USAMA Umer; XIE Lijing; WANG Xibin
2006-01-01
A two-dimensional finite element (FE) model for the high speed turning operations when orthogonally machining AISI H13 tool steel at 49HRC using poly crystalline cubic boron nitride(PCBN) is described. An arbitrary Lagrangian Eulerian (ALE) method has been adopted which does not need any chip separation criteria as opposed to the traditional Lagrangian approach. Through FE simulations temperature and stresses distributions are presented that could be helpful in predicting tool life and improving process parameters. The results show that high temperatures are generated along the tool rake face as compared to the shear zone temperatures due to high thermal conductivity of PCBN tools.
Simulation of sheet metal extrusion processes with Arbitrary Lagrangian-Eulerian method
ZHUANG Xin-cun; ZHAO Zhen; XIANG Hua; LI Cong-xin
2008-01-01
An Arbitrary Lagrangian-Eulerian(ALE) method was employed to simulate the sheet metal extrusion process, aiming at avoiding mesh distortion and improving the computational accuracy. The method was implemented based on MSC/MARC by using a fractional step method, i.e. a Lagrangian step followed by an Euler step. The Lagrangian step was a pure updated Lagrangian calculation and the Euler step was performed using mesh smoothing and remapping scheme. Due to the extreme distortion of deformation domain, it was almost impossible to complete the whole simulation with only one mesh topology. Therefore, global remeshing combined with the ALE method was used in the simulation work. Based on the numerical model of the process, some deformation features of the sheet metal extrusion process, such as distribution of localized equivalent plastic strain, and shrinkage cavity, were revealed. Furthermore, the differences between conventional extrusion and sheet metal extrusion process were also analyzed.
Ganesan, Sashikumaar
2014-01-01
An arbitrary Lagrangian--Eulerian (ALE) finite element scheme for computations of soluble surfactant droplet impingement on a horizontal surface is presented. The numerical scheme solves the time-dependent Navier--Stokes equations for the fluid flow, scalar convection-diffusion equation for the surfactant transport in the bulk phase, and simultaneously, surface evolution equations for the surfactants on the free surface and on the liquid-solid interface. The effects of surfactants on the flow dynamics are included into the model through the surfactant-dependent surface tension and dynamic contact angle. In particular, the dynamic contact angle of the droplet is defined as a function of surfactants using the nonlinear equation of state for surface tension. Further, the surface forces are included in the model using the Boussinesq-Scriven law that allows to incorporate the Marangoni effects without evaluating the gradients of surfactant concentration on the free surface. In addition to a mesh convergence study ...
Wu, C. S.; Young, D. L.; Chiu, C. L.
2013-12-01
This article aims to develop a Cartesian-grid-based numerical model to study the interaction between free-surface flow and stationary or oscillating immersed obstacle in a viscous fluid. To incorporate the effect of the free surface motion, an arbitrary Lagrangian-Eulerian (ALE) scheme is employed to accurately capture the configuration of free surface. To deal with the complex submerged obstacle in the fluid, a hybrid Cartesian/immersed boundary (HCIB) method is adopted, which allows easy implementation of the solid boundary conditions for a fixed structured grid. The two numerical techniques are combined to study the wave-structure interaction problems. The major merit of the proposed model is that the fluid grid is fixed throughout the computations during the transients, while the immersed body can move arbitrarily through the Cartesian grid. The meshes deform smoothly over the solid and free-surface boundaries, especially for representing sharp interface. There is no re-meshing process needed since this scheme only depends on the simple mesh generation to promote the efficiency of calculation. Some numerical examples are displayed respectively to validate the robustness and accuracy of the HCIB method, the ALE based finite-element scheme and their combinations. In addition, the other two numerical applications are carried out to simulate the wave-structure interaction with stationary and moving immersed body. In case studies some physical characteristics are also discussed for a range of amplitude of free-surface wave, Reynolds numbers and the proximity of structure under the liquid surface. The feasibility of the developed novel numerical model is shown through five numerical experiments.
An Arbitrary Lagrangian-Eulerian Discretization of MHD on 3D Unstructured Grids
Rieben, R N; White, D A; Wallin, B K; Solberg, J M
2006-06-12
We present an arbitrary Lagrangian-Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic dynamo equation is discretized using a compatible mixed finite element method with a 2nd order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a 2nd order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.
Erzincanli, Belkis; Sahin, Mehmet
2013-12-01
An Arbitrary Lagrangian-Eulerian (ALE) formulation based on the unstructured finite volume method is proposed for solving moving boundary problems with large displacements and rotations. The numerical method is based on the side-centered arrangement of the primitive variables that does not require any ad-hoc modifications in order to enhance pressure coupling. The continuity equation is satisfied within each element at machine precision and the summation of the continuity equations can be exactly reduced to the domain boundary, which is important for the global mass conservation. A special attention is given to construct an ALE algorithm obeying the discrete geometric conservation law (DGCL). The mesh deformation algorithm is based on the indirect Radial Basis Function (RBF) algorithm at each time level while avoiding remeshing in order to enhance numerical robustness. For the parallel solution of resulting large-scale algebraic equations in a fully coupled form, a matrix factorization is introduced similar to that of the projection method for the whole system and the parallel algebraic multigrid solver BoomerAMG is used for the scaled discrete Laplacian provided by the HYPRE library which we access through the PETSc library. The present numerical algorithm is initially validated for the decaying Taylor-Green vortex flow, the flow past an oscillating circular cylinder in a channel and the flow induced by an oscillating sphere in a cubic cavity. Then the numerical algorithm is applied to the numerical simulation of flow field around a pair of flapping Drosophila wings in hover flight. The time variation of the Eulerian coherent structures in the near wake is shown along with the aerodynamic loads.
Boscheri, Walter; Loubère, Raphaël; Dumbser, Michael
2015-07-01
In this paper we present a new family of efficient high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-MOOD finite volume schemes for the solution of nonlinear hyperbolic systems of conservation laws for moving unstructured triangular and tetrahedral meshes. This family is the next generation of the ALE ADER-WENO schemes presented in [16,20]. Here, we use again an element-local space-time Galerkin finite element predictor method to achieve a high order accurate one-step time discretization, while the somewhat expensive WENO approach on moving meshes, used to obtain high order of accuracy in space, is replaced by an a posteriori MOOD loop which is shown to be less expensive but still as accurate. This a posteriori MOOD loop ensures the numerical solution in each cell at any discrete time level to fulfill a set of user-defined detection criteria. If a cell average does not satisfy the detection criteria, then the solution is locally re-computed by progressively decrementing the order of the polynomial reconstruction, following a so-called cascade of predefined schemes with decreasing approximation order. A so-called parachute scheme, typically a very robust first order Godunov-type finite volume method, is employed as a last resort for highly problematic cells. The cascade of schemes defines how the decrementing process is carried out, i.e. how many schemes are tried and which orders are adopted for the polynomial reconstructions. The cascade and the parachute scheme are choices of the user or the code developer. Consequently the iterative MOOD loop allows the numerical solution to maintain some interesting properties such as positivity, mesh validity, etc., which are otherwise difficult to ensure. We have applied our new high order unstructured direct ALE ADER-MOOD schemes to the multi-dimensional Euler equations of compressible gas dynamics. A large set of test problems has been simulated and analyzed to assess the validity of our approach
Sahin, Mehmet
2010-01-01
A new geometrically conservative arbitrary Lagrangian-Eulerian (ALE) formulation is presented for the moving boundary problems in the swirl-free cylindrical coordinates. The governing equations are multiplied with the radial distance and integrated over arbitrary moving Lagrangian-Eulerian quadrilateral elements. Therefore, the continuity and the geometric conservation equations take very simple form similar to those of the Cartesian coordinates. The continuity equation is satisfied exactly within each element and a special attention is given to satisfy the geometric conservation law (GCL) at the discrete level. The equation of motion of a deforming body is solved in addition to the Navier-Stokes equations in a fully-coupled form. The mesh deformation is achieved by solving the linear elasticity equation at each time level while avoiding remeshing in order to enhance numerical robustness. The resulting algebraic linear systems are solved using an ILU(k) preconditioned GMRES method provided by the PETSc librar...
A Methodology to Validate 3-D Arbitrary Lagrangian Eulerian Codes with Applications to Alegra
Chhabildas, L.C.; Duggins, B.D.; Konrad, C.H.; Mosher, D.A.; Perry, J.S.; Reinhart, W.D.; Summers, R.M.; Trucano, T.G.
1998-11-04
In this study we provided an experimental test bed for validating features of the Arbitrary Lagrangian Eulerian Grid for Research Applications (ALEGRA) code over a broad range of strain rates with overlapping diagnostics that encompass the multiple responses. A unique feature of the ALEGRA code is that it allows simultaneous computational treatment, within one code, of a wide range of strain-rates varying from hydrodynamic to structural conditions. This range encompasses strain rates characteristic of shock-wave propagation (107/s) and those characteristics of structural response (102/s). Most previous code validation experimental &udies, however, have been restricted to simulating or investigating a single strain-rate regime. What is new and different in this investigation is that we have performed well-controlled and well-instrumented experiments, which capture features relevant to both hydrodynamic and structural response in a single experiment. Aluminum was chosen for use in this study because it is a well-characterized material. The current experiments span strain rate regimes of over 107/s to less than 102/s in a single experiment. The input conditions were extremely well defined. Velocity interferometers were used to record the high' strain-rate response, while low strain rate data were collected using strain gauges. Although the current tests were conducted at a nominal velocity of - 1.5 km/s, it is the test methodology that is being emphasized herein. Results of a three-dimensional experiment are also presented.
Su, Xiaohui; Cao, Yuanwei; Zhao, Yong
2016-06-01
In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.
Gaston, Laurence; Kamara, Alima; Bellet, Michel
2000-01-01
This is the pre-peer reviewed version of the following article : An arbitrary Lagrangian-Eulerian finite element approach to non-steady state turbulent fluid flow with application to mould filling in casting, Gaston L., Kamara A., Bellet M. International Journal for Numerical Methods in Fluids 34, 4 (2000) pages 341-369, which has been published in final form at http://dx.doi.org/10.1002/1097-0363(20001030)34:4%3C341::AID-FLD64%3E3.0.CO;2-K International audience This paper presents a t...
Melis, Matthew E.
2003-01-01
Explicit finite element techniques employing an Arbitrary Lagrangian-Eulerian (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.
On the integration of the arbitrary Lagrangian-Eulerian concept and non-equilibrium thermodynamics
Knobbe, E.M.
2010-01-01
The aim of this treatise is to present a harmonious mathematical formulation of an explicit moving mesh method that can be used as a basis for many numerical techniques. In most cases a moving mesh is only used to include arbitrary motions and deformations of a geometry into the simulation of a phys
On the integration of the arbitrary Lagrangian-Eulerian concept and non-equilibrium thermodynamics
Knobbe, E.M.
2010-01-01
The aim of this treatise is to present a harmonious mathematical formulation of an explicit moving mesh method that can be used as a basis for many numerical techniques. In most cases a moving mesh is only used to include arbitrary motions and deformations of a geometry into the simulation of a physical problem. The innovative part of this research is to develop a mechanism that controls the motion of interior mesh points by detecting and tracking the location of physical phenomena. The motio...
Esmaily, M. [Islamic Azad University, Karaj (Iran); Shokuhfar, A. [Advanced Materials and Nanotechnology Research Labs., Toosi University of Technology, Tehran (Iran)
2010-05-15
There are various simulation methods of processes having severe plastic deformation. Finite Elements Method is used as an appropriate and precise method in the simulation of such processes. This method is used and completed with Eulerian and Lagrangian formulation. In the present work, the combination of these two methods, namely Arbitrary Lagrangian Eulerian (ALE), has been found to be the best way of simulating events involving severe plastic deformation. The purpose of this article is to analyze the heat transfer process in friction stir welding using ANSYS software and compare the obtained data with experimental results. In this research, palates made of 7075-T6 Aluminum alloy and high carbon steel were welded and temperature measurement in the main sections was carried out by an accurate and special method during welding. Heat variation measurement was also carried out based on the time the tool operated. The process of heat transfer in friction stir welding of the selected alloys were then simulated, a comparison between simulation and experimental data shows a reasonable conformity between numerical and experimental results. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Bavo, Alessandra M; Rocatello, Giorgia; Iannaccone, Francesco; Degroote, Joris; Vierendeels, Jan; Segers, Patrick
2016-01-01
In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations' outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results. PMID:27128798
Iannaccone, Francesco; Degroote, Joris; Vierendeels, Jan; Segers, Patrick
2016-01-01
In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results. PMID:27128798
This report describes a reactor-containment code, ALICE, which uses an arbitrary Lagrangian-Eulerian method to describe the coolant motion, together with a Lagrangian method to analyze the response of the containment vessel and other solid media inside a reactor containment. The finite-difference formulation used to approximate the governing equations for the motion of the coolant can be solved in either an explicit or an implicit scheme; the finite-element formulation used to approximate the governing equations for the containment vessel and other solid media can be performed only in the explicit scheme. Thus, the ALICE code can perform two types of coupling calculations for the fluid and structure (implicit-explicit and explicit-explicit). The code is generalized so that it can apply to problems either in a two-dimensional Cartesian or in a two-dimensional cylindrical-coordinate system
Arbitrary lagrangian-eulerian formulation of quasistatic nonlinear problems
Rodríguez Ferran, Antonio
1996-01-01
En esta tesis se presenta una metodología para la simulación numérica de procesos cuasistaticos en mecánica de sólidos no lineal, basada en una formulación arbitrariamente lagrangiana-euleriana (ale) del problema. Se hace un enfoque generalista, que abarca algunas cuestiones fundamentales en mecánica computacional y en análisis numérico: la resolución de sistemas no lineales de ecuaciones algebraicas y la integración de las ecuaciones constitutivas no lineales. Como entorno de trabajo se util...
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.
Mesh update techniques for free-surface flow solvers using spectral element method
Bouffanais, Roland; Deville, Michel O.
2007-01-01
This paper presents a novel mesh-update technique for unsteady free-surface Newtonian flows using spectral element method and relying on the arbitrary Lagrangian--Eulerian kinematic description for moving the grid. Selected results showing compatibility of this mesh-update technique with spectral element method are given.
Andreussi, T; Pegoraro, F
2016-01-01
Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamical accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi {\\it et al.}\\ [Phys.\\ Plasmas {\\bf20}, 092104 (2013)] that makes it possible to reformulate Eulerian equilibria with flows as Lagrangian equilibria in the relabeled variables. The procedures detailed in the present article provide a paradigm that can be applied to more general plasma configurations and in addition extended to more general plasma descriptions where dissipation is abse...
An algebraic mistake in the rendering of the Energy Casimir stability condition for a symmetric magnetohydrodynamics plasma configuration with flows made in the article Andreussi et al. “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory,” Phys. Plasmas 20, 092104 (2013) is corrected
Yeh, Gour-Tsyh [Pennsylvania State Univ., University Park, PA (United States). Dept. of Civil and Environmental Engineering; Carpenter, S.L. [Univ. of New Mexico, Albuquerque, NM (United States). Dept. of Earth and Planetary Sciences; Hopkins, P.L.; Siegel, M.D. [Sandia National Labs., Albuquerque, NM (United States)
1995-11-01
The computer program LEHGC is a Hybrid Lagrangian-Eulerian Finite-Element Model of HydroGeo-Chemical (LEHGC) Transport Through Saturated-Unsaturated Media. LEHGC iteratively solves two-dimensional transport and geochemical equilibrium equations and is a descendant of HYDROGEOCHEM, a strictly Eulerian finite-element reactive transport code. The hybrid Lagrangian-Eulerian scheme improves on the Eulerian scheme by allowing larger time steps to be used in the advection-dominant transport calculations. This causes less numerical dispersion and alleviates the problem of calculated negative concentrations at sharp concentration fronts. The code also is more computationally efficient than the strictly Eulerian version. LEHGC is designed for generic application to reactive transport problems associated with contaminant transport in subsurface media. Input to the program includes the geometry of the system, the spatial distribution of finite elements and nodes, the properties of the media, the potential chemical reactions, and the initial and boundary conditions. Output includes the spatial distribution of chemical element concentrations as a function of time and space and the chemical speciation at user-specified nodes. LEHGC Version 1.1 is a modification of LEHGC Version 1.0. The modification includes: (1) devising a tracking algorithm with the computational effort proportional to N where N is the number of computational grid nodes rather than N{sup 2} as in LEHGC Version 1.0, (2) including multiple adsorbing sites and multiple ion-exchange sites, (3) using four preconditioned conjugate gradient methods for the solution of matrix equations, and (4) providing a model for some features of solute transport by colloids.
The computer program LEHGC is a Hybrid Lagrangian-Eulerian Finite-Element Model of HydroGeo-Chemical (LEHGC) Transport Through Saturated-Unsaturated Media. LEHGC iteratively solves two-dimensional transport and geochemical equilibrium equations and is a descendant of HYDROGEOCHEM, a strictly Eulerian finite-element reactive transport code. The hybrid Lagrangian-Eulerian scheme improves on the Eulerian scheme by allowing larger time steps to be used in the advection-dominant transport calculations. This causes less numerical dispersion and alleviates the problem of calculated negative concentrations at sharp concentration fronts. The code also is more computationally efficient than the strictly Eulerian version. LEHGC is designed for generic application to reactive transport problems associated with contaminant transport in subsurface media. Input to the program includes the geometry of the system, the spatial distribution of finite elements and nodes, the properties of the media, the potential chemical reactions, and the initial and boundary conditions. Output includes the spatial distribution of chemical element concentrations as a function of time and space and the chemical speciation at user-specified nodes. LEHGC Version 1.1 is a modification of LEHGC Version 1.0. The modification includes: (1) devising a tracking algorithm with the computational effort proportional to N where N is the number of computational grid nodes rather than N2 as in LEHGC Version 1.0, (2) including multiple adsorbing sites and multiple ion-exchange sites, (3) using four preconditioned conjugate gradient methods for the solution of matrix equations, and (4) providing a model for some features of solute transport by colloids
Numerical Simulation of Drophila Flight Based on Arbitrary Langrangian-Eulerian Method
Erzincanli, Belkis; Sahin, Mehmet
2012-11-01
A parallel unstructured finite volume algorithm based on Arbitrary Lagrangian Eulerian (ALE) method has been developed in order to investigate the wake structure around a pair of flapping Drosophila wings. The numerical method uses a side-centered arrangement of the primitive variables that does not require any ad-hoc modifications in order to enhance pressure coupling. A radial basis function (RBF) interpolation method is also implemented in order to achieve large mesh deformations. For the parallel solution of resulting large-scale algebraic equations, a matrix factorization is introduced similar to that of the projection method for the whole coupled system and two-cycle of BoomerAMG solver is used for the scaled discrete Laplacian provided by the HYPRE library which we access through the PETSc library. The present numerical algorithm is initially validated for the flow past an oscillating circular cylinder in a channel and the flow induced by an oscillating sphere in a cubic cavity. Then the numerical algorithm is applied to the numerical simulation of flow field around a pair of flapping Drosophila wing in hover flight. The time variation of the near wake structure is shown along with the aerodynamic loads and particle traces. The authors acknowledge financial support from Turkish National Scientific and Technical Research Council (TUBITAK) through project number 111M332. The authors would like to thank Michael Dickinson and Michael Elzinga for providing the experimental data.
A New Method to Simulate Free Surface Flows for Viscoelastic Fluid
Yu Cao; Xiao-Guang Ren; Xiao-Wei Guo; Miao Wang; Qian Wang; Xin-Hai Xu; Xue-Jun Yang
2015-01-01
Free surface flows arise in a variety of engineering applications. To predict the dynamic characteristics of such problems, specific numerical methods are required to accurately capture the shape of free surface. This paper proposed a new method which combined the Arbitrary Lagrangian-Eulerian (ALE) technique with the Finite Volume Method (FVM) to simulate the time-dependent viscoelastic free surface flows. Based on an open source CFD toolbox called OpenFOAM, we designed an ALE-FVM free surfa...
Heckmann, Andreas; Hartweg, Stefan; Kaiser, Ingo
2011-01-01
The bending deformation of rotating annular plates and the associated vibration behaviour is important in engineering applications which range from automotive or railway brake systems to discs that form essential components in turbomachinery. In order to extend the capabilities of the DLR FlexibleBodies library for such use cases, a new Modelica class has been implemented which is based on the analytical description of an annular Kirchhoff plate. In addition the so-called Arbitray Langra...
GO++ : A modular Lagrangian/Eulerian software for Hamilton Jacobi equations of Geometric Optics type
Benamou, Jean-David; Hoch, Philippe
2002-01-01
We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton-Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples presented.Hamilton-Jacobi,Hamiltonian System, Ray Tracing, Viscosity Solution, Upwind Scheme, Geometric Optics, C++
ALE Fractional Step Finite Element Method for Fluid-Structure Nonlinear Interaction Problem
无
2006-01-01
A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.
A multi-material ReALE method with MOF interface reconstruction
We present a comparison of a classical arbitrary Lagrangian-Eulerian (ALE) method with a new multi-material reconnection-based arbitrary-Lagrangian-Eulerian (Re-ALE) strategy devoted to the computation of multi-material compressible fluid flows using the Moment Of Fluid (MOF) interface reconstruction. In ReALE we replace the rezoning phase of classical ALE method by a rezone where we allow the connectivity between cells of the mesh to change where rezoned grid is a polygonal mesh. Nevertheless, the ability of pure Lagrangian method to deal with multi-material problem, where mesh is aligned with material interfaces, is lost. In this work we have implemented MOF interface reconstruction on polygonal mesh in ReALE framework. This leads to a formulation that recover the Lagrangian features of following material and material interface that we lose using standard ALE methods with fixed connectivity. Some numerical examples, are used to clearly illustrate the robustness and accuracy of the new method. (authors)
Siqueira, Mario; Lai, Chun-Ta; Katul, Gabriel
2000-12-01
A new method was developed to estimate canopy sources and sinks from measured mean concentration profiles within the canopy (referred to as the ``inverse'' problem). The proposed method combined many of the practical advantages of the Lagrangian localized near-field (LNF) theory and higher-order Eulerian (EUL) closure principles. Particularly, this ``hybrid'' method successfully combined the essential conservation equations of closure modeling and the robustness of the regression source inversion developed for LNF theory. The proposed method along with LNF and EUL were tested using measurements from two field experiments collected in a pine forest and published measurements from a wind tunnel experiment. The field experiments were conducted to investigate the vertical distribution of the scalar fluxes within the canopy and the temporal patterns of the scalar fluxes above the canopy. This comparison constitutes the first ``inverse method'' comparison performed using the same data sets on all three models. For the wind tunnel data, all three models well reproduced the measured flux distribution. For the field experiments, all three models recovered the measured spatial and temporal flux distribution in an ensemble sense. The agreement between these three models is desirable to the inverse problem because it adds the necessary confidence in the computed flux distributions. However, the agreement among all three models with the field measurements, on a 30-min time step, was less than satisfactory. Additionally, the divergence between models and measurements increased with departure from a near-neutral atmospheric state. Despite fundamental differences in these model approximations, this similarity in model performance suggests that the source information recovered from a measured one-dimensional mean concentration profile will not be further enhanced by a one-dimensional steady state, planar homogeneous model of neutral flows.
An ALE finite element method for baffled fuel container in yawing motion
A computational analysis of engineering problems with moving domain or/and boundary according to either Lagrangian or Eulerian approach may encounter inherent numerical difficulties, the extreme mesh distortion in the former and the material boundary indistinctness in the latter. In order to overcome such defects in classical numerical approaches, the ALE (Arbitrary Lagrangian Eulerian) method is widely being adopted in which the finite element mesh moves with arbitrary velocity. This paper is concerned with the ALE finite element formulation, aiming at the dynamic response analysis of baffled fuel-storage container in yawing motion, for which the coupled time integration scheme, the remeshing and smoothing algorithm and the mesh velocity determination are addressed. Numerical simulation illustrating theoretical works is also presented
A swept-intersection-based re-mapping method in a ReALE framework
A complete reconnection-based arbitrary Lagrangian-Eulerian (ReALE) strategy devoted to the computation of hydrodynamic applications for compressible fluid flows is presented here. In ReALE, we replace the rezoning phase of classical ALE method by a rezoning where we allow the connectivity between cells of the mesh to change. This leads to a polygonal mesh that recovers the Lagrangian features in order to follow more efficiently the flow. Those reconnections allow to deal with complex geometries and high vorticity problems contrary to ALE method. For optimizing the re-mapping phase, we have modified the idea of swept-integration-based. The new method is called swept-intersection-based re-mapping method. We demonstrate that our method can be applied to several numerical examples representative of hydrodynamic experiments. (authors)
A New Method to Simulate Free Surface Flows for Viscoelastic Fluid
Yu Cao
2015-01-01
Full Text Available Free surface flows arise in a variety of engineering applications. To predict the dynamic characteristics of such problems, specific numerical methods are required to accurately capture the shape of free surface. This paper proposed a new method which combined the Arbitrary Lagrangian-Eulerian (ALE technique with the Finite Volume Method (FVM to simulate the time-dependent viscoelastic free surface flows. Based on an open source CFD toolbox called OpenFOAM, we designed an ALE-FVM free surface simulation platform. In the meantime, the die-swell flow had been investigated with our proposed platform to make a further analysis of free surface phenomenon. The results validated the correctness and effectiveness of the proposed method for free surface simulation in both Newtonian fluid and viscoelastic fluid.
Finite element method application for turbulent and transitional flow
Sváček Petr
2016-01-01
Full Text Available This paper is interested in numerical simulations of the interaction of the fluid flow with an airfoil. Particularly, the problem of the turbulent flow around the airfoil with elastic support is considered. The main attention is paid to the numerical approximation of the flow problem using the finite element approximations. The laminar - turbulence transition of the flow on the surface airfoil is considered. The chois of the transition model is discussed. The transition model based on the two equation k−ω turbulence model is used. The structure motion is described with the aid of two degrees of freedom. The motion of the computational domain is treated with the aid of the arbitrary Lagrangian-Eulerian method. Numerical results are shown.
Methods for simulation-based analysis of fluid-structure interaction.
Barone, Matthew Franklin; Payne, Jeffrey L.
2005-10-01
Methods for analysis of fluid-structure interaction using high fidelity simulations are critically reviewed. First, a literature review of modern numerical techniques for simulation of aeroelastic phenomena is presented. The review focuses on methods contained within the arbitrary Lagrangian-Eulerian (ALE) framework for coupling computational fluid dynamics codes to computational structural mechanics codes. The review treats mesh movement algorithms, the role of the geometric conservation law, time advancement schemes, wetted surface interface strategies, and some representative applications. The complexity and computational expense of coupled Navier-Stokes/structural dynamics simulations points to the need for reduced order modeling to facilitate parametric analysis. The proper orthogonal decomposition (POD)/Galerkin projection approach for building a reduced order model (ROM) is presented, along with ideas for extension of the methodology to allow construction of ROMs based on data generated from ALE simulations.
We introduce and study numerically a scalable parallel finite element solver for the simulation of blood flow in compliant arteries. The incompressible Navier-Stokes equations are used to model the fluid and coupled to an incompressible linear elastic model for the blood vessel walls. Our method features an unstructured dynamic mesh capable of modeling complicated geometries, an arbitrary Lagrangian-Eulerian framework that allows for large displacements of the moving fluid domain, monolithic coupling between the fluid and structure equations, and fully implicit time discretization. Simulations based on blood vessel geometries derived from patient-specific clinical data are performed on large supercomputers using scalable Newton-Krylov algorithms preconditioned with an overlapping restricted additive Schwarz method that preconditions the entire fluid-structure system together. The algorithm is shown to be robust and scalable for a variety of physical parameters, scaling to hundreds of processors and millions of unknowns.
The finite-difference lattice Boltzmann method and its application in computational aero-acoustics
The application of the finite-difference lattice Boltzmann method in computational aero-acoustics is reviewed, mainly on the basis of the work of the author and his colleagues. Some models of thermal and isothermal fluids are described and the constraints for recovering the Euler equations and the Navier–Stokes equations are described. The arbitrary Lagrangian Eulerian technique is used for high Mach number flows and for simulations of moving bodies. A model of gas–liquid two-phase fluid is introduced in which the density difference is 800 times and the sound velocity difference is 4 times. Some applications of aero-acoustic problems are briefly described and the simultaneous simulation of underwater sound and sound propagating in air is also presented. The difference between the thermal model and the isothermal model is shown in the aero-acoustic problems. (paper)
AbuAlSaud, Moataz
2012-07-01
The purpose of this thesis is to solve unsteady two-dimensional compressible Navier-Stokes equations for a moving mesh using implicit explicit (IMEX) Runge- Kutta scheme. The moving mesh is implemented in the equations using Arbitrary Lagrangian Eulerian (ALE) formulation. The inviscid part of the equation is explicitly solved using second-order Godunov method, whereas the viscous part is calculated implicitly. We simulate subsonic compressible flow over static NACA-0012 airfoil at different angle of attacks. Finally, the moving mesh is examined via oscillating the airfoil between angle of attack = 0 and = 20 harmonically. It is observed that the numerical solution matches the experimental and numerical results in the literature to within 20%.
A general topology, Godunov method
Addessio, F.; Cline, M.; Dukowicz, J.
1987-01-01
A numerical technique that utilizes a general topology mesh is described. The method employs the arbitrary Lagrangian-Eulerian procedure and explicit, finite-volume, Godunov numerics. Material interfaces are resolved to eliminate fictitious mixing and nonphysical shear impedance. Cell-centered variables, including velocity, are used to provide consistent control volumes for the advection of mass, momentum, and energy, and to allow arbitrary slip between material regions. The computational mesh is composed of arbitrary polygonal cells. The constraint of a fixed logical connectivity for the mesh is removed. Consequently, geometrical mesh limitations, which are responsible for inaccuracies and code failure during the evolution of region boundaries, are absent. Arbitrary boundaries can be resolved, and the mesh is capable of changing smoothly and rapidly from regions of high to low resolution. Lack of a coherent mesh orientation minimizes numerical anisotropy. A mesh rezoning approach, based on a dual triangulation and coupled with a global remapping algorithm, allows the mesh to evolve dynamically. 9 refs., 6 figs.
Simulation method of arbitrary energy distributed nuclear signals
In this paper, according to the random characteristic of pulse amplitude and time interval of two adjacent pules, we discuss simulation methods of nuclear signal statistical distribution. When energy randomness of nuclear random signal is simulated, the statistical distribution can be decomposed into uniform distribution, Gaussian distribution, exponential distribution, Poisson distribution, multinomial distribution etc, and can be realized by methods we proposed in this paper. Arbitrary energy distributed nuclear signal that cannot be decomposed easily can also be realized by the methods, and simulation effect is excellent. (authors)
Liou, Meng-Sing
1995-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.
Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics.
Maire, Pierre-Henri; Nkonga, Boniface
2009-01-01
This work presents a multidimensional cell-centered unstructured finite volume scheme for the solution of multimaterial compressible fluid flows written in the Lagrangian formalism. This formulation is considered in the Arbitrary-Lagrangian-Eulerian (ALE) framework with the constraint that the mesh and the fluid velocity coincide. The link between the vertex velocity and the fluid motion is obtained by a formulation of the momentum conservation on a class of multi-scale encased volumes around...
Formulation of discontinuous Galerkin methods for relativistic astrophysics
Teukolsky, Saul A.
2016-05-01
The DG algorithm is a powerful method for solving pdes, especially for evolution equations in conservation form. Since the algorithm involves integration over volume elements, it is not immediately obvious that it will generalize easily to arbitrary time-dependent curved spacetimes. We show how to formulate the algorithm in such spacetimes for applications in relativistic astrophysics. We also show how to formulate the algorithm for equations in non-conservative form, such as Einstein's field equations themselves. We find two computationally distinct formulations in both cases, one of which has seldom been used before for flat space in curvilinear coordinates but which may be more efficient. We also give a new derivation of the ALE algorithm (Arbitrary Lagrangian-Eulerian) using 4-vector methods that is much simpler than the usual derivation and explains why the method preserves the conservation form of the equations. The various formulations are explored with some simple numerical experiments that also investigate the effect of the metric identities on the results. The results of this paper may also be of interest to practitioners of DG working with curvilinear elements in flat space.
CIP/multi-moment finite volume method with arbitrary order of accuracy
XIAO, FENG; Ii, Satoshi
2012-01-01
This paper presents a general formulation of the CIP/multi-moment finite volume method (CIP/MM FVM) for arbitrary order of accuracy. Reconstruction up to arbitrary order can be built on single cell by adding extra derivative moments at the cell boundary. The volume integrated average (VIA) is updated via a flux-form finite volume formulation, whereas the point-based derivative moments are computed as local derivative Riemann problems by either direct interpolation or approximate Riemann solvers.
Cheap arbitrary high order methods for single integrand SDEs
Debrabant, Kristian; Kværnø, Anne
2016-01-01
For a particular class of Stratonovich SDE problems, here denoted as single integrand SDEs, we prove that by applying a deterministic Runge-Kutta method of order $p_d$ we obtain methods converging in the mean-square and weak sense with order $\\lfloor p_d/2\\rfloor$. The reason is that the B...
Zeng, X.; Scovazzi, G.
2016-06-01
We present a monolithic arbitrary Lagrangian-Eulerian (ALE) finite element method for computing highly transient flows with strong shocks. We use a variational multiscale (VMS) approach to stabilize a piecewise-linear Galerkin formulation of the equations of compressible flows, and an entropy artificial viscosity to capture strong solution discontinuities. Our work demonstrates the feasibility of VMS methods for highly transient shock flows, an area of research for which the VMS literature is extremely scarce. In addition, the proposed monolithic ALE method is an alternative to the more commonly used Lagrangian+remap methods, in which, at each time step, a Lagrangian computation is followed by mesh smoothing and remap (conservative solution interpolation). Lagrangian+remap methods are the methods of choice in shock hydrodynamics computations because they provide nearly optimal mesh resolution in proximity of shock fronts. However, Lagrangian+remap methods are not well suited for imposing inflow and outflow boundary conditions. These issues offer an additional motivation for the proposed approach, in which we first perform the mesh motion, and then the flow computations using the monolithic ALE framework. The proposed method is second-order accurate and stable, as demonstrated by extensive numerical examples in two and three space dimensions.
On the Arbitrary Difference Precise Integration Method and Its Numerical Stability
无
2000-01-01
Based on the subdomain precise integration method, the arbitrary difference precise integration method (ADPIM) is presented to solve PDEs. While retaining all the merits of the former method, ADPIM also demonstrates advantages such as the abilities of better description of physical properties of inhomogeneous media and convenient treatment of various boundary conditions. The explicit integration schemes derived by ADPIM are proved unconditionally stable.
Compressive VOF method with skewness correction to capture sharp interfaces on arbitrary meshes
Denner, Fabian; van Wachem, Berend G. M.
2014-12-01
The accurate and efficient modelling of two-phase flows is at present mostly limited to structured, unskewed meshes, due to the additional topological and numerical complexity of arbitrary, unstructured meshes. Compressive VOF methods which discretize the interface advection with algebraic differencing schemes are computationally efficient and inherently applicable to arbitrary meshes. However, compressive VOF methods evidently suffer severely from numerical diffusion on meshes with topological skewness. In this paper we present a compressive VOF method using a state-of-the-art donor-acceptor advection scheme which includes novel modifications to substantially reduce numerical diffusion on arbitrary meshes without adding computational complexity. The new methodology accurately captures evolving interfaces on any arbitrary, non-overlapping mesh and conserves mass within the limits of the applied solver tolerance. A thorough validation of the presented methods is conducted, examining the pure advection of the interface indicator function as well as the application to evolving interfaces with surface tension. Crucially, the results on equidistant Cartesian and arbitrary tetrahedral meshes are shown to be comparable and accurate.
CHENG Min; TANG Tiantong; YAO Zhenhua; ZHU Jingping
2001-01-01
Differential algebraic method is apowerful technique in computer numerical analysisbased on nonstandard analysis and formal series the-ory. It can compute arbitrary high order derivativeswith excellent accuracy. The principle of differentialalgebraic method is applied to calculate high orderaberrations of combined electromagnetic focusing sys-tems. As an example, third-order geometric aberra-tion coefficients of an actual combined electromagneticfocusing system were calculated. The arbitrary highorder aberrations are conveniently calculated by dif-ferential algebraic method and the fifth-order aberra-tion diagrams are given.
Numerical Method for Determining Stiffness Characteristics of an Arbitrary Form Superelement
Tsybenko Alexander
2015-12-01
Full Text Available As part of the superelement approximation technology for fragments (subsystems of the analyzed structures, a numerical method of determining the characteristics of arbitrary type superelements was developed. The examples of simulation models with two-node superelements demonstrated the efficacy of the method in the structural analysis of elastic systems.
Simulating Space Capsule Water Landing with Explicit Finite Element Method
Wang, John T.; Lyle, Karen H.
2007-01-01
A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.
Flow simulation of a Pelton bucket using finite volume particle method
The objective of the present paper is to perform an accurate numerical simulation of the high-speed water jet impinging on a Pelton bucket. To reach this goal, the Finite Volume Particle Method (FVPM) is used to discretize the governing equations. FVPM is an arbitrary Lagrangian-Eulerian method, which combines attractive features of Smoothed Particle Hydrodynamics and conventional mesh-based Finite Volume Method. This method is able to satisfy free surface and no-slip wall boundary conditions precisely. The fluid flow is assumed weakly compressible and the wall boundary is represented by one layer of particles located on the bucket surface. In the present study, the simulations of the flow in a stationary bucket are investigated for three different impinging angles: 72°, 90° and 108°. The particles resolution is first validated by a convergence study. Then, the FVPM results are validated with available experimental data and conventional grid-based Volume Of Fluid simulations. It is shown that the wall pressure field is in good agreement with the experimental and numerical data. Finally, the torque evolution and water sheet location are presented for a simulation of five rotating Pelton buckets
A New Method for Locating Calculation of Arbitrary Spatial Straight Line or Plane in NC Machining
无
2002-01-01
In the manufacturing process, we often encounter so me location machining of space arbitrary straight lines and planes that are not on ly unparalleled but also not vertical with the machine tool spindle or the cutti ng tool. In the past, we can do the location machining through the methods of dr awing line and making level in the ordinary machine tool. In the numerical contr ol machining of the CNC machine tool and manufacturing center, however, the spac e location and angle of the arbitrary straight lines...
Method to calculate interior sound field of arbitrary-shaped closed thin shell
WU Jiuhui; CHEN Hualing; HU Xuanli
2001-01-01
The concept of covering-domain means that an arbitrary-shaped closed shell can be approached by a series of closed spherical shells. Based on it, the interior scattering sound field of the arbitrary-shaped closed shell is given. According to the reciprocity theory, the radiating sound field of the elastic surface due to the action of external force is presented. The method presented can also be used to calculate the interior sound fields of arbitraryshaped closed thin shells of which the thickness are either equal or unequal. It is verified to be correct by corresponding test.
A New Pseudospectral Method for Calculations of Hydrogen Atom in Arbitrary External Fields
QIAO Hao-Xue; LI Bai-Wen1
2002-01-01
A new pseudospectral method was introduced to calculate wavefunctions and energy levels of hydrogen atom in arbitrary potential. Some results of hydrogen atom in uniform magnetic fields were presented, high accuracy of results was obtained with simple calculations, and our calculations show very fast convergence. It suggests a new methodfor calculations of hydrogen atom in external fields.
Hong Luo; Luqing Luo; Robert Nourgaliev; Vincent A. Mousseau
2010-01-01
A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.
Piret, Cécile
2012-05-01
Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in . R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time. © 2012 Elsevier Inc.
Xiaoqing Wang
2016-01-01
Full Text Available Parallel analyses about the dynamic responses of a large-scale water conveyance tunnel under seismic excitation are presented in this paper. A full three-dimensional numerical model considering the water-tunnel-soil coupling is established and adopted to investigate the tunnel’s dynamic responses. The movement and sloshing of the internal water are simulated using the multi-material Arbitrary Lagrangian Eulerian (ALE method. Nonlinear fluid–structure interaction (FSI between tunnel and inner water is treated by using the penalty method. Nonlinear soil-structure interaction (SSI between soil and tunnel is dealt with by using the surface to surface contact algorithm. To overcome computing power limitations and to deal with such a large-scale calculation, a parallel algorithm based on the modified recursive coordinate bisection (MRCB considering the balance of SSI and FSI loads is proposed and used. The whole simulation is accomplished on Dawning 5000 A using the proposed MRCB based parallel algorithm optimized to run on supercomputers. The simulation model and the proposed approaches are validated by comparison with the added mass method. Dynamic responses of the tunnel are analyzed and the parallelism is discussed. Besides, factors affecting the dynamic responses are investigated. Better speedup and parallel efficiency show the scalability of the parallel method and the analysis results can be used to aid in the design of water conveyance tunnels.
Ren, Xiaodong; Xu, Kun; Shyy, Wei
2016-07-01
This paper presents a multi-dimensional high-order discontinuous Galerkin (DG) method in an arbitrary Lagrangian-Eulerian (ALE) formulation to simulate flows over variable domains with moving and deforming meshes. It is an extension of the gas-kinetic DG method proposed by the authors for static domains (X. Ren et al., 2015 [22]). A moving mesh gas kinetic DG method is proposed for both inviscid and viscous flow computations. A flux integration method across a translating and deforming cell interface has been constructed. Differently from the previous ALE-type gas kinetic method with piecewise constant mesh velocity at each cell interface within each time step, the mesh velocity variation inside a cell and the mesh moving and rotating at a cell interface have been accounted for in the finite element framework. As a result, the current scheme is applicable for any kind of mesh movement, such as translation, rotation, and deformation. The accuracy and robustness of the scheme have been improved significantly in the oscillating airfoil calculations. All computations are conducted in a physical domain rather than in a reference domain, and the basis functions move with the grid movement. Therefore, the numerical scheme can preserve the uniform flow automatically, and satisfy the geometric conservation law (GCL). The numerical accuracy can be maintained even for a largely moving and deforming mesh. Several test cases are presented to demonstrate the performance of the gas-kinetic DG-ALE method.
A WENO-type slope-limiter for a family of piecewise polynomial methods
Engwirda, Darren
2016-01-01
A new, high-order slope-limiting procedure for the Piecewise Parabolic Method (PPM) and the Piecewise Quartic Method (PQM) is described. Following a Weighted Essentially Non-Oscillatory (WENO)-type paradigm, the proposed slope-limiter seeks to reconstruct smooth, non-oscillatory piecewise polynomial profiles as a non-linear combination of the natural and monotone-limited PPM and PQM interpolants. Compared to existing monotone slope-limiting techniques, this new strategy is designed to improve accuracy at smooth extrema, while controlling spurious oscillations in the neighbourhood of sharp features. Using the new slope-limited PPM and PQM interpolants, a high-order accurate Arbitrary-Lagrangian-Eulerian framework for advection-dominated flows is constructed, and its effectiveness is examined using a series of one- and two-dimensional benchmark cases. It is shown that the new WENO-type slope-limiting techniques offer a significant improvement in accuracy compared to existing strategies, allowing the PPM- and PQ...
New finite volume methods for approximating partial differential equations on arbitrary meshes
This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)
Carrington, David Bradley [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Monayem, A. K. M. [Univ. of New Mexico, Albuquerque, NM (United States); Mazumder, H. [Univ. of New Mexico, Albuquerque, NM (United States); Heinrich, Juan C. [Univ. of New Mexico, Albuquerque, NM (United States)
2015-03-05
A three-dimensional finite element method for the numerical simulations of fluid flow in domains containing moving rigid objects or boundaries is developed. The method falls into the general category of Arbitrary Lagrangian Eulerian methods; it is based on a fixed mesh that is locally adapted in the immediate vicinity of the moving interfaces and reverts to its original shape once the moving interfaces go past the elements. The moving interfaces are defined by separate sets of marker points so that the global mesh is independent of interface movement and the possibility of mesh entanglement is eliminated. The results is a fully robust formulation capable of calculating on domains of complex geometry with moving boundaries or devises that can also have a complex geometry without danger of the mesh becoming unsuitable due to its continuous deformation thus eliminating the need for repeated re-meshing and interpolation. Moreover, the boundary conditions on the interfaces are imposed exactly. This work is intended to support the internal combustion engines simulator KIVA developed at Los Alamos National Laboratories. The model's capabilities are illustrated through application to incompressible flows in different geometrical settings that show the robustness and flexibility of the technique to perform simulations involving moving boundaries in a three-dimensional domain.
High resolution finite volume methods on arbitrary grids via wave propagation. Final report
A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Riemann problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved
A Finite Field Method for Calculating Molecular Polarizability Tensors for Arbitrary Multipole Rank
Elking, Dennis M.; Perera, Lalith; Duke, Robert; Darden, Thomas; Pedersen, Lee G.
2011-01-01
A finite field method for calculating spherical tensor molecular polarizability tensors αlm;l′m′ = ∂Δlm/∂ϕl′m′* by numerical derivatives of induced molecular multipole Δlm with respect to gradients of electrostatic potential ϕl′m′* is described for arbitrary multipole ranks l and l′. Inter-conversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up...
Pauli problem for a spin of arbitrary length: A simple method to determine its wave function
Weigert, S.
1992-01-01
The problem of determining a pure state vector from measurements is investigated for a quantum spin of arbitrary length. Generically, only a finite number of wave functions is compatible with the intensities of the spin components in two different spatial directions, measured by a Stern-Gerlach apparatus. The remaining ambiguity can be resolved by one additional well-defined measurement. This method combines efficiency with simplicity: only a small number of quantities have to be measured and...
Hong Luo; Hanping Xiao; Robert Nourgaliev; Chunpei Cai
2011-06-01
A comparative study of different reconstruction schemes for a reconstruction-based discontinuous Galerkin, termed RDG(P1P2) method is performed for compressible flow problems on arbitrary grids. The RDG method is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution via a reconstruction scheme commonly used in the finite volume method. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are implemented to obtain a quadratic polynomial representation of the underlying discontinuous Galerkin linear polynomial solution on each cell. These three reconstruction/recovery methods are compared for a variety of compressible flow problems on arbitrary meshes to access their accuracy and robustness. The numerical results demonstrate that all three reconstruction methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstruction method provides the best performance in terms of both accuracy and robustness.
You, Oubo; Bai, Benfeng; Wu, Xiaoyu; Zhu, Zhendong; Wang, Qixia
2015-12-01
The efficient steering of surface plasmon polariton (SPP) fields is a vital issue in various plasmonic applications, such as plasmonic circuitry. We present a straightforward and efficient method for generating unidirectionally propagating SPP beams with arbitrary amplitude and phase profiles by manipulating Δ-shaped nanoantennas. As an example, a second-order Hermite-Gauss SPP beam is generated with this method. The near-field distribution of the generated SPP beam is experimentally characterized to validate the effectiveness of the method. PMID:26625032
GBIQ: a non-arbitrary, non-biased method for quantification of fluorescent images
Ninomiya, Youichirou; Zhao, Wei; Saga, Yumiko
2016-01-01
Non-arbitrary and non-biased quantification of fluorescent images is an essential tool for the data-centric approach to biological systems. Typical application is high-content analysis, where various phenotypic changes in cellular components and/or morphology are measured from fluorescent image data. A standard protocol to detect cellular phenotypes is cell-segmentation, in which boundaries of cellular components, such as cell nucleus and plasma membrane, are first identified to define cell segments, then acquiring various phenotypic data of each segment. To achieve reliable outcome, cell-segmentation requires manual adjustments of many parameters; this requirement could hamper automated image processing in high-throughput workflow, whose quantification must be non-arbitrary and non-biased. As a practical alternative to the segmentation-based method, we developed GBIQ (Grid Based Image Quantification), which allows comparison of cellular information without identification of single cells. GBIQ divides an image with tiles of fixed size grids and records statistics of the grids with their location coordinates, minimizing arbitrary intervenes. GBIQ requires only one parameter (size of grid) to be set; nonetheless it robustly produces results suitable for further statistical evaluation. The simplicity of GBIQ allows it to be readily implemented in an automated high-throughput image analysis workflow. PMID:27211912
Linear dynamic analysis of arbitrary thin shells modal superposition by using finite element method
The linear dynamic behaviour of arbitrary thin shells by the Finite Element Method is studied. Plane triangular elements with eighteen degrees of freedom each are used. The general equations of movement are obtained from the Hamilton Principle and solved by the Modal Superposition Method. The presence of a viscous type damping can be considered by means of percentages of the critical damping. An automatic computer program was developed to provide the vibratory properties and the dynamic response to several types of deterministic loadings, including temperature effects. The program was written in FORTRAN IV for the Burroughs B-6700 computer. (author)
Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom
Iaroshenko, Oleksandr [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-09-01
In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.
Xiong, Jie L. [Faculty of Engineering, University of Hong Kong (Hong Kong); Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, IL, 61801 (United States); Tong, M.S. [Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, IL, 61801 (United States); Atkins, Phillip [Faculty of Engineering, University of Hong Kong (Hong Kong); Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, IL, 61801 (United States); Chew, W.C., E-mail: wcchew@hku.h [Faculty of Engineering, University of Hong Kong (Hong Kong); Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, IL, 61801 (United States)
2010-05-31
In this Letter, we generalized the surface integral equation method for the evaluation of Casimir force in arbitrary three-dimensional geometries. Similar to the two-dimensional case, the evaluation of the mean Maxwell stress tensor is cast into solving a series of three-dimensional scattering problems. The formulation and solution of the three-dimensional scattering problems are well-studied in classical computational electromagnetics. This Letter demonstrates that this quantum electrodynamic phenomenon can be studied using the knowledge and techniques of classical electrodynamics.
Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries
Williams-Rioux, Bertrand
2012-01-12
Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.
Yan, Wei; Mortensen, N. Asger; Wubs, Martijn
2013-01-01
We develop a nonlocal-response generalization to the Green's function surface-integral method (GSIM), also known as the boundary-element method. This numerically efficient method can accurately describe the linear hydrodynamic nonlocal response of arbitrarily shaped plasmonic nanowires in arbitrary...... dielectric backgrounds. All previous general-purpose methods for nonlocal response are bulk methods. We also expand the possible geometries to which the usual local-response GSIM can be applied, by showing how to regularize singularities that occur in the surface integrals when the nanoparticles touch a...... dielectric substrate. The same regularization works for nonlocal response. Furthermore, an effective theory is developed to explain the numerically observed nonlocal effects. The nonlocal frequency blueshift of a cylindrical nanowire in an inhomogeneous background generally increases as the nanowire radius...
Maskew, B.
1976-01-01
A discrete singularity method has been developed for calculating the potential flow around two-dimensional airfoils. The objective was to calculate velocities at any arbitrary point in the flow field, including points that approach the airfoil surface. That objective was achieved and is demonstrated here on a Joukowski airfoil. The method used combined vortices and sources ''submerged'' a small distance below the airfoil surface and incorporated a near-field subvortex technique developed earlier. When a velocity calculation point approached the airfoil surface, the number of discrete singularities effectively increased (but only locally) to keep the point just outside the error region of the submerged singularity discretization. The method could be extended to three dimensions, and should improve nonlinear methods, which calculate interference effects between multiple wings, and which include the effects of force-free trailing vortex sheets. The capability demonstrated here would extend the scope of such calculations to allow the close approach of wings and vortex sheets (or vortices).
Lagrangian-Eulerian simulation of slugging fluidized bed
Guorong Wu; Jie Ouyang; Binxin Yang; Qiang Li; Fang Wang
2012-01-01
This work studies gas-solid slugging fluidized beds with Type-D particles,using two-dimensional simulations based on discrete element model (DEM).DEM performance is quantitatively validated by two commonly accepted correlations for determining slugging behavior.The voidage profiles simulated with bed height corresponding to Baeyens and Geldart (1974) correlation for onset of slugging demonstrate a transitional flow pattern from free bubbling to slugging.The present calculated values for the maximum slugging bed height are in good agreement with the correlation from Matsen et al.(1969).Simulations show that fluidized beds with Type-D particles can operate in the round-nosed slugging regime and also shows that wall slugs and square-nosed slugs tend to be formed with increase in superficial gas velocity and in bed height,respectively.
Universal method for the synthesis of arbitrary polarization states radiated by a nanoantenna
Rodriguez-Fortuno, Francisco J; Griol, Amadeu; Bellieres, Laurent; Marti, Javier; Martinez, Alejandro
2015-01-01
Optical nanoantennas efficiently convert confined optical energy into free-space radiation. The polarization of the emitted radiation depends mainly on nanoantenna shape, so it becomes extremely difficult to manipulate it unless the nanostructure is physically altered. Here we demonstrate a simple way to synthetize the polarization of the radiation emitted by a single nanoantenna so that every point on the Poincar\\'e sphere becomes attainable. The nanoantenna consists of a single scatterer created on a dielectric waveguide and fed from its both sides so that the polarization of the emitted optical radiation is controlled by the amplitude and phase of the feeding signals. Our nanoantenna is created on a silicon chip using standard top-down nanofabrication tools, but the method is universal and can be applied to other materials, wavelengths and technologies. This work will open the way towards the synthesis and control of arbitrary polarization states in nano-optics.
Design method for electromagnetic cloak with arbitrary shapes based on Laplace's equation.
Hu, Jin; Zhou, Xiaoming; Hu, Gengkai
2009-02-01
In transformation optics, the space transformation is viewed as the deformation of a material. The permittivity and permeability tensors in the transformed space are found to correlate with the deformation field of the material. By solving the Laplace's equation, which describes how the material will deform during a transformation, we can design electromagnetic cloaks with arbitrary shapes if the boundary conditions of the cloak are considered. As examples, the material parameters of the spherical and elliptical cylindrical cloaks are derived based on the analytical solutions of the Laplace's equation. For cloaks with irregular shapes, the material parameters of the transformation medium are determined numerically by solving the Laplace's equation. Full-wave simulations based on the Maxwell's equations validate the designed cloaks. The proposed method can be easily extended to design other transformation materials for electromagnetic and acoustic wave phenomena. PMID:19188959
Papamichael, K.; Beltran, L.
1993-04-01
A new method to simulate the daylight performance of fenestration systems and spaces is presented. This new method, named IDC (Integration of Directional Coefficients), allows the simulation of the daylight performance of fenestration systems and spaces of arbitrary complexity, under any sun, sky, and ground conditions. The IDC method is based on the combination of scale model photometry and computer-based simulation. Physical scale models are used to experimentally determine a comprehensive set of 'directional illuminance coefficients' at reference points of interest, which are then used in analytical, computer-based routines, to determine daylight factors or actual daylight illuminance values under any sun, sky, and ground conditions. The main advantage of the IDC method is its applicability to any optically complex environment. Moreover, the computer-based analytical routines are fast enough to allow for hourly simulation of the daylight performance over the course of an entire year. However, the method requires appropriate experimental facilities for the determination of the Directional Coefficients. The IDC method has been implemented and used successfully in inter-validation procedures with various daylight simulation computer programs. Currently, it is used to simulate the daylight performance of fenestration systems that incorporate optically complex components, such as Venetian blinds, optically treated light shelves and light pipes.
Design Numerical Method for Nonsingular Invisibility Cloak-Carpet with Arbitrary Shapes
V.I. Vyunnik; A.A. Zvyagintsev
2012-01-01
The using of the nonsingular invisibility cloak similarly as invisibility carpet was proposed. The possibility of fully numerical approach to calculation arbitrary nonsingular invisibility cloak, by a choice of elliptic coordinate system during coordinate transformation, was shown. The numerical modeling nonsingular cloak and cloak-carpet of arbitrary form and the estimation of efficiency while using, was completed.
Design Numerical Method for Nonsingular Invisibility Cloak-Carpet with Arbitrary Shapes
V. I. Vyunnik
2012-11-01
Full Text Available The using of the nonsingular invisibility cloak similarly as invisibility carpet was proposed. The possibility of fully numerical approach to calculation arbitrary nonsingular invisibility cloak, by a choice of elliptic coordinate system during coordinate transformation, was shown. The numerical modeling nonsingular cloak and cloak-carpet of arbitrary form and the estimation of efficiency while using, was completed.
Ayzatsky, M I
2016-01-01
We present the short description of the methods for calculation of the coupling coefficients in the Coupling Cavity Model of arbitrary chain of resonators. In the first part the procedure that is based on the Mode Matching Method is given. Then we present the new method that used only one eigen vector.
Vibration analysis of pipelines with arbitrary branches by absorbing transfer matrix method
Liu, Gongmin; Li, Shuaijun; Li, Yanhua; Chen, Hao
2013-11-01
Branched pipes of arbitrary shapes are prevalent in pipe systems. Considering fluid-structure interaction (FSI), an absorbing transfer matrix method in frequency domain for fluid-filled pipelines with any branched pipes is proposed in this paper. A dominant chain of pipeline would be selected, and the point transfer matrix of each junction on the dominant chain would be determined. Here, the point transfer matrix, representing the influence of branched pipes at the junction on the dominant pipeline, was "absorbed" by the dominant chain. Based on these, with transfer matrixes of other elements, the fluid and structure dynamics problem could be solved following the chain transfer matrix method process. Several numerical examples with different constraints are presented to illustrate the application of the proposed method. Moreover, the experiment of cross-shaped pipes with various boundary conditions was carried out. And results from the present approach were validated by measured and numerical data. Then, the forced vibrations of branched pipes were analyzed by considering the effects of various parameters, which shows the fluid pressure and vibrations can be optimized by changing the branch angles and positions. Through these examples, it is shown that the proposed method is efficient and can be used to calculate branched pipes of any shape.
SZOPOS, E.
2012-05-01
Full Text Available This paper presents an iterative method for designing FIR filters that implement arbitrary magnitude characteristics, defined by the user through a set of frequency-magnitude points (frequency samples. The proposed method is based on the non-uniform frequency sampling algorithm. For each iteration a new set of frequency samples is generated, by processing the set used in the previous run; this implies changing the samples location around the previous frequency values and adjusting their magnitude through interpolation. If necessary, additional samples can be introduced, as well. After each iteration the magnitude characteristic of the resulting filter is determined by using the non-uniform DFT and compared with the required one; if the errors are larger than the acceptable levels (set by the user a new iteration is run; the length of the resulting filter and the values of its coefficients are also taken into consideration when deciding a re-run. To demonstrate the efficiency of the proposed method a tool for designing FIR filters that match human audiograms was implemented in LabVIEW. It was shown that the resulting filters have smaller coefficients than the standard one, and can also have lower order, while the errors remain relatively small.
A finite field method for calculating molecular polarizability tensors for arbitrary multipole rank.
Elking, Dennis M; Perera, Lalith; Duke, Robert; Darden, Thomas; Pedersen, Lee G
2011-11-30
A finite field method for calculating spherical tensor molecular polarizability tensors α(lm;l'm') = ∂Δ(lm)/∂ϕ(l'm')* by numerical derivatives of induced molecular multipole Δ(lm) with respect to gradients of electrostatic potential ϕ(l'm')* is described for arbitrary multipole ranks l and l'. Interconversion formulae for transforming multipole moments and polarizability tensors between spherical and traceless Cartesian tensor conventions are derived. As an example, molecular polarizability tensors up to the hexadecapole-hexadecapole level are calculated for water using the following ab initio methods: Hartree-Fock (HF), Becke three-parameter Lee-Yang-Parr exchange-correlation functional (B3LYP), Møller-Plesset perturbation theory up to second order (MP2), and Coupled Cluster theory with single and double excitations (CCSD). In addition, intermolecular electrostatic and polarization energies calculated by molecular multipoles and polarizability tensors are compared with ab initio reference values calculated by the Reduced Variation Space method for several randomly oriented small molecule dimers separated by a large distance. It is discussed how higher order molecular polarizability tensors can be used as a tool for testing and developing new polarization models for future force fields. PMID:21915883
Tsugio Fukuchi
2014-06-01
Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
Rancourt, D.G.; Ping, J.Y. (Ottawa-Carleton Inst. for Physics, Ottawa Univ., Ontario (Canada))
1991-05-01
We introduce a powerful approach for obtaining arbitrary-shape static hyperfine parameter distributions from thickness corrected Moessbauer spectra. The distributions are taken to be sums of Gaussian components and the corresponding spectra are shown analytically to be sums of Voigt lines. Three cases are worked out in detail for distributions of: (1) center shifts, (2) quadrupole splittings with linear coupling to center shifts, and (3) hyperfine fields with linear couplings to center shifts and quadrupole splittings. The domain of validity of our method is described, with particular attention given to recognizing the presence of dynamic effects. An application of hyperfine field distributions to the spectra of Fe-Ni alloys is given. In all cases, convergence is rapid and unambiguous with only two or three Gaussian components being needed for ideal fits. Adding more components does not destabilize the solution but only results in the same distribution and the same value sof all the parameters being obtained. Problems occurring with other methods are eliminated by design - given the intrinsic suitability of an expansion in terms of Gaussians. (orig.).
Method for measuring the entanglement of formation for arbitrary-dimensional pure states
Li, Ming; Fei, Shao-Ming
2012-01-01
Entanglement of formation is an important measure of quantum entanglement. We present an experimental way to measure the entanglement of formation for arbitrary dimensional pure states. The measurement only evolves local quantum mechanical observables.
Simulation of free airfoil vibrations in incompressible viscous flow – comparison of FEM and FVM
Sváček, P.; Horáček, Jaromír; Honzátko, R.; Kozel, K.
2012-01-01
Roč. 52, č. 6 (2012), s. 104-114. ISSN 1210-2709 R&D Projects: GA ČR(CZ) GAP101/11/0207 Institutional research plan: CEZ:AV0Z20760514 Keywords : laminar flow * finite volume method * finite element method * arbitrary Lagrangian-Eulerian method * nonlinear aeroelasticity Subject RIV: BI - Acoustics
Real-time arbitrary view synthesis method for ultra-HD auto-stereoscopic display
Cai, Yuanfa; Sang, Xinzhu; Duo, Chen; Zhao, Tianqi; Fan, Xin; Guo, Nan; Yu, Xunbo; Yan, Binbin
2013-08-01
An arbitrary view synthesis method from 2D-Plus-Depth image for real-time auto-stereoscopic display is presented. Traditional methods use depth image based rendering (DIBR) technology, which is a process of synthesizing "virtual" views of a scene from still or moving images and associated per-pixel depth information. All the virtual view images are generated and then the ultimate stereo-image is synthesized. DIBR can greatly decrease the number of reference images and is flexible and efficient as the depth images are used. However it causes some problems such as the appearance of holes in the rendered image, and the occurrence of depth discontinuity on the surface of the object at virtual image plane. Here, reversed disparity shift pixel rendering is used to generate the stereo-image directly, and the target image won't generate holes. To avoid duplication of calculation and also to be able to match with any specific three-dimensional display, a selecting table is designed to pick up appropriate virtual viewpoints for auto-stereoscopic display. According to the selecting table, only sub-pixels of the appropriate virtual viewpoints are calculated, so calculation amount is independent of the number of virtual viewpoints. In addition, 3D image warping technology is used to translate depth information to parallax between virtual viewpoints and parallax, and the viewer can adjust the zero-parallax-setting-plane (ZPS) and change parallax conveniently to suit his/her personal preferences. The proposed method is implemented with OPENGL and demonstrated on a laptop computer with a 2.3 GHz Intel Core i5 CPU and NVIDA GeForce GT540m GPU. We got a frame rate 30 frames per second with 4096×2340 video. High synthesis efficiency and good stereoscopic sense can be obtained. The presented method can meet the requirements of real-time ultra-HD super multi-view auto-stereoscopic display.
Manzini, Gianmarco [Los Alamos National Laboratory
2012-07-13
We develop and analyze a new family of virtual element methods on unstructured polygonal meshes for the diffusion problem in primal form, that use arbitrarily regular discrete spaces V{sub h} {contained_in} C{sup {alpha}} {element_of} N. The degrees of freedom are (a) solution and derivative values of various degree at suitable nodes and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived. The connection with the Mimetic Finite Difference method is also discussed. Numerical experiments confirm the convergence rate that is expected from the theory.
On numerical solution of compressible flow in time-dependent domains
Feistauer, M.; Horáček, Jaromír; Kučera, V.; Prokopová, Jaroslava
2012-01-01
Roč. 137, č. 1 (2012), s. 1-16. ISSN 0862-7959 R&D Projects: GA MŠk OC09019 Institutional research plan: CEZ:AV0Z20760514 Keywords : compressible Navier-Stokes equations * arbitrary Lagrangian -Eulerian method * discontinuous Galerkin finite element method * interior and boundary penalty Subject RIV: BI - Acoustics
Second order multidimensional sign-preserving remapping for ALE methods
Hill, Ryan N [Los Alamos National Laboratory; Szmelter, J. [LOUGHBOROUGH UNIV.
2010-12-15
A second-order conservative sign-preserving remapping scheme for Arbitrary Lagrangian-Eulerian (ALE) methods is developed utilising concepts of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The algorithm is inherently multidimensional, and so does not introduce splitting errors. The remapping is implemented in a two-dimensional, finite element ALE solver employing staggered quadrilateral meshes. The MPDATA remapping uses a finite volume discretization developed for volume coordinates. It is applied for the remapping of density and internal energy arranged as cell centered, and velocity as nodal, dependent variables. In the paper, the advection of scalar fields is examined first for test cases with prescribed mesh movement. A direct comparison of MPDATA with the performance of the van Leer MUSCL scheme indicates advantages of a multidimensional approach. Furthermore, distinctly different performance between basic MPDATA and the infinite gauge option is illustrated using benchmarks involving transport of a sign changing velocity field. Further development extends the application of MPDATA remapping to the full ALE solver with a staggered mesh arrangement for density, internal energy and momentum using volume coordinates. At present, two options of the algorithm - basic and infinite gauge - are implemented. To ensure a meaningful assessment, an identical Lagrangian solver and computational mesh update routines are used with either MPDATA or van Leer MUSCL remapping. The evaluation places particular focus on the abilities of both schemes to accurately model multidimensional problems. Theoretical considerations are supported with numerical examples. In addition to the prescribed mesh movement cases for advection of scalars, the demonstrations include two-dimensional Eulerian and ALE flow simulations on quadrilateral meshes with both fixed and variable timestep control. The key comparisons include the standard test cases of Sod and Noh
A Nonconforming Arbitrary Quadrilateral Finite Element Method for Approximating Maxwell's Equations
Dongyang Shi; Lifang Pei; Shaochun Chen
2007-01-01
The main aim of this paper is to provide convergence analysis of Quasi-Wilson nonconforming finite element to Maxwell's equations under arbitrary quadrilateral meshes. The error estimates are derived, which are the same as those for conforming elements under conventional regular meshes.
SALE-3D, 3-D Fluid Flow, Navier Stokes Equation Using Lagrangian or Eulerian Method
1 - Description of problem or function: SALE-3D calculates three- dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a three-dimensional network of arbitrarily shaped, six-sided deformable cells, and a variety of user-selectable boundary conditions are provided in the program. 2 - Method of solution: SALE3D uses an ICED-ALE technique, which combines the ICE method of treating flow speeds and the ALE mesh treatment to calculate three-dimensional fluid flow. The finite- difference approximations to the conservation of mass, momentum, and specific internal energy differential equations are solved in a sequence of time steps on a network of deformable computational cells. The basic hydrodynamic part of each cycle is divided into three phases: (1) an explicit solution of the Lagrangian equations of motion updating the velocity field by the effects of all forces, (2) an implicit calculation using Newton-Raphson iterative scheme that provides time-advanced pressures and velocities, and (3) the addition of advective contributions for runs that are Eulerian or contain some relative motion of grid and fluid. A powerful feature of this three-phases approach is the ease with which
M. A. Sharaf; M. A. Banajh; A. A. Alshaary
2007-03-01
In this paper, an efficient iterative method of arbitrary integer order of convergence ≥ 2 has been established for solving the hyperbolic form of Kepler’s equation. The method is of a dynamic nature in the sense that, moving from one iterative scheme to the subsequent one, only additional instruction is needed. Most importantly, the method does not need any prior knowledge of the initial guess. A property which avoids the critical situations between divergent and very slow convergent solutions that may exist in other numerical methods which depend on initial guess. Computational Package for digital implementation of the method is given and is applied to many case studies.
Dong Tang
2016-01-01
Full Text Available An analytical procedure for free vibration analysis of circular cylindrical shells with arbitrary boundary conditions is developed with the employment of the method of reverberation-ray matrix. Based on the Flügge thin shell theory, the equations of motion are solved and exact solutions of the traveling wave form along the axial direction and the standing wave form along the circumferential direction are obtained. With such a unidirectional traveling wave form solution, the method of reverberation-ray matrix is introduced to derive a unified and compact form of equation for natural frequencies of circular cylindrical shells with arbitrary boundary conditions. The exact frequency parameters obtained in this paper are validated by comparing with those given by other researchers. The effects of the elastic restraints on the frequency parameters are examined in detail and some novel and useful conclusions are achieved.
Design Method for Electromagnetic Cloak with Arbitrary Shapes Based on Laplace's Equation
Hu, Jin; Zhou, Xiaoming; Hu, Gengkai
2008-01-01
In transformation optics, the space transformation is viewed as the deformation of a material. The permittivity and permeability tensors in the transformed space are found to correlate with the deformation field of the material. By solving the Laplace's equation, which describes how the material will deform during a transformation, we can design electromagnetic cloaks with arbitrary shapes if the boundary conditions of the cloak are considered. As examples, the material parameters of the sphe...
SALE-2D, 2-D Fluid Flow, Navier Stokes Equation Using Lagrangian or Eulerian Method
1 - Description of problem or function: SALE2D calculates two- dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a two-dimensional network of quadrilateral cells for either cylindrical or Cartesian coordinates, and a variety of user-selectable boundary conditions are provided in the program. 2 - Method of solution: The basic hydrodynamic part of each cycle of SALE is divided into three phases. Phase 1 is a typical explicit Lagrangian calculation in which the velocity field is updated by the effects of all forces. Phase 2 is a Newton-Raphson iteration that provides time-advanced pressures and velocities. It is used for calculations in the low-speed and even completely incompressible regimes. Phase 3 performs all the advective flux calculations. It is required for runs that are Eulerian or contain some other form of mesh rezoning. A powerful feature of SALE is the ease with which different phases can be combined to suit the requirements of individual problems
Preece, D.S.; Weatherby, J.R.; Attaway, S.W.; Swegle, J.W.; Matalucci, R.V.
1998-06-01
Coupled blast-structural computational simulations using supercomputer capabilities will significantly advance the understanding of how complex structures respond under dynamic loads caused by explosives and earthquakes, an understanding with application to the surety of both federal and nonfederal buildings. Simulation of the effects of explosives on structures is a challenge because the explosive response can best be simulated using Eulerian computational techniques and structural behavior is best modeled using Lagrangian methods. Due to the different methodologies of the two computational techniques and code architecture requirements, they are usually implemented in different computer programs. Explosive and structure modeling in two different codes make it difficult or next to impossible to do coupled explosive/structure interaction simulations. Sandia National Laboratories has developed two techniques for solving this problem. The first is called Smoothed Particle Hydrodynamics (SPH), a relatively new gridless method comparable to Eulerian, that is especially suited for treating liquids and gases such as those produced by an explosive. The SPH capability has been fully implemented into the transient dynamics finite element (Lagrangian) codes PRONTO-2D and -3D. A PRONTO-3D/SPH simulation of the effect of a blast on a protective-wall barrier is presented in this paper. The second technique employed at Sandia National Laboratories uses a relatively new code called ALEGRA which is an ALE (Arbitrary Lagrangian-Eulerian) wave code with specific emphasis on large deformation and shock propagation. ALEGRA is capable of solving many shock-wave physics problems but it is especially suited for modeling problems involving the interaction of decoupled explosives with structures.
Stephen Phillips
2013-09-01
Full Text Available States have international obligations to ensure that all deprivations of an individual’s liberty are consistent with international human rights law. The majority of provisions in the international human rights law instruments that deal with such deprivations of liberty contain the term ‘arbitrary’, yet there is no clear definition of what this entails. Arbitrariness is defined differently by different supervisory bodies in different cases, and in different contexts; understanding it requires awareness of the different factors affecting how individual deprivations of liberty are examined and understood.A longer version of this article can be found at:http://tinyurl.com/HRD-arbitrary-August2013
Hill, Peter; Dudson, Ben
2016-01-01
We present a technique for handling Dirichlet boundary conditions with the Flux Coordinate Independent (FCI) parallel derivative operator with arbitrary-shaped material geometry in general 3D magnetic fields. The FCI method constructs a finite difference scheme for $\
Stephen Phillips
2013-01-01
States have international obligations to ensure that all deprivations of an individual’s liberty are consistent with international human rights law. The majority of provisions in the international human rights law instruments that deal with such deprivations of liberty contain the term ‘arbitrary’, yet there is no clear definition of what this entails. Arbitrariness is defined differently by different supervisory bodies in different cases, and in different contexts; understanding it requires ...
Shibukawa, Atsushi; Okamoto, Atsushi; Takabayashi, Masanori; Tomita, Akihisa
2014-02-24
We propose a spatial cross modulation method using a random diffuser and a phase-only spatial light modulator (SLM), by which arbitrary complex-amplitude fields can be generated with higher spatial resolution and diffraction efficiency than off-axis and double-phase computer-generated holograms. Our method encodes the original complex object as a phase-only diffusion image by scattering the complex object using a random diffuser. In addition, all incoming light to the SLM is consumed for a single diffraction order, making a diffraction efficiency of more than 90% possible. This method can be applied for holographic data storage, three-dimensional displays, and other such applications. PMID:24663718
A variationaly consistent finite element formulation for constrained problems free from shear or membrane locking is applied to axisymetric shells subjected to arbitrary loading. The governing equations are writen according to Love's classical theory for a problem of bending of axisymetric thin and moderately thick shells accounting for shear deformation. The mixed variational formulation, in terms of stresses and displacements here presented consists of classical Galerkin method plus mesh-dependent least-square type terms employed with equal-order finite element polynomials. The additional terms enhance stability and accuracy of the original Galerkin method, as already proven theoretically and confirmed trough numerical experiments. Numerical results of some examples are presented to demonstrate the good stability and accuracy of the formulation. (author)
Mejlbro, Leif
1997-01-01
An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians....
The ordinary least-square fitting with polynomial is used in both the dynamic phase of the watt balance method and the weighting phase of joule balance method but few researches have been conducted to evaluate the uncertainty of the fitting data in the electrical balance methods. In this paper, a matrix-calculation method for evaluating the uncertainty of the polynomial fitting data is derived and the properties of this method are studied by simulation. Based on this, another two derived methods are proposed. One is used to find the optimal fitting order for the watt or joule balance methods. Accuracy and effective factors of this method are experimented with simulations. The other is used to evaluate the uncertainty of the integral of the fitting data for joule balance, which is demonstrated with an experiment from the NIM-1 joule balance. (paper)
TEMPELS, Heat Conduction for Arbitrary Geometry by Finite Element Method (FEM)
1 - Description of problem or function: Simultaneous temperature and stress analysis in solids of a axisymmetric shape, subject to thermal and mechanical loading, used for fuel elements with fuel - cladding interaction. 2 - Method of solution: The finite-element body of revolution method in two dimensions is applied, using linear triangular finite elements with nodes at the vertices. The same procedure is used both for temperature and structural computation, and sets of linear equations are obtained to be solved by an iterative method
Jeromen, Andrej; Grabec, Igor; Govekar, Edvard
2015-01-01
A laser pulse transient method for measuring normal spectral emissivity is described. In this method, a laser pulse (l=1064 nm) irradiates the top surface of a flat specimen. A two-dimensional temperature response of the bottom surface is measured with a calibrated thermographic camera. By solving an axisymmetric boundary value heat conduction problem, the normal spectral emissivity at 1064 nm is determined by using an iterative nonlinear least-squares estimation procedure. The method can be ...
This paper describes the development of two optimal discontinuous finite element (FE) Riemann methods and their application to the one-speed Boltzmann transport equation in the steady-state. The proposed methods optimise the amount of dissipation applied in the streamline direction. This dissipation is applied within an element using a novel Riemann FE method, which is based on an analogy between control volume discretisation methods and finite element methods when integration by parts is applied to the transport terms. In one-dimension the optimal finite element solutions match the analytical solution exactly at each outlet node. Both schemes couple elements in space via a Riemann approach. The first of the two schemes is a Petrov-Galerkin (PG) method which introduces dissipation via the equation residual. The second scheme uses a streamline diffusion stabilisation term in the discretisation. These two methods provide a discontinuous Petrov-Galerkin (DPG) scheme that can stabilise an element across the full range of radiation regimes, obtaining robust solutions with suppressed oscillation. Three basis functions in angle of particle travel have been implemented in an optimal DPG Riemann solver, which include the PN (spherical harmonic), SN (discrete ordinate) and LWN (linear octahedral wavelet) angular expansions. These methods are applied to a series of demanding two-dimensional radiation transport problems
Zhou Qi
2012-01-01
To a large degree,language is arbitrary. But there are exceptions to prove that language is not always arbitrary. However,non-arbitrariness is itself inevitably arbitrary. In fact,arbitrariness and non-arbitrariness work together to complete a language. It seems that they contradict to each other, but they actually coexist as a whole in the same unity.
Neutron spectra have been measured by the foil-activation method in 13 different environments in and around the Sandia Pulsed Reactor, the White Sands Missile Range Fast Burst Reactor, and the Sandia Annular Core Research Reactor. The spectra were obtained by using the SANDII code in a manner that was not dependent on the initial trial. This altered technique is better suited for the determination of spectra in environments that are difficult to predict by calculation, and it tends to reveal features that may be biased out by the use of standard trial-dependent methods. For some of the configurations, studies have also been made of how well the solution is determined in each energy region. The experimental methods and the techniques used in the analyses are thoroughly explained. 34 refs., 51 figs., 40 tabs
Digital Penalized LMS method for filter synthesis with arbitrary constraints and noise
A new method to calculate optimum digital filters for applicative fields requiring high resolution measurements, such as nuclear spectroscopy, is presented. This method easily works in experimental measurement setups, as optimum filter is synthesized with regard to the assigned time and frequency domain constraints (e.g. finite duration, flat top, peaking time, zero area, etc.) and by taking into account the real environmental noise or disturbance present in the system and identified from data sets of straightforward signal acquisitions. The method is fully developed and compared with other state of the art techniques for synthesis of optimized numerical filters. It can be easily implemented into DSP based processors and can be used as a tool to optimize the digital filter section of reconfigurable processing setups
The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative transfer
In this paper the weighted-sum-of-gray-gases approach for radiative transfer in non-gray participating media, first developed by Hottel in the context of the zonal method, has been shown to be applicable to the general radiative equation of transfer. Within the limits of the weighted-sum-of-gray-gases model (non-scattering media within a black-walled enclosure) any non-gray radiation problem can be solved by any desired solution method after replacing the medium by an equivalent small number of gray media with constant absorption coefficients. Some examples are presented for isothermal media and media at radiative equilibrium, using the exact integral equations as well as the popular P-1 approximation of the equivalent gray media solution. The results demonstrate the equivalency of the method with the quadrature of spectral results, as well as the tremendous computer times savings (by a minimum of 95%) which are achieved
Sozer, Emre; Brehm, Christoph; Kiris, Cetin C.
2014-01-01
A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable properties
An Efficient ICT Method for Analysis of Co-planar Dipole Antenna Arrays of Arbitrary Lengths
Imoro, Adam Icarus; Aoki, Ippo; Inagaki, Naoki; Kikuma, Nobuyoshi; キクマ, ノブヨシ; 菊間, 信良
1998-01-01
A more judicious choice of trial functions to implement the Improved Circuit Theory (ICT) application to multi-element antennas is achieved. These new trial functions, based on Tai's modified variational implementation for single element antennas, leads to an ICT implementation applicable to much longer co-planar dipole arrays. The accuracy of the generalized impedance formulas is in good agreement with the method of moments. Moreover, all these generalized formulas including the radiation pa...
Arbitrary pattern fabrication with a LCD reticle-free exposure method
Morimoto, Tatsuo; Nakamura, Kazumitsu; Kubota, Hiroshi; Nakada, Akira; Akamichi, Takayuki; Inokuchi, Tsuneo; Kosaka, Kouji
2003-08-01
We describe a newly developed technique that uses optical projection lithography with a liquid crystal display (LCD) in place of a conventional reticle, in order to minimize turn-around-time and production cost. Circuit pattern data, generated by a computer aided design (CAD) system, is transferred directly to a control computer. The control computer converts the data into an equivalent dot matrix representation of the design for use on a LCD. The LCD is placed in a conventional optical stepper. One feature of this system is the simplicity of the data management scheme which permits the data to be handled by a computer file directly; without any of the manual assistance normally needed in conventional reticle fabrication. It is a very convenient method to reverse reticle tone by changing the LCD mode; easy compared to a conventional reticle manufacturing process. The minimum resolution of this proposed system is very similar to conventional systems that use optical reticles. We have demonstrated that this LCD Reticle-Free Exposure Method has the potential of replacing conventional reticles in optical stepper lithography. This method is applicable for manufacturing devices with relatively large fabrication rules and low production quantities, such as System-in-Package applications.
Acousto-optics bandwidth broadening in a Bragg cell based on arbitrary synthesized signal methods.
Peled, Itay; Kaminsky, Ron; Kotler, Zvi
2015-06-01
In this work, we present the advantages of driving a multichannel acousto-optical deflector (AOD) with a digitally synthesized multifrequency RF signal. We demonstrate a significant bandwidth broadening of ∼40% by providing well-tuned phase control of the array transducers. Moreover, using a multifrequency, complex signal, we manage to suppress the harmonic deflections and return most of the spurious energy to the main beam. This method allows us to operate the AOD with more than an octave of bandwidth with negligible spurious energy going to the harmonic beams and a total bandwidth broadening of over 70%. PMID:26192666
Use of the foil activation method with arbitrary trial functions to determine neutron energy spectra
Neutron Spectra have been measured by the foil activation method in thirteen different environments in and around the Sandia Pulsed Reactor (SPR-III), the White Sands Missile Range FBR, and the Annular Core Research Reactor (ACRR). The unfolded spectra were obtained by using the SANDII code in a manner which was not dependent on the initial trial. This altered technique is, therefore, better suited for the determination of spectra in environments that are difficult to predict by calculation, and it tends to reveal features that may be biased out by the use of standard trial functions
Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics
Maire, Pierre-Henri; Nkonga, Boniface
2009-02-01
This work presents a multi-dimensional cell-centered unstructured finite volume scheme for the solution of multimaterial compressible fluid flows written in the Lagrangian formalism. This formulation is considered in the Arbitrary-Lagrangian-Eulerian (ALE) framework with the constraint that the mesh velocity and the fluid velocity coincide. The link between the vertex velocity and the fluid motion is obtained by a formulation of the momentum conservation on a class of multi-scale encased volumes around mesh vertices. The vertex velocity is derived with a nodal Riemann solver constructed in such a way that the mesh motion and the face fluxes are compatible. Finally, the resulting scheme conserves both momentum and total energy and, it satisfies a semi-discrete entropy inequality. The numerical results obtained for some classical 2D and 3D hydrodynamic test cases show the robustness and the accuracy of the proposed algorithm.
MacAlpine, Sara; Deline, Chris
2015-09-15
It is often difficult to model the effects of partial shading conditions on PV array performance, as shade losses are nonlinear and depend heavily on a system's particular configuration. This work describes and implements a simple method for modeling shade loss: a database of shade impact results (loss percentages), generated using a validated, detailed simulation tool and encompassing a wide variety of shading scenarios. The database is intended to predict shading losses in crystalline silicon PV arrays and is accessed using basic inputs generally available in any PV simulation tool. Performance predictions using the database are within 1-2% of measured data for several partially shaded PV systems, and within 1% of those predicted by the full, detailed simulation tool on an annual basis. The shade loss database shows potential to considerably improve performance prediction for partially shaded PV systems.
A method for the solution of arbitrary bosonic and fermionic many-particle systems
In the present dissertation different classes of quantum mechanical many body systems are investigated numerically and analytically considering symmetries in the formalism of second quantization. All algebraic ideas which are neccessary to develop a numerical computer code which is able to calculate the eigenvalues and eigenstates of a very general quantum many body hamiltonian are explained. The two most crucial problems are branching rules and the calculation of isoscalar factors. Methods are presented to solve these problems numerically for the general case. The most important point is the calculation of isoscalar factors with a nonrecursive method and without any numerical error. All presented ideas were implemented in the program '' ArbModel''. With this very flexible computer code at hand, systems of identical particles were investigated in general. General formulas were derived for the presence of dynamical symmetry. Weaker conditions are neccessary for the conservation of the so called seniority quantum number. This situation is called partial dynamical symmetry. These conditions were investigated in detail. Althouth other authors have previously investigated this problem, some new cases were discovered and new conditions could be derived. Most surprisingly, cases were found in which the seniority quantum number is generally broken except for some specific states. These states are solvable and formulae for their energies are presented. All analytically derived results were checked with ''ArbModel''. As further applications for the code, two selected models with distinguishable particles are investigated. The predictions of a very new theory, which connects quantum phase transitions and exceptional points, are verified with the sd-Interacting-Boson-Model 1 (sd-IBM1) and a very high particle number. For the Interacting-Boson-Fermion-Model a selected dynamical symmetry was investigated. The branching rules for this Bose-Fermi-Symmetry were calculated in detail
High-Order Moving Overlapping Grid Methodology in a Spectral Element Method
Merrill, Brandon E.
A moving overlapping mesh methodology that achieves spectral accuracy in space and up to second-order accuracy in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The targeted applications are in aerospace and mechanical engineering domains and involve problems in turbomachinery, rotary aircrafts, wind turbines and others. The methodology is built within the dual-session communication framework initially developed for stationary overlapping meshes. The methodology employs semi-implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. Mesh movement is enabled through the Arbitrary Lagrangian-Eulerian formulation of the governing equations, which allows for prescription of arbitrary velocity values at discrete mesh points. The stationary and moving overlapping mesh methodologies are thoroughly validated using two- and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal global convergence, for both methods, is documented and is in agreement with the nominal order of accuracy of the underlying solver. Stationary overlapping mesh methodology was validated to assess the influence of long integration times and inflow-outflow global boundary conditions on the performance. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics are validated against the available data. Moving overlapping mesh simulations are validated on the problems of two-dimensional oscillating cylinder and a three-dimensional rotating sphere. The aerodynamic forces acting on these moving rigid bodies are determined, and all results are compared with published data. Scaling tests, with both methodologies
Desforges, Jean; Deschamps, Clément; Gauvin, Serge
2015-08-01
The determination of the complex refractive index of thin films usually requires the highest accuracy. In this paper, we report on a new and accurate method based on a spectral rectifying process of a single transmittance curve. The agreements with simulated and real experimental data show the helpfulness of the method. The case of materials having arbitrary absorption bands at midpoint in spectral range, such as pigments in guest-host polymers, is also encompassed by this method.
Stein, David B.; Guy, Robert D.; Thomases, Becca
2016-01-01
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit-explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems.
Kovács, Balázs; Guerra, Christian Andreas Power
2014-01-01
A linear evolving surface partial differential equation is first discretized in space by an arbitrary Lagrangian Eulerian (ALE) evolving surface finite element method, and then in time either by a Runge-Kutta method, or by a backward difference formula. The ALE technique allows to maintain the mesh regularity during the time integration, which is not possible in the original evolving surface finite element method. Unconditional stability and optimal order convergence of the full discretizatio...
Sváček, P.; Horáček, Jaromír
2012-01-01
Roč. 12, č. 3 (2012), s. 789-806. ISSN 1815-2406 R&D Projects: GA MŠk OC09019; GA ČR(CZ) GAP101/11/0207 Institutional research plan: CEZ:AV0Z20760514 Keywords : finite element method * arbitrary Lagrangian -Eulerian method * biomechanics of voice production Subject RIV: BI - Acoustics Impact factor: 1.863, year: 2012 http://www.global-sci.com/
Wick, Thomas
2011-01-01
In this work, we apply a fluid-structure interaction method to a long axis heart valve simulation. Our method of choice is based on a monolithic coupling scheme for fluid-structure interaction, where the fluid equations are rewritten in the arbitrary Lagrangian Eulerian' framework. To prevent back-flow of waves in the structure due to its hyperbolic nature, a damped structure equation is solved on an artificial layer that prolongates the computational domain. This coupling is stable on th...
Dawes, Alan Sidney [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Malone, Christopher M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-07-07
In this report a number of new verification test problems for multimaterial diffusion will be shown. Using them we will show that homogenization of multimaterial cells in either Arbitrary Lagrangian Eulerian (ALE) or Eulerian simulations can lead to errors in the energy flow at the interfaces. Results will be presented that show that significant improvements and predictive capability can be gained by using either a surrogate supermesh, such as Thin Mesh in FLAG, or the emerging method based on Static Condensation.
Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.
2006-11-01
The simulation of biological systems by means of current empirical force fields presents shortcomings due to their lack of accuracy, especially in the description of the nonbonded terms. We have previously introduced a force field based on density fitting termed the Gaussian electrostatic model-0 (GEM-0) J.-P. Piquemal et al. [J. Chem. Phys. 124, 104101 (2006)] that improves the description of the nonbonded interactions. GEM-0 relies on density fitting methodology to reproduce each contribution of the constrained space orbital variation (CSOV) energy decomposition scheme, by expanding the electronic density of the molecule in s-type Gaussian functions centered at specific sites. In the present contribution we extend the Coulomb and exchange components of the force field to auxiliary basis sets of arbitrary angular momentum. Since the basis functions with higher angular momentum have directionality, a reference molecular frame (local frame) formalism is employed for the rotation of the fitted expansion coefficients. In all cases the intermolecular interaction energies are calculated by means of Hermite Gaussian functions using the McMurchie-Davidson [J. Comput. Phys. 26, 218 (1978)] recursion to calculate all the required integrals. Furthermore, the use of Hermite Gaussian functions allows a point multipole decomposition determination at each expansion site. Additionally, the issue of computational speed is investigated by reciprocal space based formalisms which include the particle mesh Ewald (PME) and fast Fourier-Poisson (FFP) methods. Frozen-core (Coulomb and exchange-repulsion) intermolecular interaction results for ten stationary points on the water dimer potential-energy surface, as well as a one-dimensional surface scan for the canonical water dimer, formamide, stacked benzene, and benzene water dimers, are presented. All results show reasonable agreement with the corresponding CSOV calculated reference contributions, around 0.1 and 0.15kcal/mol error for
Arbitrary shape surface Fresnel diffraction
Shimobaba, Tomoyoshi; Masuda, Nobuyuki; Ito, Tomoyoshi
2012-01-01
Fresnel diffraction calculation on an arbitrary shape surface is proposed. This method is capable of calculating Fresnel diffraction from a source surface with an arbitrary shape to a planar destination surface. Although such calculation can be readily calculated by the direct integral of a diffraction calculation, the calculation cost is proportional to $O(N^2)$ in one dimensional or $O(N^4)$ in two dimensional cases, where $N$ is the number of sampling points. However, the calculation cost ...
A new 2D neutron transport code AutoMOC for arbitrary geometry has been developed. This code is based on the method of characteristics (MOCs) and the customization of AutoCAD. The MOC solves the neutron transport equation along characteristic lines. It is independent of the geometric shape of boundaries and regions. So theoretically, this method can be used to solve the neutron transport equation in highly complex geometries. However, it is important to describe the geometry and calculate intersection points of each characteristic line with every boundary and region in advance. In complex geometries, due to the complications of treating the arbitrary domain, the selection of geometric shapes and efficiency of ray tracing are generally limited. The geometry treatment through the customization of AutoCAD, a widely used computer-aided design software package, is given in this paper. Thanks to the powerful capability of AutoCAD, the description of arbitrary geometry becomes quite convenient. Moreover, with the language Visual Basic for Applications (VBAs), AutoCAD can be customized to carry out the ray tracing procedure with a high flexibility in geometry. The numerical results show that AutoMOC can solve 2D neutron transport problems in a complex geometry accurately and effectively
Mirela Kohr
2004-09-01
Full Text Available We study the low Reynolds number flow of an incompressible Newtonian fluid of infinite expanse past a cylinder of arbitrary cross section by using the method of matched asymptotic expansions. The analysis that will be made in this paper is equivalent to that developed by Power (1990 in order to solve the resulting inner (or Stokes problems with the completed double-layer boundary integral equation method (CDLBIEM due to Power and Miranda (1987. We will solve these problems by the boundary integral method developed by Hsiao and Kress (1985.
Arbitrary shape surface Fresnel diffraction.
Shimobaba, Tomoyoshi; Masuda, Nobuyuki; Ito, Tomoyoshi
2012-04-01
Fresnel diffraction calculation on an arbitrary shape surface is proposed. This method is capable of calculating Fresnel diffraction from a source surface with an arbitrary shape to a planar destination surface. Although such calculation can be readily calculated by the direct integral of a diffraction calculation, the calculation cost is proportional to O(N²) in one dimensional or O(N⁴) in two dimensional cases, where N is the number of sampling points. However, the calculation cost of the proposed method is O(N log N) in one dimensional or O(N² log N) in two dimensional cases using non-uniform fast Fourier transform. PMID:22513646
Arbitrary shape surface Fresnel diffraction
Shimobaba, Tomoyoshi; Ito, Tomoyoshi
2012-01-01
Fresnel diffraction calculation on an arbitrary shape surface is proposed. This method is capable of calculating Fresnel diffraction from a source surface with an arbitrary shape to a planar destination surface. Although such calculation can be readily calculated by the direct integral of a diffraction calculation, the calculation cost is proportional to $O(N^2)$ in one dimensional or $O(N^4)$ in two dimensional cases, where $N$ is the number of sampling points. However, the calculation cost of the proposed method is $O(N \\log N)$ in one dimensional or $O(N^2 \\log N)$ in two dimensional cases using non-uniform fast Fourier transform.
Bell inequalities for arbitrary situations
We present a simple way based on the joint global probability distribution to derive CHSH inequalities. Inspired by this derivation we develop a simple method that gives a set of conditions which are necessary for a model to be a local variable theory. This method generates candidate Bell inequalities for models of arbitrary situations in which there are an arbitrary number of particles, measurements and outcomes. With the help of a type of distribution it will be clear that all necessary conditions are Bell inequalities. This work gives a unified way to write Bell inequalities for arbitrary situations. - Highlights: • Constructing CHSH inequalities based on joint global probability distribution. • Constructing conditions which are necessary for a model to be local and realistic. • Bell inequalities for general situations
A Novel VOF-Type Volume-Tracking Method for Free-Surface Flows Based on Unstructured Triangular Mesh
JI Chun-ning; WANG Yuan-zhan; WANG Jian-feng
2005-01-01
A novel VOF-type volume-tracking method for two-dimensional free-surface flows based on the unstructured triangular mesh is presented. Owing to the inherent merit of the unstructured triangular mesh in fitting curved boundaries, this method can handle the free-surface problems with complex geometries accurately and directly, without introducing any complicated boundary treatment or artificial diffusion. The method solves the volume transport equation geometrically through the Modified Lagrangian-Eulerian Re-map (MLER) method, which is applied to advective fluid volumes. Moreover, the PLIC method is adopted to give a second-order reconstructed interface approximation. To validate this method, two advection tests were performed for the establishment of the accuracy and convergence rate of the solutions. Numerical results for these complex tests provide convincing evidence for the excellent solution quality and fidelity of the method.
This paper describes the ALICE-II analysis of and comparison with complex vessel experiments. Tests SM-2 through SM-5 were performed by SRI International in 1978 in studying the structural response of 1/20 scale models of the Clinch River Breeder Reactor to a simulated hypothetical core-disruptive accident. These experiments provided quality data for validating treatments of the nonlinear fluid-structure interactions and many complex excursion phenomena, such as flow through perforated structures, large material distortions, multi-dimensional sliding interfaces, flow around sharp corners, and highly contorted fluid boundaries. Correlations of the predicted pressures with the test results of all gauges are made. Wave characteristics and arrival times are also compared. Results show that the ALICE-II code predicts the pressure profile well. Despite the complexity, the code gave good results for the SM-5 test
An evaluation method of the neutron fluence and mean spectrum with which samples have been irradiated is proposed. The principle is based on measuring the change of the isotopic abundance ratios of arbitrary pairs of nuclides having different neutron absorption cross sections for both thermal and intermediate neutrons. Advantages of the method are as follows, although sensitivity is lower than that of the ordinary activation method in a short irradiation period. i) Any sample can be used irrespective of irradiation history. ii) Nuclides present as impurities in samples can be used as detectors. iii) Neutron fluences and mean spectra with which samples have been heavily irradiated can be measured with reasonable accuracy, thus making it possible to offer the direct information to radiation damage studies. The present study deals with the principle and applicability of the method. (author)
Analytic methods for ﬁeld induced tunneling in quantum wells with arbitrary potential proﬁles
S Panda; B K Panda
2001-06-01
Electric ﬁeld induced tunneling is studied in three different types of quantum wells by solving time-independent effective mass equation in analytic methods based on three different Airy function approaches. Comparison of different Airy function methods indicates that they are identical and connected to each other by the Breit–Wigner formula.
Wong, Michael K. W.; Summers, Randall M.; Petney, Sharon Joy Victor; Luchini, Christopher Bernard; Drake, Richard Roy; Carroll, Susan K.; Hensinger, David M.; Garasi, Christopher Joseph; Robinson, Allen Conrad; Voth, Thomas Eugene; Haill, Thomas A.; Mehlhorn, Thomas Alan; Robbins, Joshua H.; Brunner, Thomas A.
2005-01-01
ALEGRA is an arbitrary Lagrangian-Eulerian multi-material finite element code used for modeling solid dynamics problems involving large distortion and shock propagation. This document describes the basic user input language and instructions for using the software.
Garasi, Christopher Joseph; Haill, Thomas A.; Robinson, Allen Conrad
2003-11-01
ALEGRA is an arbitrary Lagrangian-Eulerian finite element code that emphasizes large distortion and shock propagation in inviscid fluids and solids. This document describes user options for modeling magnetohydrodynamic, thermal conduction, and radiation emission effects.
Garasi, Christopher Joseph; Cochrane, Kyle Robert; Mehlhorn, Thomas Alan; Haill, Thomas A.; Summers, Randall M.; Robinson, Allen Conrad
2005-01-01
ALEGRA is an arbitrary Lagrangian-Eulerian finite element code that emphasizes large distortion and shock propagation in inviscid fluids and solids. This document describes user options for modeling resistive magnetohydrodynamic, thermal conduction, and radiation emission effects.
Using a combination of Runge-Kutta and Jacobi iterative method, we could solve the nonlinear Schroedinger equation describing the pulse propagation in FBGs. By decomposing the electric field to forward and backward components in fiber Bragg grating and utilizing the Fourier series analysis technique, the boundary value problem of a set of coupled equations governing the pulse propagation in FBG changes to an initial condition coupled equations which can be solved by simple Runge-Kutta method.
Kasimov, Nurlybek; Brown-Dymkoski, Eric; Vasilyev, Oleg V.
2015-11-01
A novel volume penalization method to enforce immersed boundary conditions in Navier-Stokes and Euler equations is presented. Previously, Brinkman penalization has been used to introduce solid obstacles modeled as porous media, although it is limited to Dirichlet-type conditions on velocity and temperature. This method builds upon Brinkman penalization by allowing Neumann conditions to be applied in a general fashion. Correct boundary conditions are achieved through characteristic propagation into the thin layer inside of the obstacle. Inward pointing characteristics ensure nonphysical solution inside the obstacle does not propagate outside to the fluid. Dirichlet boundary conditions are enforced similarly to Brinkman method. Penalization parameters act on a much faster timescale than the characteristic timescale of the flow. Main advantage of the method is systematic means of the error control. This talk is focused on the progress that was made towards the extension of the method to the 3D flows around irregular shapes. This work was supported by ONR MURI on Soil Blast Modeling.
Bergrun, N. R.
1951-01-01
An empirical method for the determination of the area, rate, and distribution of water-drop impingement on airfoils of arbitrary section is presented. The procedure represents an initial step toward the development of a method which is generally applicable in the design of thermal ice-prevention equipment for airplane wing and tail surfaces. Results given by the proposed empirical method are expected to be sufficiently accurate for the purpose of heated-wing design, and can be obtained from a few numerical computations once the velocity distribution over the airfoil has been determined. The empirical method presented for incompressible flow is based on results of extensive water-drop. trajectory computations for five airfoil cases which consisted of 15-percent-thick airfoils encompassing a moderate lift-coefficient range. The differential equations pertaining to the paths of the drops were solved by a differential analyzer. The method developed for incompressible flow is extended to the calculation of area and rate of impingement on straight wings in subsonic compressible flow to indicate the probable effects of compressibility for airfoils at low subsonic Mach numbers.
Zuo Yan-Lei; Jiang Dong-Bin; Zhu Qi-Hua; Dong Jun; Zen Xiao-Ming; Huang Xiao-Jun; Huang Zheng
2012-01-01
We present a new method that can be used to calculate pulse-front distortion by measuring the spectral interference of two point-diffraction fields in their overlapped district.We demonstrate,for the first time,the measurement of the pulse-front distortion of the pulse from a complex multi-pass amplification system,which exists in almost all high-power laser systems,and obtain the irregular pulse-front distribution.The method presented does not need any reference light or assumption about the pulse-front distribution,and has an accuracy of several femtoseconds.
We inquire into spin and pseudospin symmetries of the Dirac equation under a Moebius square-type potential using the Nikiforov-Uvarov method to calculate the bound state solutions. We numerically discuss the problem and include various explanatory figures. (authors)
An efficient Method for Synthesizing the Arbitrary View of a Large-Scale Object in a Scene
Thin Lai Lai Thein
2012-09-01
Full Text Available A robust method for panorama view reconstruction from multiple viewpoints of the large-scale object is presented. The desired object must be acquired from multiple viewpoints. The information of the feature points of an object is obtained by establishing correspondence between views. We present a robust method based on image mosaicing approach and panorama synthesizing. First, the feature of each object is extracted. Then the corresponding feature points of an object between the images are estimated. The different of minimum threshold value between two images is computed. After that, the full-view of an object is reconstructed by integrating two images based on image mosaicing approach.This research describes how to establish feature correspondences between images accurately and effectively. Image registration technique provides an initial estimation for establishing feature correspondences of point features. The linear solution with the reliable correspondences makes the computation of the geometric transformation between two images, called homography.
Lamah, C. A.; Harris, W. L.
1983-01-01
A novel analytical-numerical method for calculating unsteady small disturbance transonic flow over airfoils has been developed. The method uses an extended integral equation technique, based on both the velocity potential and the acceleration potential, to predict unsteady aerodynamic loading on airfoils oscillating in subcritical transonic free stream conditions. The formulation is an extension of the work of Sivaneri and Harris (1980) for steady, non-lifting flows and utilizes the linear theory of Landahl (1961) for decoupling of steady and unsteady components. The analytical-numerical procedure involves several intnegrating schemes and applies to general frequencies of oscillations. The technique is illustrated by computing the transonic flow about parabolic arc airfoils. Specific unsteady results for reduced frequencies based on semi-chord of 0.01, 0.1, 0.3, 0.4 and 0.6 are given. Comparison of results with those obtained by an ADI finite difference scheme is made.
Mishra, SK
2012-01-01
In this paper we demonstrate that Pena’s method of construction of a synthetic indicator is very sensitive to the order in which the constituent variables (whose linear aggregation yields the synthetic indicator) are arranged. Since m number of constituent variables may be arranged in m-factorial ways, even a moderately large m can give rise to a very large number of synthetic indicators from which one cannot choose the one which best represents the constituent variables. Given that an analys...
Moiseev, N. Ya.; Silant'eva, I. Yu.
2008-07-01
An approach to the construction of second-and higher order accurate difference schemes in time and space is described for solving the linear one-and multidimensional advection equations with constant coefficients by the Godunov method with antidiffusion. The differential approximations for schemes of up to the fifth order are constructed and written. For multidimensional advection equations with constant coefficients, it is shown that Godunov schemes with splitting over spatial variables are preferable, since they have a smaller truncation error than schemes without splitting. The high resolution and efficiency of the difference schemes are demonstrated using test computations.
Xue, Kan-Hao; Miao, Xiang-Shui
2016-01-01
The LDA-1/2 method expands Slater's half occupation technique to infinite solid state materials by introducing a self-energy potential centered at the anions to cancel the energy associated with electron-hole self-interaction. To avoid an infinite summation of long-ranged self-energy potentials they must be trimmed at a variationally-defined cutoff radius. The method has been successful in predicting accurate band gaps for a large number of elementary and binary semiconductors. Nevertheless, there has been some confusion regarding carbon and silicon, both in the cubic diamond structure, which require different ionizations of the valence charge, 1/2 for carbon and 1/4 for silicon respectively, to yield band gaps in agreement with experimental data. We here analyze the spatial distribution of the valence electrons of these two materials to conclude that in silicon and in carbon LDA-1/4 and LDA-1/2, respectively, must be adopted for the proper cancellation of the self-energies. Such analysis should be applied to...
Arbitrary Spin Galilean Oscillator
Hagen, C R
2014-01-01
The so-called Dirac oscillator was proposed as a modification of the free Dirac equation which reproduces many of the properties of the simple harmonic oscillator but accompanied by a strong spin-orbit coupling term. It has yet to be extended successfully to the arbitrary spin S case primarily because of the unwieldiness of general spin Lorentz invariant wave equations. It is shown here using the formalism of totally symmetric multispinors that the Dirac oscillator can, however, be made to accommodate spin by incorporating it into the framework of Galilean relativity. This is done explicitly for spin zero and spin one as special cases of the arbitrary spin result. For the general case it is shown that the coefficient of the spin-orbit term has a 1/S behavior by techniques which are virtually identical to those employed in the derivation of the g-factor carried out over four decades ago.
Dynamic Deployment Simulations of Inflatable Space Structures
Wang, John T.
2005-01-01
The feasibility of using Control Volume (CV) method and the Arbitrary Lagrangian Eulerian (ALE) method in LSDYNA to simulate the dynamic deployment of inflatable space structures is investigated. The CV and ALE methods were used to predict the inflation deployments of three folded tube configurations. The CV method was found to be a simple and computationally efficient method that may be adequate for modeling slow inflation deployment sine the inertia of the inflation gas can be neglected. The ALE method was found to be very computationally intensive since it involves the solving of three conservative equations of fluid as well as dealing with complex fluid structure interactions.
Arbitrary laser beam propagation in free space
Arpali, Çağlar; Baykal, Yahya; Nakiboğlu, Cem
2009-08-01
The propagation of arbitrary laser beams in free space is examined. For this purpose, starting with an incident field of arbitrary field distribution, the intensity at the receiver plane is formulated via Huygens Fresnel diffraction integral. Arbitrary source field profile is produced by decomposing the source into incremental areas (pixels). The received field through the propagation in free space is found by superposing the contributions from all source incremental areas. The proposed method enables us to evaluate the received intensity originating from any type of source field. Using the arbitrary beam excitation, intensity of various laser beams such as cos-Gaussian, cosh-Gaussian, general type beams are checked to be consistent with the already existing results in literature, and the received intensity distributions are obtained for some original arbitrary beam field profiles. Our received intensity formulation for the arbitrary source field profiles presented in this paper can find application in optics communication links, reflection from rough surfaces, optical cryptography and optical imaging systems.
Two dimensional simulation of fluid-structure interaction in human vocal folds
Hasnedlová, J.; Feistauer, M.; Horáček, Jaromír; Kosík, A.; Kučera, V.
Pilsen : University of West Bohemia Pilsen, 2011 - (Adámek, V.; Zajíček, M.). s. 1-2 ISBN 978-80-261-0027-0. [Computational Mechanics 2011 /27./. 07.11.2011-09.11.2011, Plzeň] R&D Projects: GA ČR(CZ) GAP101/11/0207 Institutional research plan: CEZ:AV0Z20760514 Keywords : compressible Navier-Stokes equations * Arbitrary Lagrangian -Eulerian method * discontinuous Galerkin finite element method Subject RIV: BI - Acoustics
Computational fluid dynamic analysis of flutter characteristics for self-anchored suspension bridges
Zhiwen ZHU; Zhaoxiang WANG; Zhengqing CHEN
2008-01-01
This paper outlines the essentials and proce-dures of computational fluid dynamics (CFD) simulation applicable to evaluating flutter derivatives of bridge decks. An arbitrary Lagrangian-Eulerian (ALE) description of the flow around the moving rigid box girder combined with the finite volume discretization and multi-grid algorithm is pre-sented. The proposed methods are employed to identify flutter derivatives of the bridge deck of the Sanchaji Self-anchored Suspension Bridge. The results agree well with ones from wind tunnel tests. It demonstrates accuracy and efficiency of the present method.
Heinze, Stefan
2008-04-18
In the present dissertation different classes of quantum mechanical many body systems are investigated numerically and analytically considering symmetries in the formalism of second quantization. All algebraic ideas which are neccessary to develop a numerical computer code which is able to calculate the eigenvalues and eigenstates of a very general quantum many body hamiltonian are explained. The two most crucial problems are branching rules and the calculation of isoscalar factors. Methods are presented to solve these problems numerically for the general case. The most important point is the calculation of isoscalar factors with a nonrecursive method and without any numerical error. All presented ideas were implemented in the program '' ArbModel''. With this very flexible computer code at hand, systems of identical particles were investigated in general. General formulas were derived for the presence of dynamical symmetry. Weaker conditions are neccessary for the conservation of the so called seniority quantum number. This situation is called partial dynamical symmetry. These conditions were investigated in detail. Althouth other authors have previously investigated this problem, some new cases were discovered and new conditions could be derived. Most surprisingly, cases were found in which the seniority quantum number is generally broken except for some specific states. These states are solvable and formulae for their energies are presented. All analytically derived results were checked with ''ArbModel''. As further applications for the code, two selected models with distinguishable particles are investigated. The predictions of a very new theory, which connects quantum phase transitions and exceptional points, are verified with the sd-Interacting-Boson-Model 1 (sd-IBM1) and a very high particle number. For the Interacting-Boson-Fermion-Model a selected dynamical symmetry was investigated. The branching rules for this Bose
Simulation of a viscous fluid spreading by a bidimensional shallow water model
Di Martino, Bernard; Paoli, Jean-Martin; Simonnet, Pierre; 10.1016/j.apm.2011.01.015
2011-01-01
In this paper we propose a numerical method to solve the Cauchy problem based on the viscous shallow water equations in an horizontally moving domain. More precisely, we are interested in a flooding and drying model, used to modelize the overflow of a river or the intrusion of a tsunami on ground. We use a non conservative form of the two-dimensional shallow water equations, in eight velocity formulation and we build a numerical approximation, based on the Arbitrary Lagrangian Eulerian formulation, in order to compute the solution in the moving domain.
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.
Second-order sign-preserving conservative interpolation (remapping) on general grids
An accurate conservative interpolation (remapping) algorithm is an essential component of most arbitrary Lagrangian-Eulerian (ALE) methods. In this paper we describe a local remapping algorithm for a positive scalar function. This algorithm is second-order accurate, conservative, and sign preserving. The algorithm is based on estimating the mass exchanged between cells at their common interface, and so is equally applicable to structured and unstructured grids. We construct the algorithm in a series of steps, clearly delineating the assumptions and errors made at each step. We validate our theory with a suite of numerical examples, analyzing the results from the viewpoint of accuracy and order of convergence
Application of the VOF method based on unstructured quadrilateral mesh
JI Chun-ning; SHI Ying
2008-01-01
To simulate two-dimensional free-surface flows with complex boundaries directly and accurately, a novel VOF (Volume-of-fluid) method based on unstructured quadrilateral mesh is presented. Without introducing any complicated boundary treatment or artificial diffusion, this method treated curved boundaries directly by utilizing the inherent merit of unstructured mesh in fitting curves. The PLIC (Piecewise Linear Interface Calculation) method was adopted to obtain a second-order accurate linearized reconstruction approximation and the MLER (Modified Lagrangian-Eulerian Re-map) method was introduced to advect fluid volumes on unstructured mesh. Moreover, an analytical relation for the interface's line constant vs. the volume clipped by the interface was developed so as to improve the method's efficiency. To validate this method, a comprehensive series of large straining advection tests were performed. Numerical results provide convincing evidences for the method's high volume conservative accuracy and second-order shape error convergence rate. Also, a dramatic improvement on computational accuracy over its unstructured triangular mesh counterpart is checked.
Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions
2008-01-01
Based on a linear finite element space,two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and analyzed.Some relationships between the finite element method and the finite difference method are addressed,too.
Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions
DAI Xiaoying; YANG Zhang; ZHOU Aihui
2008-01-01
Based on a linear finite element space, two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and analyzed. Some relationships between the finite element method and the finite difference method are addressed, too.
Potential flow about arbitrary biplane wing sections
Garrick, I E
1937-01-01
A rigorous treatment is given of the problem of determining the two-dimensional potential flow around arbitrary biplane cellules. The analysis involves the use of elliptic functions and is sufficiently general to include the effects of such elements as the section shapes, the chord ratio, gap, stagger, and decalage, which elements may be specified arbitrarily. The flow problem is resolved by making use of the methods of conformal representation. Thus the solution of the problem of transforming conformally two arbitrary contours into two circles is expressed by a pair of simultaneous integral equations, for which a method of numerical solution is outlined. As an example of the numerical process, the pressure distribution over certain arrangements of the NACA 4412 airfoil in biplane combinations is presented and compared with the monoplane pressure distribution.
Strong field ionization in arbitrary laser polarizations
Protopapas, M.; Lappas, D. G.; Knight, P. L.
1997-01-01
We present a new method for investigating the nonperturbative quantum mechanical interaction of light with atoms in two dimensions, without a basis expansion. This enables us to investigate intense laser-atom interactions with light of arbitrary polarization without approximation, within the model restrictions. Results are presented for the dependence of ionization and high harmonic generation on ellipticity seen in recent experiments. Strong evidence of stabilization in circular polarization...
On Arbitrary Phases in Quantum Amplitude Amplification
Hoyer, P
2000-01-01
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\\tan(\\phi/2)=\\tan(\\phi/2)(1-2a)$, where $\\phi$ and $\\phi$ are the phases used and where $a$ is the success probability of the given algorithm. Thus the choice of phases depends nontrivially and nonlinearly on the success probability. Utilizing this condition, we give methods for constructing quantum algorithms that succeed with certainty and for implementing arbitrary rotations. We also conclude that phase errors of order up to $\\frac{1}{\\sqrt{a}}$ can be tolerated in amplitude amplification.
姚贞光; 刘巧芳
2014-01-01
无论是在实体足球比赛还是智能体机器人足球比赛中，近距离的任意球破门收益率较高。研究智能体足球机器人比赛的任意球轨迹修正和优化控制问题，进而指导足球训练提高任意球得分率。提出一种基于灰色靶关联分析的智能体任意球轨迹修正方法，首先对整个机器人足球的环境态势和球员行为体选择进行模型构建，然后给出了灰色靶关联分析的任意球轨迹修正算法，进行球体着力点和应力点的适应值分析，构建基于灰色靶关联分析的任意球应力衰减特性分析模型，指导任意球轨迹修正，最后在智能体足球世界杯3D仿真平台进行实验验证了算法的优越性能。实验结果得出，采用该算法能有效指导任意球发球着力点控制，优化任意球的攻击轨迹，提高智能体机器人足球的任意球进球成功率，预测和控制精度提高。%Either in the real football game or agent in the robot soccer competition, a free kick near distance and higher rate is perfect. Correction of arbitrary ball trajectory is researched for intelligent robot soccer competition and the optimal con⁃trol problem, and then guide the football training is proposed to improve the kick rate. A correction method of grey correla⁃tion analysis of agent is proposed based on arbitrary trajectory of the ball, first to the robot soccer environment situation and player behavior selection of model construction, and then gives the ball trajectory analysis of grey correlation algorithm, sphere to point and stress value analysis, construction of arbitrary ball analysis the grey target association based on the stress analysis model attenuation characteristics, guiding the ball trajectory correction, finally verify the superior perfor⁃mance of the algorithm in intelligent football World Cup in 3D simulation platform. Experimental results show that, the algo⁃rithm can effectively guide the
The Interpretation of Saussure’s Arbitrariness
王艳
2015-01-01
According to Saussure,The arbitrary nature of language is"first principle of linguistic".With the development of cognitive science,some exaggerate the importance of iconicity;some even suggest iconicity should replace arbitrariness.What leads to this extreme view is the misunderstanding of arbitrariness.The paper aims at advocating an overall and objective view towards the arbitrary nature of language,putting forward that arbitrariness and iconicity are not incompatible but complementary.
The mixed dual finite element method is usually used for the resolution of the SPN transport equations (simplified PN equations) in 3D homogenized geometries (composed by homogenized rectangles or hexagons). This method produces fast results with little memory requirements. We have extended the previous method to the treatment of unstructured geometries composed by quadrilaterals (for the moment limited to 2D), allowing us to treat geometries where fuel pins are exactly represented. The iterative resolution of the resulting matrix system is a generalization of the one already developed for the cartesian and the hexagonal geometries. In order to illustrate and to show the efficiency of this method, results on the NEA-C5G7-MOX benchmark are given. The previous benchmark has been extended for the hexagonal geometry and we provide here some results. This method is a first step towards the treatment of pin by pin core calculations without homogenization. The present solver is a prototype. It shows the efficiency of the method and it has to be extended to 3D calculations as well as to exact transport calculations. We also intend to extend the method to the treatment of unstructured geometries composed by quadrilaterals with curved edges (sectors of a circle).The iterative algorithm has yet to be accelerated using multigrid techniques through a coupling with the present homogenized solver (MINOS). In the future, it will be included in the next generation neutronic toolbox DESCARTES currently under development
Lautard, J.J.; Flumiani, T. [CEA Saclay, Direction de l' Energie Nucleaire (DEN/SERMA), Service d' Etude des Reacteurs et de Modelisations Avancees, 91 - Gif sur Yvette (France)
2003-07-01
The mixed dual finite element method is usually used for the resolution of the SPN transport equations (simplified PN equations) in 3D homogenized geometries (composed by homogenized rectangles or hexagons). This method produces fast results with little memory requirements. We have extended the previous method to the treatment of unstructured geometries composed by quadrilaterals (for the moment limited to 2D), allowing us to treat geometries where fuel pins are exactly represented. The iterative resolution of the resulting matrix system is a generalization of the one already developed for the cartesian and the hexagonal geometries. In order to illustrate and to show the efficiency of this method, results on the NEA-C5G7-MOX benchmark are given. The previous benchmark has been extended for the hexagonal geometry and we provide here some results. This method is a first step towards the treatment of pin by pin core calculations without homogenization. The present solver is a prototype. It shows the efficiency of the method and it has to be extended to 3D calculations as well as to exact transport calculations. We also intend to extend the method to the treatment of unstructured geometries composed by quadrilaterals with curved edges (sectors of a circle).The iterative algorithm has yet to be accelerated using multigrid techniques through a coupling with the present homogenized solver (MINOS). In the future, it will be included in the next generation neutronic toolbox DESCARTES currently under development.
Gomez-Sousa, Hipolito; Martinez-Lorenzo, Jose Angel; Arias-Acuña, Marcos
2015-01-01
This paper presents a new method, based on the well-known method of moments (MoM), for the numerical electromagnetic analysis of scattering and radiation from metallic or dielectric structures, or both structure types in the same simulation, that are in contact with other metallic or dielectric structures. The proposed method for solving the MoM junction problem consists of two separate algorithms, one of which comprises a generalization for bodies in contact of the surface integral equation (SIE) formulations. Unlike some other published SIE generalizations in the field of computational electromagnetics, this generalization does not require duplicating unknowns on the dielectric separation surfaces. Additionally, this generalization is applicable to any ordinary single-scatterer SIE formulations employed as baseline. The other algorithm deals with enforcing boundary conditions and Kirchhoff's Law, relating the surface current flow across a junction edge. Two important features inherent to this latter algorit...
Friedman, D. M.
1974-01-01
The surface-source method of calculating potential flow is improved by refining the underlying numerical analysis. The present analysis uses parabolic elements and linearly-varying source density which results in a large increase in computing speed and accuracy. The computer program including all relevant input and output is described.
Joint Signal Polarization and DOA Estimation Method for Arbitrary Array%一种适用于任意阵列的极化和二维DOA联合估计算法
郑均杰; 刘国峰; 王晓东
2014-01-01
提出了一种适用于任意阵列的极化和二维DOA联合估计算法。该算法基于信号空时二维结构特征，利用空域采样和时域采样构造时空矩阵，通过DOA矩阵方法进行极化和二维DOA参数估计，不需要二维谱峰搜索，计算量小。仿真实验证明了算法的有效性。%A joint estimation method of polarization and 2D (two-dimensional) DOA was proposed for arbitrary array. Based on the space-time eigenstructure of signals, space-time matrixes were constructed by spatial domain sampling and time domain sampling. The DOA matrix method was utilized to estimate the parameters in this method. It doesn't need spectral peak searching and complex computation. The simulation validated effectiveness of this method.
In nuclear power plants, a number of cracks attributed to stress corrosion cracking (SCC) have been detected in welds made with nickel alloy weld metals. One of characteristics of these cracks is that the crack depth is greater than one half of the crack length. When a crack is detected in a component of a nuclear power plant during an in-service inspection, a flaw evaluation is conducted according to the requirement of fitness-for-service codes such as the JSME Rules on Fitness-for-Service for Nuclear Power Plants and the ASME Boiler and Pressure Vessel Code. Here, the stress intensity factor plays an important role for predicting crack growth behavior due to fatigue and/or SCC. Although several solutions of the stress intensity factor are already given in the codes, no solutions are available for the cracks having an aspect ratio greater than unity. Surface cracks with an aspect ratio greater than unity are characterized as semicircular. To evaluate these cracks in a rational manner, we developed a database of influence coefficients by means of the influence function method in conjunction with the finite element method. By using these influence coefficients, a solution for the stress intensity factor was developed for a semi-elliptical surface crack with high-aspect-ratio up to 8.0 subjected to a fifth-order-polynomial stress distribution
Application of CLEAR-VOF method to wave and flow simulations
Ying-wei SUN
2012-03-01
Full Text Available A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid (CLEAR-VOF method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.
Simulation of Marine Hydrokinetic Turbines in Unsteady Flow using Vortex Particle Method
Sale, Danny; Aliseda, Alberto
2013-11-01
A vortex particle method has been developed to study the performance and wake characteristics of Marine Hydrokinetic turbines. The goals are to understand mean flow and turbulent eddy effects on wake evolution, and the unsteady loading on the rotor and support structures. The vorticity-velocity formulation of the Navier-Stokes equations are solved using a hybrid Lagrangian-Eulerian method involving both vortex particle and spatial mesh discretizations. Particle strengths are modified by vortex stretching, diffusion, and body forces; these terms in the vorticity transport equation involve differential operators and are computed more efficiently on a Cartesian mesh using finite differences. High-order and moment-conserving interpolations allow the particles and mesh to exchange field quantities and particle strengths. An immersed boundary method which introduces a penalization term in the vorticity transport equations provides an efficient way to satisfy the no-slip boundary condition on solid boundaries. To provide further computational speedup, we investigate the use of multicore processors and graphics processing units using the OpenMP and OpenCL interfaces within the Parallel Particle-Mesh Library.
Gaussian quadrature formulae for arbitrary positive measures.
Fernandes, Andrew D; Atchley, William R
2006-01-01
We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student's t, inverse-gamma, beta, and Fisher's F) we present exact formulae for computing the respective quadrature scheme. PMID:19455218
Gaussian Quadrature Formulae for Arbitrary Positive Measures
William R. Atchley
2006-01-01
Full Text Available We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student’s t, inversegamma, beta, and Fisher’s F we present exact formulae for computing the respective quadrature scheme.
Sampling to estimate arbitrary subset sums
Duffield, Nick; Lund, Carsten; Thorup, Mikkel
2005-01-01
Starting with a set of weighted items, we want to create a generic sample of a certain size that we can later use to estimate the total weight of arbitrary subsets. For this purpose, we propose priority sampling which tested on Internet data performed better than previous methods by orders of magnitude. Priority sampling is simple to define and implement: we consider a steam of items i=0,...,n-1 with weights w_i. For each item i, we generate a random number r_i in (0,1) and create a priority ...
Garbage-free reversible constant multipliers for arbitrary integers
Mogensen, Torben Ægidius
2013-01-01
We present a method for constructing reversible circuitry for multiplying integers by arbitrary integer constants. The method is based on Mealy machines and gives circuits whose size are (in the worst case) linear in the size of the constant. This makes the method unsuitable for large constants, ......, but gives quite compact circuits for small constants. The circuits use no garbage or ancillary lines....
High order methods for incompressible fluid flow: Application to moving boundary problems
Bjoentegaard, Tormod
2008-04-15
Fluid flows with moving boundaries are encountered in a large number of real life situations, with two such types being fluid-structure interaction and free-surface flows. Fluid-structure phenomena are for instance apparent in many hydrodynamic applications; wave effects on offshore structures, sloshing and fluid induced vibrations, and aeroelasticity; flutter and dynamic response. Free-surface flows can be considered as a special case of a fluid-fluid interaction where one of the fluids are practically inviscid, such as air. This type of flows arise in many disciplines such as marine hydrodynamics, chemical engineering, material processing, and geophysics. The driving forces for free-surface flows may be of large scale such as gravity or inertial forces, or forces due to surface tension which operate on a much smaller scale. Free-surface flows with surface tension as a driving mechanism include the flow of bubbles and droplets, and the evolution of capillary waves. In this work we consider incompressible fluid flow, which are governed by the incompressible Navier-Stokes equations. There are several challenges when simulating moving boundary problems numerically, and these include - Spatial discretization - Temporal discretization - Imposition of boundary conditions - Solution strategy for the linear equations. These are some of the issues which will be addressed in this introduction. We will first formulate the problem in the arbitrary Lagrangian-Eulerian framework, and introduce the weak formulation of the problem. Next, we discuss the spatial and temporal discretization before we move to the imposition of surface tension boundary conditions. In the final section we discuss the solution of the resulting linear system of equations. (Author). refs., figs., tabs
Simulation of Free Airfoil Vibrations in Incompressible Viscous Flow — Comparison of FEM and FVM
Petr Sváček
2012-01-01
Full Text Available This paper deals with a numerical solution of the interaction of two-dimensional (2-D incompressible viscous flow and a vibrating profile NACA 0012 with large amplitudes. The laminar flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. The profile with two degrees of freedom (2-DOF can rotate around its elastic axis and oscillate in the vertical direction. Its motion is described by a nonlinear system of two ordinary differential equations. Deformations of the computational domain due to the profile motion are treated by the arbitrary Lagrangian-Eulerianmethod. The finite volume method and the finite element method are applied, and the numerical results are compared.
Baruah, P. K.; Bussoletti, J. E.; Chiang, D. T.; Massena, W. A.; Nelson, F. D.; Furdon, D. J.; Tsurusaki, K.
1981-01-01
The Maintenance Document is a guide to the PAN AIR software system, a system which computes the subsonic or supersonic linear potential flow about a body of nearly arbitrary shape, using a higher order panel method. The document describes the over-all system and each program module of the system. Sufficient detail is given for program maintenance, updating and modification. It is assumed that the reader is familiar with programming and CDC (Control Data Corporation) computer systems. The PAN AIR system was written in FORTRAN 4 language except for a few COMPASS language subroutines which exist in the PAN AIR library. Structured programming techniques were used to provide code documentation and maintainability. The operating systems accommodated are NOS 1.2, NOS/BE and SCOPE 2.1.3 on the CDC 6600, 7600 and Cyber 175 computing systems. The system is comprised of a data management system, a program library, an execution control module and nine separate FORTRAN technical modules. Each module calculates part of the posed PAN AIR problem. The data base manager is used to communicate between modules and within modules. The technical modules must be run in a prescribed fashion for each PAN AIR problem. In order to ease the problem of supplying the many JCL cards required to execute the modules, a separate module called MEC (Module Execution Control) was created to automatically supply most of the JCL cards. In addition to the MEC generated JCL, there is an additional set of user supplied JCL cards to initiate the JCL sequence stored on the system.
Purdon, David J.; Baruah, Pranab K.; Bussoletti, John E.; Epton, Michael A.; Massena, William A.; Nelson, Franklin D.; Tsurusaki, Kiyoharu
1990-01-01
The Maintenance Document Version 3.0 is a guide to the PAN AIR software system, a system which computes the subsonic or supersonic linear potential flow about a body of nearly arbitrary shape, using a higher order panel method. The document describes the overall system and each program module of the system. Sufficient detail is given for program maintenance, updating, and modification. It is assumed that the reader is familiar with programming and CRAY computer systems. The PAN AIR system was written in FORTRAN 4 language except for a few CAL language subroutines which exist in the PAN AIR library. Structured programming techniques were used to provide code documentation and maintainability. The operating systems accommodated are COS 1.11, COS 1.12, COS 1.13, and COS 1.14 on the CRAY 1S, 1M, and X-MP computing systems. The system is comprised of a data base management system, a program library, an execution control module, and nine separate FORTRAN technical modules. Each module calculates part of the posed PAN AIR problem. The data base manager is used to communicate between modules and within modules. The technical modules must be run in a prescribed fashion for each PAN AIR problem. In order to ease the problem of supplying the many JCL cards required to execute the modules, a set of CRAY procedures (PAPROCS) was created to automatically supply most of the JCL cards. Most of this document has not changed for Version 3.0. It now, however, strictly applies only to PAN AIR version 3.0. The major changes are: (1) additional sections covering the new FDP module (which calculates streamlines and offbody points); (2) a complete rewrite of the section on the MAG module; and (3) strict applicability to CRAY computing systems.
Controlling arbitrary humidity without convection.
Wasnik, Priyanka S; N'guessan, Hartmann E; Tadmor, Rafael
2015-10-01
In this paper we show a way that allows for the first time to induce arbitrary humidity of desired value for systems without convective flow. To enable this novelty we utilize a semi-closed environment in which evaporation is not completely suppressed. In this case, the evaporation rate is determined both by the outer (open) humidity and by the inner (semi-closed) geometry including the size/shape of the evaporating medium and the size/shape of the semi-closure. We show how such systems can be used to induce desired humidity conditions. We consider water droplet placed on a solid surface and study its evaporation when it is surrounded by other drops, hereon "satellite" drops and covered by a semi-closed hemisphere. The main drop's evaporation rate is proportional to its height, in agreement with theory. Surprisingly, however, the influence of the satellite drops on the main drop's evaporation suppression is not proportional to the sum of heights of the satellite drops. Instead, it shows proportionality close to the satellite drops' total surface area. The resultant humidity conditions in the semi-closed system can be effectively and accurately induced using different satellite drops combinations. PMID:26072445
Probabilistic Teleportation of an Arbitrary n-Particle Entangled State
XIYong-Jun; FANGJian-Xing; ZHUShi-Qun; GUOZhan-Ying
2005-01-01
A scheme for teleporting an arbitrary n-particle entangled state via n pairs of non-maximally entangled states is proposed. The probability of successful teleportation is determined only by the smaller coefficients of the partially entangled pairs. The method is very easy to be realized.
Garasi, Christopher Joseph; Cochrane, Kyle Robert; Mehlhorn, Thomas Alan; Haill, Thomas A.; Brunner, Thomas A.; Summers, Randall M.; Robinson, Allen Conrad
2005-02-01
ALEGRA is an arbitrary Lagrangian-Eulerian finite element code that emphasizes large distortion and shock propagation in inviscid fluids and solids. This document describes user options for modeling resistive magnetohydrodynamics, thermal conduction, and radiation transport effects, and two material temperature physics.
Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
Hanada, Masanori; Honda, Masazumi; Honma, Yoshinori; Nishimura, Jun; Shiba, Shotaro; Yoshida, Yutaka
2012-05-01
We show that the ABJM theory, which is an {N} = {6} superconformal U( N) × U( N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS4/CFT3 duality at the quantum level. Here we calculate the free energy, and confirm the N 3/2 scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models.
Solving the Homogeneous Boltzmann Equation with Arbitrary Scattering Kernel
Hohenegger, A.
2008-01-01
With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space homogeneous Boltzmann equation with isotropic distribution function to arbitrary matrix elements. The method is based on the expansion of the matrix element in terms of two cosines of the "scattering angles". The scattering functions used by previous authors in particle physics for matrix elements in Fermi-approximation are retrieved as lowest order results in this expansion. Th...
ON THE SCATTERING OF ARBITRARY SHAPE MICROSTRIP PATCH
He Xiulian; Gong Shuxi; Liu Qizhong
2004-01-01
In this letter, discrete complex image method is employed to compute the Green's functions in the spatial domain, which improves the speed of evaluating the impedance matrix.The triangle vector basis function--RWG, is used to simulate the current distribution in order to compute the scattering properties of arbitrary shape microstrip patch without the staircase approximation. The numerical result shows the validity of the proposed method.
Arbitrary Finite-time Tracking Control for Magnetic Levitation Systems
Xuan-Toa Tran; Hee-Jun Kang
2014-01-01
In this paper, an arbitrary finite-time tracking control (AFTC) method is developed for magnetic levitation systems with uncertain dynamics and external disturbances. By introducing a novel augmented sliding- mode manifold function, the proposed method can eliminate the singular problem in traditional terminal sliding-mode control, as well as the reaching-phase problem. Moreover, the tracking errors can reach the reference value with faster convergence and better tracking precision in arbitra...
Arbitrary orbital angular momentum of photons
Pan, Yue; Ren, Zhi-Cheng; Wang, Xi-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2015-01-01
Orbital angular momentum (OAM) of photons, as a new fundamental degree of freedom, has excited a great diversity of interest, because of a variety of emerging applications. Arbitrarily tunable OAM has gained much attention, but its creation remains still a tremendous challenge. We demonstrate the realization of well-controlled arbitrary OAM in both theory and experiment. We present the concept of general OAM, which extends the OAM carried by the scalar vortex field to the OAM carried by the azimuthally varying polarized vector field. The arbitrary OAM has the same characteristics as the well-defined integer OAM: intrinsic OAM, uniform local OAM and intensity ring, and propagation stability. The arbitrary OAM has unique natures: it is allowed to be flexibly tailored and the radius of the focusing ring can have various choices for a desired OAM, which are of great significance to the benefit of surprising applications of the arbitrary OAM.
THE EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES
Wen Li; Jian-xin Chen
2006-01-01
In this paper we present some new absolute and relative perturbation bounds for the eigenvalue for arbitrary matrices, which improves some recent results. The eigenvalue inclusion region is also discussed.
A fast algorithm for simulating multiphase flows through periodic geometries of arbitrary shape
Marple, Gary; Barnett, Alex; Gillman, Adrianna; Veerapaneni, Shravan
2015-01-01
This paper presents a new boundary integral equation (BIE) method for simulating particulate and multiphase flows through periodic channels of arbitrary smooth shape in two dimensions. The authors consider a particular system---multiple vesicles suspended in a periodic channel of arbitrary shape---to describe the numerical method and test its performance. Rather than relying on the periodic Green's function as classical BIE methods do, the method combines the free-space Green's function with ...
The Sugawara generators at arbitrary level
Gebert, R.; Koepsell, K.; Nicolai, H.
1996-01-01
We construct an explicit representation of the Sugawara generators for arbitrary level in terms of the homogeneous Heisenberg subalgebra, which generalizes the well-known expression at level 1. This is achieved by employing a physical vertex operator realization of the affine algebra at arbitrary level, in contrast to the Frenkel--Kac--Segal construction which uses unphysical oscillators and is restricted to level 1. At higher level, the new operators are transcendental functions of DDF ``osc...
Quantum polar codes for arbitrary channels
Wilde, Mark M.; Renes, Joseph M.
2012-01-01
We construct a new entanglement-assisted quantum polar coding scheme which achieves the symmetric coherent information rate by synthesizing "amplitude" and "phase" channels from a given, arbitrary quantum channel. We first demonstrate the coding scheme for arbitrary quantum channels with qubit inputs, and we show that quantum data can be reliably decoded by O(N) rounds of coherent quantum successive cancellation, followed by N controlled-NOT gates (where N is the number of channel uses). We a...
Arbitrary Dimensional Schwarzschild-FRW Black Holes
Gao, Chang Jun
2004-01-01
The metric of arbitrary dimensional Schwarzschild black hole in the background of Friedman-Robertson-Walker universe is presented in the cosmic coordinates system. In particular, the arbitrary dimensional Schwarzschild-de Sitter metric is rewritten in the Schwarzschild coordinates system and basing on which the even more generalized higher dimensional Schwarzschild-de Sitter metric with another extra dimensions is found. The generalized solution shows that the cosmological constant may roots ...
A multi-material CCALE-MOF approach in cylindrical geometry
Friess, Marie Billaud; Galera, Stephane; Maire, Pierre-Henri; Shashkov, Mikhail
2011-01-01
In this paper we present recent developments concerning a Cell-Centered Arbitrary Lagrangian Eulerian (CCALE) strategy using the Moment Of Fluid (MOF) interface reconstruction for the numerical simulation of multi-material compressible fluid flows on general unstructured grids in cylindrical geometries. Especially, our attention is focused here on the following points. First, we propose a new formulation of the scheme used during the Lagrangian phase in the particular case of axisymmetric geometries. Then, the MOF method is considered for multi-interface reconstruction in cylindrical geometry. Subsequently, a method devoted to the rezoning of polar meshes is detailed. Finally, a generalization of the hybrid remapping to cylindrical geometries is presented. These explorations are validated by mean of several test cases that clearly illustrate the robustness and accuracy of the new method.
On the computation of multi-material flows using ALE formulation
Computation of compressible multi-fluid flows with a general equation of state using interface tracking and moving grid approach is discussed in this paper. The AUSM+, HLLC, and Godunov methods are presented and implemented in the context of arbitrary Lagrangian-Eulerian formulation for solving the unsteady compressible Euler equations. The developed methods are fully conservative, and used to compute a variety of multi-component flow problems, where the equations of state can be drastically different and stiff. Numerical results indicate that both ALE HLLC and Godunov schemes demonstrate their simplicity and robustness for solving such multi-phase flow problems, and yet ALE AUSM+ scheme exhibits strong oscillations around material interfaces even using a first order monotone scheme and therefore is not suitable for this class of problems
Mola, Andrea; DeSimone, Antonio
2012-01-01
We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-differential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Differentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare ou...
Analysis and numerical simulation of dynamic effect on rock under high pressure water jet
LI Xiao-hong; SI Hu; WANG Dan-dan
2008-01-01
Based on continuum mechanics and rock dynamics, analyzed the micro-structure damage of rock and the impulsive effect under high pressure water jet and developed the dynamic model. Further, on the assumption of that rock was homogeneous and isotropic, a computational model was established based on nonlinear finite element and Arbitrary Lagrangian-Eulerian(ALE) method. The dynamic effect impacted on rock under high pressure water jet was simulated by the dynamic contact method. The propagation of stress wave in rock was numerically simulated at different impacting velocity. The results show that the propagation velocity of stress wave is proportional to the impacting velocity of high pressure water jet. The faster the impacting velocity is, the quicker the comedown of stress wave.
LES of non-evaporative diesel fuel spray
Jonnalagedda, S.; Zhou, B. [Windsor Univ., ON (Canada). Dept. of Mechanical, Automotive and Materials Engineering
2009-07-01
Mixture formation and fluid flow in internal combustion engines are unsteady and anisotropic due to the engine's complex geometry, piston movement, flow rotation, and 2-phase mixing. The wide range of eddy sizes in turbulent flow enhances turbulence mixing. In this study, a large eddy simulation (LES) was used to characterize the turbulent unsteady structure of diesel fuel spray. A 1-equation LES model was implemented in a KIVA solver based on arbitrary Lagrangian Eulerian methods. Predictions obtained using the method were then compared with Navier Stokes simulations of transient, 2-, and 3-dimensional reactive fluid flows. Results of the study indicated that the LES approach accurately characterized the inhomogenous, unsteady structure of the fuel spray. Spray tip penetration and spray structure and vector plots were compared. Results were more accurate than those obtained using a Reynolds Averaged Navier-Stokes (RANS) approach. 5 refs., 3 tabs., 7 figs.
Dynamic response with arbitrary initial conditions using the FFT
U. Lee
2006-08-01
Full Text Available Purpose: An FFT-based dynamic analysis method is proposed for damped linear discrete dynamic systemssubjected to arbitrary nonzero initial conditions.Design/methodology/approach: The DFT theory is used to develop an FFT-based spectral analysis method.The total dynamic response is considered as the sum of the forced vibration response part and the free vibrationresponse part. The forced vibration response part is obtained from the dynamic stiffness matrix and the Fouriercomponents of excitation force based on the concept of Duhamel’s integral, and the free vibration response partis obtained by determining its integral constant to satisfy arbitrary initial conditions in the frequency-domain.Findings: Through some numeral examples, the proposed FFT-based dynamic analysis method is shown toprovide very successful solutions which satisfy all arbitrary non-zero initial conditions.Research limitations/implications: (not applicable.Practical implications: (not applicable.Originality/value: The present FFT-based method is unique because it does not use the superposition ofcorrective free vibration solution or the pseudo-force concept used by other researchers to take into account thenon-zero initial conditions.
The arbitrary l continuum states of the hyperbolic molecular potential
Wei, Gao-Feng, E-mail: fgwei_2000@163.com [School of Physics and Mechatronics Engineering, Xi' an University of Arts and Science, Xi' an 710065 (China); Chen, Wen-Li, E-mail: physwlchen@163.com [Department of Basic Science, Xi' an Peihua University, Xi' an 710065 (China); Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D.F. 07738 (Mexico); Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001 (United States)
2014-06-27
Within the framework of partial-wave method, we study in this Letter the arbitrary l continuum states of the Schrödinger equation with the hyperbolic molecular potential in terms of an improved approximation to the centrifugal term. We present the normalized radial wave functions and obtain analytical formula of phase shifts. In addition, the corresponding bound states are also discussed by studying the analytical properties of the scattering amplitude. We calculate the energy spectra and scattering phase shifts by the improved, previous approximations and the accurate methods, respectively and find that the improved approximation is better than the previous one since the present results are in better agreement with the accurate ones. - Highlights: • The hyperbolic potential with arbitrary l state is solved. • Improved approximation to centrifugal term is used. • Phase shift formula is derived analytically. • Accurate results are compared with the present results.
Matrix diffusion, a diffusive mass transfer process,in the structured soils and geologic units at ORNL, is believe to be an important subsurface mass transfer mechanism; it may affect off-site movement of radioactive wastes and remediation of waste disposal sites by locally exchanging wastes between soil/rock matrix and macropores/fractures. Advective mass transfer also contributes to waste movement but is largely neglected by researchers. This report presents the first documented 2-D multiregion solute transport code (MURT) that incorporates not only diffusive but also advective mass transfer and can be applied to heterogeneous porous media under transient flow conditions. In this report, theoretical background is reviewed and the derivation of multiregion solute transport equations is presented. Similar to MURF (Gwo et al. 1994), a multiregion subsurface flow code, multiplepore domains as suggested by previous investigators (eg, Wilson and Luxmoore 1988) can be implemented in MURT. Transient or steady-state flow fields of the pore domains can be either calculated by MURF or by modelers. The mass transfer process is briefly discussed through a three-pore-region multiregion solute transport mechanism. Mass transfer equations that describe mass flux across pore region interfaces are also presented and parameters needed to calculate mass transfer coefficients detailed. Three applications of MURT (tracer injection problem, sensitivity analysis of advective and diffusive mass transfer, hillslope ponding infiltration and secondary source problem) were simulated and results discussed. Program structure of MURT and functions of MURT subroutiness are discussed so that users can adapt the code; guides for input data preparation are provided in appendices
Arbitrary rotation and entanglement of flux SQUID qubits
Kis, Z
2003-01-01
We propose a new approach for the arbitrary rotation of a three-level SQUID qubit and describe a new strategy for the creation of coherence transfer and entangled states between two three-level SQUID qubits. The former is succeeded by exploring the coupled-uncoupled states of the system when irradiated with two microwave pulses, and the latter is succeeded by placing the SQUID qubits into a microwave cavity and used adiabatic passage methods for their manipulation.
Electrodynamics in Arbitrary Reference Frames and in Arbitrary Material Media
Full text: The investigation of electromagnetic phenomena in material media still belongs to the most difficult tasks of electrodynamics. Complexity and variability of material media practically exclude effective applications of methods and computational techniques elaborated in the framework of standard microscopic electrodynamics with classical vacuum as a ground state. In order to obtain satisfactorily exact descriptions of electromagnetic properties of complex material media one is enforced to use methods and approximations which are difficult to control. Moreover, they usually break covariance properties and the results obtained are valid in one reference frame which choice remains subjective and model dependent. Some time ago we have proposed a reformulation of Maxwell electrodynamics which opens new ways in study of electromagnetic processes in material media. The formalism gets rid of assumptions characteristic for vacuum electrodynamics only and it avoids the usage of constitutive relations as primary relations put on quantities needed for a complete description of an electromagnetic system. Fundamental properties of all electromagnetic quantities are their uniquely defined transformation rules and their analysis allows to determine the possible relations between them. Within such a scheme it is possible to introduce constitutive relations which do not have analogies in macroscopic classical electrodynamics. They may be used in description of microscopic electromagnetic processes in a different way than it is done in the framework of quantum electrodynamics. (author)
Trajectory approach to the Schrödinger-Langevin equation with linear dissipation for ground states
Chou, Chia-Chun
2015-11-01
The Schrödinger-Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger-Langevin equation yields the complex quantum Hamilton-Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.
Time-discrete higher order ALE formulations: a priori error analysis
Bonito, Andrea
2013-03-16
We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our estimates hold without any restrictions on the time steps for dG with exact integration or Reynolds\\' quadrature. They involve a mild restriction on the time steps for the practical Runge-Kutta-Radau methods of any order. The key ingredients are the stability results shown earlier in Bonito et al. (Time-discrete higher order ALE formulations: stability, 2013) along with a novel ALE projection. Numerical experiments illustrate and complement our theoretical results. © 2013 Springer-Verlag Berlin Heidelberg.
Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline
2001-12-01
Discrete geometric conservation laws (DGCLs) govern the geometric parameters of numerical schemes designed for the solution of unsteady flow problems on moving grids. A DGCL requires that these geometric parameters, which include among others grid positions and velocities, be computed so that the corresponding numerical scheme reproduces exactly a constant solution. Sometimes, this requirement affects the intrinsic design of an arbitrary Lagrangian Eulerian (ALE) solution method. In this paper, we show for sample ALE schemes that satisfying the corresponding DGCL is a necessary and sufficient condition for a numerical scheme to preserve the nonlinear stability of its fixed grid counterpart. We also highlight the impact of this theoretical result on practical applications of computational fluid dynamics.
Kamm, James R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Love, Edward [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Robinson, Allen C. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Young, Joseph G. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ridzal, Denis [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2013-12-01
We review the edge element formulation for describing the kinematics of hyperelastic solids. This approach is used to frame the problem of remapping the inverse deformation gradient for Arbitrary Lagrangian-Eulerian (ALE) simulations of solid dynamics. For hyperelastic materials, the stress state is completely determined by the deformation gradient, so remapping this quantity effectively updates the stress state of the material. A method, inspired by the constrained transport remap in electromagnetics, is reviewed, according to which the zero-curl constraint on the inverse deformation gradient is implicitly satisfied. Open issues related to the accuracy of this approach are identified. An optimization-based approach is implemented to enforce positivity of the determinant of the deformation gradient. The efficacy of this approach is illustrated with numerical examples.
Perturbation Theory for Arbitrary Coupling Strength ?
Mahapatra, B P
2016-01-01
We demonstrate Borel summability for arbitrary coupling strength in a new formulation of perturbation theory (designated here as "Mean Field Perturbation Theory (MFPT)") by applying it to one dimensional anharmonic-interactions, which includes the case of the quartic and sextic anharmonic oscillators(AHO) and the quartic double-well-oscillator (QDWO).It is well known that the perturbation-series is not Borel-summable for the QDWO in the standard formulation of perturbation theory(SFPT). In contrast, MFPT leads to a Borel-summable perturbation series and accurate values for the energy-spectra for arbitrary (physical) value of the coupling strength in each case as stated above. The general nature and the simplicity of the formulation underlying MFPT leads us to conjecture that this scheme may be applicable to arbitrary interactions in quantum theory.
Generation of Electromagnetic Waves with Arbitrary Orbital Angular Momentum Modes
Cheng, Li; Hong, Wei; Hao, Zhang-Cheng
2014-01-01
Recently, much attention has been focused on beams carrying orbital angular momentum (OAM) for radio communication. Here we experimentally demonstrate a planar-spiral phase plate (planar-SPP) for generating arbitrary mixed OAM beams. This proposed planar-SPP uses the concept of transmit array antenna having a perforated substrate to control the outputting phase for generating beams carrying OAM with arbitrary modes. As demonstrations, three planar-SPPs with a single OAM mode and two mixed OAM modes around 94 GHz have been investigated with design and experiments in this paper, respectively. The typical experimental intensity and phase patterns show that the proposed method of generating OAM beams really works. PMID:24770669
Optimizing the controllability of arbitrary networks with genetic algorithm
Li, Xin-Feng; Lu, Zhe-Ming
2016-04-01
Recently, as the controllability of complex networks attracts much attention, how to optimize networks' controllability has become a common and urgent problem. In this paper, we develop an efficient genetic algorithm oriented optimization tool to optimize the controllability of arbitrary networks consisting of both state nodes and control nodes under Popov-Belevitch-Hautus rank condition. The experimental results on a number of benchmark networks show the effectiveness of this method and the evolution of network topology is captured. Furthermore, we explore how network structure affects its controllability and find that the sparser a network is, the more control nodes are needed to control it and the larger the differences between node degrees, the more control nodes are needed to achieve the full control. Our framework provides an alternative to controllability optimization and can be applied to arbitrary networks without any limitations.
Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields
Li, Yuan-Yuan; Cao, Junpeng [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Yang, Wen-Li [Institute of Modern Physics, Northwest University, Xian 710069 (China); Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048 (China); Shi, Kangjie [Institute of Modern Physics, Northwest University, Xian 710069 (China); Wang, Yupeng, E-mail: yupeng@iphy.ac.cn [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2014-02-15
The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.
Isotope specific arbitrary material sorter
Barty, Christopher P.J.
2015-12-08
A laser-based mono-energetic gamma-ray source is used to provide a rapid and unique, isotope specific method for sorting materials. The objects to be sorted are passed on a conveyor in front of a MEGa-ray beam which has been tuned to the nuclear resonance fluorescence transition of the desired material. As the material containing the desired isotope traverses the beam, a reduction in the transmitted MEGa-ray beam occurs. Alternately, the laser-based mono-energetic gamma-ray source is used to provide non-destructive and non-intrusive, quantitative determination of the absolute amount of a specific isotope contained within pipe as part of a moving fluid or quasi-fluid material stream.
Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness
Matt, Michael Andreas
2012-01-01
Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and Cr macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation method is based on cubic C1 splines over type-4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C2 splines. It is based on arbitrary tetrahedral partitions using splines of degree nine. The author constructs trivariate macro-elements based on the Alfeld split, where each tetrahedron
Morlino, G.; P. Blasi(INAF Arcetri); Vietri, M.
2007-01-01
A mathematical approach to investigate particle acceleration at shock waves moving at arbitrary speed in a medium with arbitrary scattering properties was first discussed in (Vietri 2003) and (Blasi & Vietri 2005}. We use this method and somewhat extend it in order to include the effect of a large scale magnetic field in the upstream plasma, with arbitrary orientation with respect to the direction of motion of the shock. We also use this approach to investigate the effects of anisotropic scat...
Spectral measures with arbitrary Hausdorff dimensions
Dai, Xin-Rong; Sun, Qiyu
2014-01-01
In this paper, we consider spectral properties of Riesz product measures supported on homogeneous Cantor sets and we show the existence of spectral measures with arbitrary Hausdorff dimensions, including non-atomic zero-dimensional spectral measures and one-dimensional singular spectral measures.
Vacuum Birefringence Caused by Arbitrary Spin Particles
Kruglov, S. I.
2007-01-01
We study the propagation of a linearly polarized laser beam in the external transverse magnetic field taking into consideration the vacuum polarization by arbitrary spin particles. Induced ellipticity of the beam are evaluated using the effective Lagrangian. With the help of the PVLAS experimental data, we obtain bounds on masses of charged higher spin particles contributed to ellipticity.
Kraus representation for arbitrary open qubit system
Tong, D M; Kwek, L C; Oh, C H; Chen, Jing-Ling
2003-01-01
We show that the time evolution of an arbitrary open qubit system can always be described in terms of the Kraus representation irrespective of the presence of initial correlations between the open system and its environment. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can be generalized to open higher dimensional quantum systems.
Arbitrary Phase Vocoders by means of Warping
Gianpaolo Evangelista
2013-08-01
Full Text Available The Phase Vocoder plays a central role in sound analysis and synthesis, allowing us to represent a sound signal in both time and frequency, similar to a music score – but possibly at much finer time and frequency scales – describing the evolution of sound events. According to the uncertainty principle, time and frequency are not independent variables so that any time-frequency representation is the result of a compromise between time and frequency resolutions, the product of which cannot be smaller than a given constant. Therefore, finer frequency resolution can only be achieved with coarser time resolution and, similarly, finer time resolution results in coarser frequency resolution.While most of the conventional methods for time-frequency representations are based on uniform time and uniform frequency resolutions, perception and physical characteristics of sound signals suggest the need for nonuniform analysis and synthesis. As the results of psycho-acoustic research show, human hearing is naturally organized in nonuniform frequency bands. On the physical side, the sounds of percussive instruments as well as piano in the low register, show partials whose frequencies are not uniformly spaced, as opposed to the uniformly spaced partial frequencies found in harmonic sounds. Moreover, the different characteristics of sound signals at the onset transients with respect to stationary segments suggest the need for nonuniform time resolution. In the effort to exploit the time-frequency resolution compromise at its best, a tight time-frequency suit should be tailored to snuggly fit the sound body.In this paper we overview flexible design methods for phase vocoders with nonuniform resolutions. The methods are based on remapping the time or the frequency axis, or both, by employing suitable functions acting as warping maps, which locally change the characteristics of the time-frequency plane. As a result, the sliding windows may have time dependent
Self-forces on static bodies in arbitrary dimensions
Harte, Abraham I.; Flanagan, Éanna É.; Taylor, Peter
2016-06-01
We derive exact expressions for the scalar and electromagnetic self-forces and self-torques acting on arbitrary static extended bodies in arbitrary static spacetimes with any number of dimensions. Nonperturbatively, our results are identical in all dimensions. Meaningful point particle limits are quite different in different dimensions, however. These limits are defined and evaluated, resulting in simple "regularization algorithms" which can be used in concrete calculations. In these limits, self-interaction is shown to be progressively less important in higher numbers of dimensions; it generically competes in magnitude with increasingly high-order extended-body effects. Conversely, we show that self-interaction effects can be relatively large in 1 +1 and 2 +1 dimensions. Our motivations for this work are twofold: First, no previous derivation of the self-force has been provided in arbitrary dimensions, and heuristic arguments presented by different authors have resulted in conflicting conclusions. Second, the static self-force problem in arbitrary dimensions provides a valuable test bed with which to continue the development of general, nonperturbative methods in the theory of motion. Several new insights are obtained in this direction, including a significantly improved understanding of the renormalization process. We also show that there is considerable freedom to use different "effective fields" in the laws of motion—a freedom which can be exploited to optimally simplify specific problems. Different choices give rise to different inertias, gravitational forces, and electromagnetic or scalar self-forces, but there is a sense in which none of these quantities are individually accessible to experiment. Certain combinations are observable, however, and these remain invariant under all possible field redefinitions.
Pose Estimation from a Single Depth Image for Arbitrary Kinematic Skeletons
Ly, Daniel L; Lipson, Hod
2011-01-01
We present a method for estimating pose information from a single depth image given an arbitrary kinematic structure without prior training. For an arbitrary skeleton and depth image, an evolutionary algorithm is used to find the optimal kinematic configuration to explain the observed image. Results show that our approach can correctly estimate poses of 39 and 78 degree-of-freedom models from a single depth image, even in cases of significant self-occlusion.
Quantum Fidelity for Arbitrary Gaussian States
Banchi, Leonardo; Braunstein, Samuel L.; Pirandola, Stefano
2015-12-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
Quantum fidelity for arbitrary Gaussian states
Banchi, Leonardo; Pirandola, Stefano
2015-01-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
Arbitrary protein−protein docking targets biologically relevant interfaces
Martin Juliette
2012-05-01
Full Text Available Abstract Background Protein-protein recognition is of fundamental importance in the vast majority of biological processes. However, it has already been demonstrated that it is very hard to distinguish true complexes from false complexes in so-called cross-docking experiments, where binary protein complexes are separated and the isolated proteins are all docked against each other and scored. Does this result, at least in part, reflect a physical reality? False complexes could reflect possible nonspecific or weak associations. Results In this paper, we investigate the twilight zone of protein-protein interactions, building on an interesting outcome of cross-docking experiments: false complexes seem to favor residues from the true interaction site, suggesting that randomly chosen partners dock in a non-random fashion on protein surfaces. Here, we carry out arbitrary docking of a non-redundant data set of 198 proteins, with more than 300 randomly chosen "probe" proteins. We investigate the tendency of arbitrary partners to aggregate at localized regions of the protein surfaces, the shape and compositional bias of the generated interfaces, and the potential of this property to predict biologically relevant binding sites. We show that the non-random localization of arbitrary partners after protein-protein docking is a generic feature of protein structures. The interfaces generated in this way are not systematically planar or curved, but tend to be closer than average to the center of the proteins. These results can be used to predict biological interfaces with an AUC value up to 0.69 alone, and 0.72 when used in combination with evolutionary information. An appropriate choice of random partners and number of docking models make this method computationally practical. It is also noted that nonspecific interfaces can point to alternate interaction sites in the case of proteins with multiple interfaces. We illustrate the usefulness of arbitrary docking
Arbitrary protein−protein docking targets biologically relevant interfaces
Protein-protein recognition is of fundamental importance in the vast majority of biological processes. However, it has already been demonstrated that it is very hard to distinguish true complexes from false complexes in so-called cross-docking experiments, where binary protein complexes are separated and the isolated proteins are all docked against each other and scored. Does this result, at least in part, reflect a physical reality? False complexes could reflect possible nonspecific or weak associations. In this paper, we investigate the twilight zone of protein-protein interactions, building on an interesting outcome of cross-docking experiments: false complexes seem to favor residues from the true interaction site, suggesting that randomly chosen partners dock in a non-random fashion on protein surfaces. Here, we carry out arbitrary docking of a non-redundant data set of 198 proteins, with more than 300 randomly chosen "probe" proteins. We investigate the tendency of arbitrary partners to aggregate at localized regions of the protein surfaces, the shape and compositional bias of the generated interfaces, and the potential of this property to predict biologically relevant binding sites. We show that the non-random localization of arbitrary partners after protein-protein docking is a generic feature of protein structures. The interfaces generated in this way are not systematically planar or curved, but tend to be closer than average to the center of the proteins. These results can be used to predict biological interfaces with an AUC value up to 0.69 alone, and 0.72 when used in combination with evolutionary information. An appropriate choice of random partners and number of docking models make this method computationally practical. It is also noted that nonspecific interfaces can point to alternate interaction sites in the case of proteins with multiple interfaces. We illustrate the usefulness of arbitrary docking using PEBP (Phosphatidylethanolamine binding
Arbitrary orbital angular momentum of photons
Pan, Yue; Gao, Xu-Zhen; Ren, Zhi-Cheng; Wang, Xi-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2015-01-01
Orbital angular momentum (OAM) of photons, as a new fundamental degree of freedom, has excited a great diversity of interest, because of a variety of emerging applications. Arbitrarily tunable OAM has gained much attention, but its creation remains still a tremendous challenge. We demonstrate the realization of well-controlled arbitrary OAM in both theory and experiment. We present the concept of general OAM, which extends the OAM carried by the scalar vortex field to the OAM carried by the a...
Acoustic Casimir Pressure for Arbitrary Media
Barcenas, J.; Reyes, L.; Esquivel-Sirvent, R.
2004-01-01
In this paper we derive a general expression for the acoustic Casimir pressure between two parallel slabs made of arbitrary materials and whose acoustic reflection coefficients are not equal. The formalism is based on the calculation of the local density of modes using a Green's function approach. The results for the Casimir acoustic pressure are generalized to a sphere/plate configuration using the proximity theorem
A collection of 13 transposon mutants deficient in pyoverdine production was analyzed using an arbitrary polymerase chain reaction (PCR) approach to map the sites of Tn5 insertions in the genome of Pseudomonas fluorescens Pf-5. The arbitrary PCR method involved two rounds of reactions, with the fi...
Phase Matching of SHG in Arbitrary Directions of Biaxial Crystals
YANG Shengli; CHEN Mouzhi
2002-01-01
In this paper, propagation and polarization characteristics of optical waves in arbitrary directions in a biaxial crystal are analyzed, and universal relationships of refractive index dependence on their propagation directions and the principal refractive indices for two perpendicular polarization waves propagating in arbitrarily directions are derived from indicatrix equation. By using these relationships, methods of collinear phase matching (PM) of SHG are developed, and general expressions of the collinear PM angle dependent of the principal indices are given for SHG in arbitrarily directions. The expressions may be used to make optimization design of PM by computer for the SHG and to select optimum PM direction and to raise the SHG conversion efficiencies.
Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix
Fengjuan Zhu
2013-01-01
Full Text Available In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed.
Classification of arbitrary multipartite entangled states under local unitary equivalence
We propose a practical method for finding the canonical forms of arbitrary dimensional multipartite entangled states, either pure or mixed. By extending the technique developed in one of our recent works, the canonical forms for the mixed N-partite entangled states are constructed where they have inherited local unitary symmetries from their corresponding N + 1 pure state counterparts. A systematic scheme to express the local symmetries of the canonical form is also presented, which provides a feasible way of verifying the local unitary equivalence for two multipartite entangled states. (paper)
Duality for massive spin two theories in arbitrary dimensions
Gonzalez, B; Khoudeir, A.; Montemayor, R.; Urrutia, L. F.
2008-01-01
Using the parent Lagrangian approach we construct a dual formulation, in the sense originally proposed by Curtright and Freund, of a massive spin two Fierz-Pauli theory in arbitrary dimensions $D$. This is achieved in terms of a mixed symmetry tensor $T_{A[B_{1}B_{2}... B_{D-2}]}$, without the need of auxiliary fields. The relation of this method with an alternative formulation based on a gauge symmetry principle proposed by Zinoviev is elucidated. We show that the latter formulation in four ...
A symplectic integrator with arbitrary vector and scalar potentials
We study a new class of symplectic integrators for particles in arbitrary, time-dependent vector and scalar potentials. The methods were introduced in [Y.K. Wu, E. Forest, D.S. Robin, Phys. Rev. E 68 (2003) 046502] and are based on the ability to integrate Hamiltonians of the form (pi-ai(q))2 exactly for a finite time-step. We show that the integrators are symplectic in the non-relativistic case but not symplectic in the full six-dimensional phase space for relativistic Hamiltonians
NEW DESIGN OF ROBUST OPTIMAL ARBITRARY TIME-DELAY FILTER
WANG Xiaojun; SHAO Huihe
2007-01-01
Zero placement method in the frequency domain is utilized to design robust multi-hump EI optimal arbitrary time-delay filter (OATF) by placing two or more filter zeros near the system poles. A total insensitive OATF can be also achieved if the problem of insensitivity to damping errors is considered. This design strategy is easier to derive and implement. Applications in the anti-swing control of overhead cranes verify the fine performance of this strategy. A better suppression of the load vibrations is obtained using the proposed new OATF, which is more robust to the variation of the cable length.
Multiboson Correlation Interferometry with arbitrary single-photon pure states
Tamma, Vincenzo; Laibacher, Simon
2014-01-01
We provide a compact full description of multiboson correlation measurements of arbitrary order N in passive linear interferometers with arbitrary input single-photon pure states. This allows us to physically analyze the novel problem of multiboson correlation sampling at the output of random linear interferometers. Our results also describe general multiboson correlation landscapes for an arbitrary number of input single photons and arbitrary interferometers. In particular, we use two differ...
Arbitrary Finite-time Tracking Control for Magnetic Levitation Systems
Xuan-Toa Tran
2014-10-01
Full Text Available In this paper, an arbitrary finite-time tracking control (AFTC method is developed for magnetic levitation systems with uncertain dynamics and external disturbances. By introducing a novel augmented sliding- mode manifold function, the proposed method can eliminate the singular problem in traditional terminal sliding-mode control, as well as the reaching-phase problem. Moreover, the tracking errors can reach the reference value with faster convergence and better tracking precision in arbitrarily determined finite time. In addition, a fuzzy-arbitrary finite-time tracking control (F- AFTC scheme that combines a fuzzy technique with AFTC to enhance the robustness and sliding performance is also proposed. A fuzzy logic system is used to replace the discontinuous control term. Thus, the chattering phenomenon is resolved without degrading the tracking performance. The stability of the closed-loop system is guaranteed by the Lyapunov theory. Finally, the effectiveness of the proposed methods is illustrated by simulation and experimental study in a real magnetic levitation system.
Circuits with arbitrary gates for random operators
Jukna, S.; Schnitger, G.
2010-01-01
We consider boolean circuits computing n-operators f:{0,1}^n --> {0,1}^n. As gates we allow arbitrary boolean functions; neither fanin nor fanout of gates is restricted. An operator is linear if it computes n linear forms, that is, computes a matrix-vector product y=Ax over GF(2). We prove the existence of n-operators requiring about n^2 wires in any circuit, and linear n-operators requiring about n^2/\\log n wires in depth-2 circuits, if either all output gates or all gates on the middle laye...
Path integrals for arbitrary canonical transformations
Some aspects of the path integral formulation of quantum mechanics are studied. This formalism is generalized to arbitrary canonical transformations, by means of an association between path integral probalility amplitudes and classical generators of transformations, analogous to the usual Hamiltonian time development phase space expression. Such association turns out to be equivalent to the Weyl quantization rule, and it is also shown that this formalism furnishes a path integral representation for a Lie algebra of a given set of classical generators. Some physical considerations about the path integral quantization procedure and about the relationship between classical and quantum dynamical structures are also discussed. (Author)
Solving the Homogeneous Boltzmann Equation with Arbitrary Scattering Kernel
Hohenegger, A
2008-01-01
With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space homogeneous Boltzmann equation with isotropic distribution function to arbitrary matrix elements. The method is based on the expansion of the matrix element in terms of two cosines of the "scattering angles". The scattering functions used by previous authors in particle physics for matrix elements in Fermi-approximation are retrieved as lowest order results in this expansion. The method is designed for the unified treatment of reactive mixtures of particles obeying different scattering laws, including the quantum statistical terms for blocking or stimulated emission, in possibly large networks of Boltzmann equations. Although our notation is the relativistic one, as it is used in astroparticle physics, the results can also be applied in the classical case.
Solving the homogeneous Boltzmann equation with arbitrary scattering kernel
With applications in astroparticle physics in mind, we generalize a method for the solution of the nonlinear, space-homogeneous Boltzmann equation with an isotropic distribution function to arbitrary matrix elements. The method is based on the expansion of the scattering kernel in terms of two cosines of the 'scattering angles'. The scattering functions used by previous authors in particle physics for matrix elements in the Fermi approximation are retrieved as lowest order results in this expansion. The method is designed for the unified treatment of reactive mixtures of particles obeying different scattering laws, including the quantum statistical terms for blocking or stimulated emission, in possibly large networks of Boltzmann equations. Although our notation is the relativistic one, as it is used in astroparticle physics, the results can also be applied in the classical case.
Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits
We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates. The plates represent shielding due to the vacuum chamber. The vertical distribution of charge is an arbitrary fixed function. Our goal is to follow the time evolution of the phase space distribution by solving the Vlasov-Maxwell equations in the time domain. This provides simulations with lower numerical noise than the macroparticle method, and allows one to study such issues as emittance degradation and microbunching due to CSR in bunch compressors. The fields excited by the bunch are computed in the laboratory frame from a new formula that leads to much simpler computations than the usual retarded potentials or Lienard-Wiechert potentials. The nonlinear Vlasov equation, formulated in the interaction picture, is integrated in the beam frame by approximating the Perron-Frobenius operator. The distribution function is represented by B-splines, in a scheme preserving positivity and normalization of the distribution. For application to a chicane bunch compressor we take steps to deal with energy chirp, an initial near-perfect correlation of energy with position in the bunch
Double layers and double wells in arbitrary degenerate plasmas
Akbari-Moghanjoughi, M.
2016-06-01
Using the generalized hydrodynamic model, the possibility of variety of large amplitude nonlinear excitations is examined in electron-ion plasma with arbitrary electron degeneracy considering also the ion temperature effect. A new energy-density relation is proposed for plasmas with arbitrary electron degeneracy which reduces to the classical Boltzmann and quantum Thomas-Fermi counterparts in the extreme limits. The pseudopotential method is employed to find the criteria for existence of nonlinear structures such as solitons, periodic nonlinear structures, and double-layers for different cases of adiabatic and isothermal ion fluids for a whole range of normalized electron chemical potential, η0, ranging from dilute classical to completely degenerate electron fluids. It is observed that there is a Mach-speed gap in which no large amplitude localized or periodic nonlinear excitations can propagate in the plasma under consideration. It is further revealed that the plasma under investigation supports propagation of double-wells and double-layers the chemical potential and Mach number ranges of which are studied in terms of other plasma parameters. The Mach number criteria for nonlinear waves are shown to significantly differ for cases of classical with η0 0 regimes. It is also shown that the localized structure propagation criteria possess significant dissimilarities for plasmas with adiabatic and isothermal ions. Current research may be generalized to study the nonlinear structures in plasma containing positrons, multiple ions with different charge states, and charged dust grains.
Spin susceptibility of Anderson impurities in arbitrary conduction bands
Fang, Tie-Feng; Tong, Ning-Hua; Cao, Zhan; Sun, Qing-Feng; Luo, Hong-Gang
2015-10-01
Spin susceptibility of Anderson impurities is a key quantity in understanding the physics of Kondo screening. Traditional numerical renormalization group (NRG) calculation of the impurity contribution χimp to susceptibility, defined originally by Wilson in a flat wide band, has been generalized before to structured conduction bands. The results brought about non-Fermi-liquid and diamagnetic Kondo behaviors in χimp, even when the bands are not gapped at the Fermi energy. Here, we use the full density-matrix (FDM) NRG to present high-quality data for the local susceptibility χloc and to compare them with χimp obtained by the traditional NRG. Our results indicate that those exotic behaviors observed in χimp are unphysical. Instead, the low-energy excitations of the impurity in arbitrary bands only without gap at the Fermi energy are still a Fermi liquid and paramagnetic. We also demonstrate that unlike the traditional NRG yielding χloc less accurate than χimp, the FDM method allows a high-precision dynamical calculation of χloc at much reduced computational cost, with an accuracy at least one order higher than χimp. Moreover, artifacts in the FDM algorithm to χimp and origins of the spurious non-Fermi-liquid and diamagnetic features are clarified. Our work provides an efficient high-precision algorithm to calculate the spin susceptibility of impurity for arbitrary structured bands, while negating the applicability of Wilson's definition to such cases.
Vlasov treatment of coherent synchrotron radiation from arbitrary planar orbits
Warnock, R.; Bassi, G.; Ellison, J. A.
2006-03-01
We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates which represent the vacuum chamber. Our goal is to follow the time evolution of the phase space distribution by solving the Vlasov-Maxwell equations in the time domain. This should provide simulations with lower numerical noise than the macro-particle method, and allow one to study such issues as emittance degradation and microbunching due to CSR in bunch compressors. The fields excited by the bunch are computed in the laboratory frame from a new formula that leads to much simpler computations than usual methods. The nonlinear Vlasov equation, formulated in the interaction picture, is integrated in the beam frame by approximating the Perron-Frobenius operator. For application to a chicane bunch compressor we take steps to deal with energy chirp.