetric Spore Trap, Hybrid Single Particle Lagrangian Integrated Trajectory Model and Geographic Information System

There are many species among the Alternaria genus, which hosts on economically important crops causing significant yield losses. Less attention has been paid to fungi hosting on plants constituting substantial components of pastures and meadows. Alternaria spp. spores are also recognised as important allergens. A 7-day volumetric spore trap was used to monitor the concentration of airborne fungal spores. Air samples were collected in Worcester, England (2006–2010). Days with a high spore count were then selected. The longest episode that occurred within a five year study was chosen for modelling. Two source maps presenting distribution of crops under rotation and pastures in the UK were produced. Back trajectories were calculated using the HYSPLIT model. In ArcGIS clusters of trajectories were studied in connection with source maps by including the height above ground level and the speed of the air masses. During the episode no evidence for a long distance transport from the continent of Alternaria spp. spores was detected. The overall direction of the air masses fell within the range from South-West to North. The back trajectories indicated that the most important sources of Alternaria spp. spores were located in the West Midlands of England.

Detecting a shallow surface layer in Barkley Sound from Lagrangian drifter trajectories

Senior thesis written for Oceanography 444

Fast Geodesic Active Fields for Image Registration Based on Splitting and Augmented Lagrangian Approaches.

In this paper, we present an efficient numerical scheme for the recently introduced geodesic active fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, and the parametrization invariance allows working with images of nonflat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach; data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this paper, we compare the geodesic active fields method with the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow, MRF image registration, and landmark-enhanced large displacement optical flow. Thus, we can show the advantages of the proposed FastGAF method. It compares favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework.

Lagrangian-informed mixed integer programming reformulations

La programmation linéaire en nombres entiers est une approche robuste qui permet de résoudre rapidement de grandes instances de problèmes d'optimisation discrète. Toutefois, les problèmes gagnent constamment en complexité et imposent parfois de fortes limites sur le temps de calcul. Il devient alors nécessaire de développer des méthodes spécialisées afin de résoudre approximativement ces problèmes, tout en calculant des bornes sur leurs valeurs optimales afin de prouver la qualité des solutions obtenues. Nous proposons d'explorer une approche de reformulation en nombres entiers guidée par la relaxation lagrangienne. Après l'identification d'une forte relaxation lagrangienne, un processus systématique permet d'obtenir une seconde formulation en nombres entiers. Cette reformulation, plus compacte que celle de Dantzig et Wolfe, comporte exactement les mêmes solutions entières que la formulation initiale, mais en améliore la borne linéaire: elle devient égale à la borne lagrangienne. L'approche de reformulation permet d'unifier et de généraliser des formulations et des méthodes de borne connues. De plus, elle offre une manière simple d'obtenir des reformulations de moins grandes tailles en contrepartie de bornes plus faibles. Ces reformulations demeurent de grandes tailles. C'est pourquoi nous décrivons aussi des méthodes spécialisées pour en résoudre les relaxations linéaires. Finalement, nous appliquons l'approche de reformulation à deux problèmes de localisation. Cela nous mène à de nouvelles formulations pour ces problèmes; certaines sont de très grandes tailles, mais nos méthodes de résolution spécialisées les rendent pratiques.

Superheavy nuclei in relativistic effective Lagrangian model

Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond Z=82 and N=126 within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as spherical doubly magic superheavy nuclei, whereas N=184 and Z=114 show some magic character depending on the parameter set. The magicity of a particular neutron (proton) number in the analyzed mass region is found to depend on the number of protons (neutrons) present in the nucleus.

Lagrangian approximations and weak solutions of the Navier-Stokes equations

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations.