Coordinate Transformation (coordinate + transformation)

Distribution by Scientific Domains
Distribution within Engineering

Selected Abstracts

General Gyrokinetic Equations for Edge Plasmas

H. Qin
Abstract During the pedestal cycle of H-mode edge plasmas in tokamak experiments, large-amplitude pedestal build-up and destruction coexist with small-amplitude drift wave turbulence. The pedestal dynamics simultaneously includes fast time-scale electromagnetic instabilities, long time-scale turbulence-induced transport processes, and more interestingly the interaction between them. To numerically simulate the pedestal dynamics from first principles, it is desirable to develop an effective algorithm based on the gyrokinetic theory. However, existing gyrokinetic theories cannot treat fully nonlinear electromagnetic perturbations with multi-scale-length structures in spacetime, and therefore do not apply to edge plasmas. A set of generalized gyrokinetic equations valid for the edge plasmas has been derived. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. It turns out that the most general gyrokinetic theory can be geometrically formulated. The Poincaré-Cartan-Einstein 1-form on the 7D phase space determines particles' worldlines in the phase space, and realizes the momentum integrals in kinetic theory as fiber integrals. The infinitesimal generator of the gyro-symmetry is then asymptotically constructed as the base for the gyrophase coordinate of the gyrocenter coordinate system. This is accomplished by applying the Lie coordinate perturbation method to the Poincaré-Cartan-Einstein 1-form. General gyrokinetic Vlasov-Maxwell equations are then developed as the Vlasov-Maxwell equations in the gyrocenter coordinate system, rather than a set of new equations. Because the general gyrokinetic system developed is geometrically the same as the Vlasov-Maxwell equations, all the coordinate-independent properties of the Vlasov-Maxwell equations, such as energy conservation, momentum conservation, and phase space volume conservation, are automatically carried over to the general gyrokinetic system. The pullback transformation associated with the coordinate transformation is shown to be an indispensable part of the general gyrokinetic Vlasov-Maxwell equations. As an example, the pullback transformation in the gyrokinetic Poisson equation is explicitly expressed in terms of moments of the gyrocenter distribution function, with the important gyro-orbit squeezing effect due to the large electric field shearing in the edge and the full finite Larmour radius effect for short wavelength fluctuations. The familiar "polarization drift density" in the gyrocenter Poisson equation is replaced by a more general expression. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Speed estimation of induction motor drive using d -axis slot harmonics and parameter identification method

Toshihiko Noguchi
Abstract This paper describes a rotor speed estimation technique of an induction motor, which utlizes slot harmonics on the d -axis caused by permeance variation across the air gap. The frequency of the slot harmonics is a multiple of the actual rotor speed, and is proportional to the number of rotor slots. In order to extract the slot harmonics, a novel adaptive bandpass filter incorporating coordinate transformation is proposed, which is effective to estimate the rotor speed from 400 to 2000 rpm. This rotor speed estimation is applied to a field-oriented controller as well as a speed controller. In addition, performance improvement is carried out by compensating a motor parameter mismatch. Feasibility of the proposed technique is confirmed through several tests, using a prototype experimental setup. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 171(2): 50,58, 2010; Published online in Wiley InterScience (www. DOI 10.1002/eej.20901 [source]

Is there a role of visual cortex in spatial hearing?

Ulrike Zimmer
Abstract The integration of auditory and visual spatial information is an important prerequisite for accurate orientation in the environment. However, while visual spatial information is based on retinal coordinates, the auditory system receives information on sound location in relation to the head. Thus, any deviation of the eyes from a central position results in a divergence between the retinal visual and the head-centred auditory coordinates. It has been suggested that this divergence is compensated for by a neural coordinate transformation, using a signal of eye-in-head position. Using functional magnetic resonance imaging, we investigated which cortical areas of the human brain participate in such auditory,visual coordinate transformations. Sounds were produced with different interaural level differences, leading to left, right or central intracranial percepts, while subjects directed their gaze to visual targets presented to the left, to the right or straight ahead. When gaze was to the left or right, we found the primary visual cortex (V1/V2) activated in both hemispheres. The occipital activation did not occur with sound lateralization per se, but was found exclusively in combination with eccentric eye positions. This result suggests a relation of neural processing in the visual cortex and the transformation of auditory spatial coordinates responsible for maintaining the perceptual alignment of audition and vision with changes in gaze direction. [source]

Numerical analysis of turbulent flow separation in a rectangular duct with a sharp 180-degree turn by algebraic Reynolds stress model

Hitoshi Sugiyama
Abstract Turbulent flow in a rectangular duct with a sharp 180-degree turn is difficult to predict numerically because the flow behavior is influenced by several types of forces, including centrifugal force, pressure-driven force, and shear stress generated by anisotropic turbulence. In particular, this type of flow is characterized by a large-scale separated flow, and it is difficult to predict the reattachment point of a separated flow. Numerical analysis has been performed for a turbulent flow in a rectangular duct with a sharp 180-degree turn using the algebraic Reynolds stress model. A boundary-fitted coordinate system is introduced as a method for coordinate transformation to set the boundary conditions next to complicated shapes. The calculated results are compared with the experimental data, as measured by a laser-Doppler anemometer, in order to examine the validity of the proposed numerical method and turbulent model. In addition, the possibility of improving the wall function method in the separated flow region is examined by replacing the log-law velocity profile for a smooth wall with that for a rough wall. The analysis results indicated that the proposed algebraic Reynolds stress model can be used to reasonably predict the turbulent flow in a rectangular duct with a sharp 180-degree turn. In particular, the calculated reattachment point of a separated flow, which is difficult to predict in a turbulent flow, agrees well with the experimental results. In addition, the calculation results suggest that the wall function method using the log-law velocity profile for a rough wall over a separated flow region has some potential for improving the prediction accuracy. Copyright © 2007 John Wiley & Sons, Ltd. [source]

On the use of high-order finite-difference discretization for LES with double decomposition of the subgrid-scale stresses

J. Meyers
Abstract Large eddy simulation (LES) with additional filtering of the non-linear term, also coined LES with double decomposition of the subgrid-scale stress, is considered. In the literature, this approach is mainly encountered in combination with pseudo-spectral discretization methods. In this case, the additional filter is a sharp cut-off filter, which appears in the eventual computational algorithm as the 2/3-dealiasing procedure. In the present paper, the LES approach with additional filtering of the non-linear term is evaluated in a spatial, finite-difference discretization approach. The sharp cut-off filter used in pseudo-spectral methods is then replaced by a ,spectral-like' filter, which is formulated and discretized in physical space. As suggested in the literature, the filter width , of this spectral-like filter corresponds at least to 3/2 times the grid spacing h to avoid aliasing. Furthermore, spectral-like discretization of the derivatives are constructed such that derivative-discretization errors are low in the wavenumber range resolved by the filter, i.e. 0,kh,2,/3. The resulting method in combination with a Smagorinsky model is tested for decaying homogeneous isotropic turbulence and compared to standard lower-order discretization methods. Further, an analysis is elaborated of the Galilean-invariance problem, which arises when LES in double decomposition approach is combined with filters, which do not correspond to an orthogonal projection. The effects of a Galilean coordinate transformation on LES results, are identified in simulations, and we demonstrate that a Galilean transformation leads to wavenumber-dependent shifts of the energy spectra. Copyright © 2007 John Wiley & Sons, Ltd. [source]

A ,-coordinate three-dimensional numerical model for surface wave propagation

Pengzhi Lin
Abstract A three-dimensional numerical model based on the full Navier,Stokes equations (NSE) in , -coordinate is developed in this study. The , -coordinate transformation is first introduced to map the irregular physical domain with the wavy free surface and uneven bottom to the regular computational domain with the shape of a rectangular prism. Using the chain rule of partial differentiation, a new set of governing equations is derived in the , -coordinate from the original NSE defined in the Cartesian coordinate. The operator splitting method (Li and Yu, Int. J. Num. Meth. Fluids 1996; 23: 485,501), which splits the solution procedure into the advection, diffusion, and propagation steps, is used to solve the modified NSE. The model is first tested for mass and energy conservation as well as mesh convergence by using an example of water sloshing in a confined tank. Excellent agreements between numerical results and analytical solutions are obtained. The model is then used to simulate two- and three-dimensional solitary waves propagating in constant depth. Very good agreements between numerical results and analytical solutions are obtained for both free surface displacements and velocities. Finally, a more realistic case of periodic wave train passing through a submerged breakwater is simulated. Comparisons between numerical results and experimental data are promising. The model is proven to be an accurate tool for consequent studies of wave-structure interaction. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Adaptive backstepping control for a class of time delay systems with nonlinear perturbations

Chang-Chun Hua
Abstract The sliding mode control method has been extensively employed to stabilize time delay systems with nonlinear perturbations. Although the resulting closed-loop systems have good transient and steady-state performances, the designed controllers are dependent on the time delays. But one knows that it is difficult to obtain the precise delay time in practical systems, especially when it is time varying. In this paper, we revisit the problem and use the backstepping method to construct the state feedback controller. First, a coordinate transformation is used to obtain a cascade time delay system. Then, a linear virtual control law is designed for the first subsystem. The memoryless controller is further constructed based on adaptive method for the second subsystem with the uncertainties bounded by linear function. By choosing new Lyapunov,Krasovskii functional, we show that the system state converges to zero asymptotically. Via the proposed approach, we also discuss the case that the uncertainties are bounded by nonlinear functions. Finally, simulations are done to verify the effectiveness of the main results obtained. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Observer design for nonlinear discrete-time systems: Immersion and dynamic observer error linearization techniques

Jian Zhang
Abstract This paper focuses on the observer design for nonlinear discrete-time systems by means of nonlinear observer canonical form. At first, sufficient and necessary conditions are obtained for a class of autonomous nonlinear discrete-time systems to be immersible into higher dimensional observer canonical form. Then a method called dynamic observer error linearization is developed. By introducing a dynamic auxiliary system, the augmented system is shown to be locally equivalent to the generalized observer form, whose nonlinear terms contain auxiliary states and output of the system. A constructive algorithm is also provided to obtain the state coordinate transformation. These results are an extension of their counterparts of nonlinear continuous-time systems to nonlinear discrete-time systems (Syst. Control Lett. 1986; 7:133,142; SIAM. J. Control Optim. 2003; 41:1756,1778; Int. J. Control 2004; 77:723,734; Automatica 2006; 42:321,328; IEEE Trans. Automat. Control 2007; 52:83,88; IEEE Trans. Automat. Control 2004; 49:1746,1750; Automatica 2006; 42:2195,2200; IEEE Trans. Automat. Control 1996; 41:598,603; Syst. Control Lett. 1997; 31:115,128). Copyright © 2009 John Wiley & Sons, Ltd. [source]

Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model

Wei Liu
Summary A simultaneous confidence band provides a variety of inferences on the unknown components of a regression model. There are several recent papers using confidence bands for various inferential purposes; see for example, Sun et al. (1999), Spurrier (1999), Al-Saidy et al. (2003), Liu et al. (2004), Bhargava & Spurrier (2004), Piegorsch et al. (2005) and Liu et al. (2007). Construction of simultaneous confidence bands for a simple linear regression model has a rich history, going back to the work of Working & Hotelling (1929). The purpose of this article is to consolidate the disparate modern literature on simultaneous confidence bands in linear regression, and to provide expressions for the construction of exact 1 ,, level simultaneous confidence bands for a simple linear regression model of either one-sided or two-sided form. We center attention on the three most recognized shapes: hyperbolic, two-segment, and three-segment (which is also referred to as a trapezoidal shape and includes a constant-width band as a special case). Some of these expressions have already appeared in the statistics literature, and some are newly derived in this article. The derivations typically involve a standard bivariate t random vector and its polar coordinate transformation. Résumé Un intervalle de confiance simultanée fournit une variété d'inférences sur les composantes inconnues d'un modéle de régression. Plusieurs articles récents utilisent des intervalles de confiance dans des buts variés; voir par exemple Sun, Raz et Faraway (1999), Spurrier (1999), Al-Saidy et al. (2003), Liu, Jamshidian et Zhang (2004), Bhargava et Spurrier (2004), Piegorsch et al. (2005), Liu et al. (2007). La construction d'intervalles de confiance simultanés pour un simple modéle de régression linéaire a une histoire riche, qui remonte aux travaux de Working et hotelling (1929). L'objet de cet article est de consolider la littérature moderne disparate sur les intervalles de confiance simultanés dans la régression linéaire, de fournir des expressions pour la construction d'intervalles de confiance simultanés de niveau exact 1 ,, pour un modéle de régression linéaire simple ou pour des formes unilatérales ou bilatérales. Nous concentrons notre attention sur les trois formes les plus reconnues: hyperbolique, à deux segments et à trois segments (qui est aussi appelée forme trapézoïdale et inclut un intervalle de largeur constante comme cas spécial). Certaines de ces expressions sont déjà apparues dans la littérature statistique, d'autres sont nouvellement introduites dans cet article. Les dérivations comprennent typiquement un vecteur aléatoire standard bivarié t et sa transformation en coordonnées polaires. [source]

Human perception of verticality: Psychophysical experiments on the centrifuge and their neuronal implications

Fred W. Mast
The role of the otoliths in the perception of verticality is analyzed in two different gravitational environments, 1 g and 1.5 g, and in different roll body positions between upright and upside down. The subjective visual vertical (SVV) is determined when a subject judges the orientation of an indicator as apparently vertical. An increase of g level hardly affects the SVV in the subject's frontal plane (y-z plane). However, for the first time, a three-dimensionally adjustable indicator was used for the SVV and this revealed a new phenomenon: An increase of g level induces a backward slant of the SVV into subject's median plane (x-z plane). The data are discussed with regard to Mittelstaedt's SVV theory; particular emphasis is given to the otolith-head coordinate transformation and the normalization of afferent otolith components. The results of this study provide evidence that the former is implemented at an earlier level and thus precedes the latter. [source]

Electromagnetic metamorphosis: Reshaping scatterers via conformal anisotropic metamaterial coatings

Ozlem Ozgun
Abstract We introduce a new technique (in the context of time-harmonic electromagnetic scattering), which renders an object (or scatterer) to be perceived as if it has a different shape, irrespective of the location of the observer. This is achieved through the usage of an anisotropic metamaterial layer, which is designed as conformal to the surface of the scatterer by employing the concept of coordinate transformation. We report some numerical results for finite element simulations of two-dimensional anisotropic metamaterial coatings. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2386,2392, 2007; Published online in Wiley InterScience ( DOI 10.1002/mop.22784 [source]

Locally-conformal perfectly matched layer implementation for finite element mesh truncation

Ozlem Ozgun
Abstract In this article, we introduce the locally conformal perfectly matched layer (PML) technique, which is an easily implementable conformal PML implementation, obtained via complex coordinate transformation, for the purpose of mesh truncation in the finite element method. After deriving the governing equations, we test this technique using electromagnetic scattering problems. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1836,1839, 2006; Published online in Wiley InterScience ( DOI 10.1002/mop.21788 [source]

Two-wave approximation in surface effects in asymmetric Laue crystals

M. Guida
This paper is a study of surface effects, e.g. roughness or asymmetrical cut, in the Laue diffraction of X-rays by crystals, based on the Takagi,Taupin equations. By means of Riemann,Green integrals, first a formal solution has been obtained when the entrance and the exit surfaces are arbitrary. Then a coordinate transformation mapping a propagation domain with arbitrary boundaries into a rectangular domain with straight boundaries is given. Potential measurement errors in -ray wavelength and silicon lattice-parameter measurements by double-crystal diffractometry and X-ray interferometry, respectively, are outlined and anticipated by studying, in the two-wave approximation, the reflection peak shift and extra phase originating from an asymmetrically cut crystal. A relationship between analyser displacement, interferometer-signal phase and relative uncertainty in lattice-parameter measurement is also given. [source]

Scaling turbulent atmospheric stratification.

III: Space, time stratification of passive scalars from lidar data
Abstract In this third and final part of the series, we concentrate on the temporal behaviour of atmospheric passive scalars. We first recall that,although the full (x, y, z, t) turbulent processes respect an anisotropic scale invariance,that due to advection,the generator will generally not be a diagonal matrix. This implies that the scaling of (1-D) temporal series will generally involve three exponents in real space: 1/3, 1/2, 3/5, for spectra ,, = 5/3, 2, 11/5, with the first and last corresponding to domination by advection (horizontal and vertical respectively), and the second to pure temporal development (no advection). We survey the literature and find that almost all the empirical ,, values are indeed in the range 5/3 to 2. We then use meteorological analyses to argue that, although pure temporal development is unlikely to be dominant for time-scales less than the eddy turnover time of the largest structures (about 2 weeks), an intermittent vertical velocity could quite easily explain the occasionally observed ,, , 2 spectra. We then use state-of-the-art vertically pointing lidar data of backscatter ratios from both aerosols and cirrus clouds yielding several (z, t) vertical space,time cross-sections with resolution of 3.75 m in the vertical, 0.5,30 s in time and spanning 3,4 orders of magnitude in temporal scale. We first test the predictions of the anisotropic, multifractal extension of the Corrsin-Obukhov law in the vertical and in time, separately finding that the cirrus and aerosol backscatters both followed the theoretical (anisotropic) scalings accurately; three of the six cases show dominance by the horizontal wind, the others by the vertical wind. In order to test the theory in arbitrary directions in this (z, t) space, and in order to get more complete information about the underlying physical scale, we develop and apply a new Anisotropic Scaling Analysis Technique (ASAT) which is based on a nonlinear space,time coordinate transformation. This transforms the original differential scaling into standard self-similar scaling; there remains only a ,trivial' anisotropy. This method is used in real space on 2-D structure functions. It is applied to both the new (z, t) data as well as the (x, z) data discussed in part II. Using ASAT, we verify the theory to within about 10% over more than three orders of magnitude of space,time scales in arbitrary directions in (x, z) and (z, t) spaces. By considering the high- (and low-) order structure functions, we verify the theory for both weak and strong structures; as predicted, their average anisotropies are apparently the same. Putting together the results for (x, z) and (z, t), and assuming that there is no overall stratification in the horizontal (x, y) plane, we find that the overall (x, y, z, t) space is found to have an effective ,elliptical dimension' characterizing the overall space,time stratification equal to Deff, st = 3.21 ± 0.05. Copyright © 2008 Royal Meteorological Society [source]

Electrodynamics in accelerated frames revisited

J.W. Maluf
Abstract Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space-time. We assume the existence of a general distribution of charges and currents in an inertial frame. Tetrad fields are used to project the electromagnetic fields and sources on accelerated frames. The purpose is to study several configurations of fields and observers that in the literature are understood as paradoxes. For instance, are the two situations, (i) an accelerated charge in an inertial frame, and (ii) a charge at rest in an inertial frame described from the perspective of an accelerated frame, physically equivalent? Is the electromagnetic radiation the same in both frames? Normally in the analysis of these paradoxes the electromagnetic fields are transformed to (uniformly) accelerated frames by means of a coordinate transformation of the Faraday tensor. In the present approach coordinate and frame transformations are disentangled, and the electromagnetic field in the accelerated frame is obtained through a frame (local Lorentz) transformation. Consequently the fields in the inertial and accelerated frames are described in the same coordinate system. This feature allows the investigation of paradoxes such as the one mentioned above. [source]

Is there a role of visual cortex in spatial hearing?

Ulrike Zimmer
Abstract The integration of auditory and visual spatial information is an important prerequisite for accurate orientation in the environment. However, while visual spatial information is based on retinal coordinates, the auditory system receives information on sound location in relation to the head. Thus, any deviation of the eyes from a central position results in a divergence between the retinal visual and the head-centred auditory coordinates. It has been suggested that this divergence is compensated for by a neural coordinate transformation, using a signal of eye-in-head position. Using functional magnetic resonance imaging, we investigated which cortical areas of the human brain participate in such auditory,visual coordinate transformations. Sounds were produced with different interaural level differences, leading to left, right or central intracranial percepts, while subjects directed their gaze to visual targets presented to the left, to the right or straight ahead. When gaze was to the left or right, we found the primary visual cortex (V1/V2) activated in both hemispheres. The occipital activation did not occur with sound lateralization per se, but was found exclusively in combination with eccentric eye positions. This result suggests a relation of neural processing in the visual cortex and the transformation of auditory spatial coordinates responsible for maintaining the perceptual alignment of audition and vision with changes in gaze direction. [source]

Complete semi-analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method

Athanasios G. Polimeridis
Abstract A complete semi-analytical treatment of the four-dimensional (4-D) weakly singular integrals over coincident, edge adjacent and vertex adjacent triangles, arising in the Galerkin discretization of mixed potential integral equation formulations, is presented. The overall analysis is based on the direct evaluation method, utilizing a series of coordinate transformations, together with a re-ordering of the integrations, in order to reduce the dimensionality of the original 4-D weakly singular integrals into, respectively, 1-D, 2-D and 3-D numerical integrations of smooth functions. The analytically obtained final formulas can be computed by using typical library routines for Gauss quadrature readily available in the literature. A comparison of the proposed method with singularity subtraction, singularity cancellation and fully numerical methods, often used to tackle the multi-dimensional singular integrals evaluation problem, is provided through several numerical examples, which clearly highlights the superior accuracy and efficiency of the direct evaluation scheme. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Flow simulation on moving boundary-fitted grids and application to fluid,structure interaction problems

Martin Engel
Abstract We present a method for the parallel numerical simulation of transient three-dimensional fluid,structure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non-overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time-dependent domains. To this end, we present a technique to solve the incompressible Navier,Stokes equation in three-dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time-dependent coordinate transformations. It corresponds to a discretization of the arbitrary Lagrangian,Eulerian formulation of the Navier,Stokes equations. Here the grid velocity is treated in such a way that the so-called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well-known MAC-method to a staggered mesh in moving boundary-fitted coordinates which uses grid-dependent velocity components as the primary variables. To validate our method, we present some numerical results which show that second-order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluid,structure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid,structure interaction problems. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A fourth-order accurate, Numerov-type, three-point finite-difference discretization of electrochemical reaction-diffusion equations on nonuniform (exponentially expanding) spatial grids in one-dimensional space geometry

aw K. Bieniasz
Abstract The validity for finite-difference electrochemical kinetic simulations, of the extension of the Numerov discretization designed by Chawla and Katti [J Comput Appl Math 1980, 6, 189,196] for the solution of two-point boundary value problems in ordinary differential equations, is examined. The discretization is adapted to systems of time-dependent reaction-diffusion partial differential equations in one-dimensional space geometry, on nonuniform space grids resulting from coordinate transformations. The equations must not involve first spatial derivatives of the unknowns. Relevant discrete formulae are outlined and tested in calculations on two example kinetic models. The models describe potential step chronoamperometry under limiting current conditions, for the catalytic EC, and Reinert-Berg CE reaction mechanisms. Exponentially expanding space grid is used. The discretization considered proves the most accurate and efficient, out of all the three-point finite-difference discretizations on such grids, that have been used thus far in electrochemical kinetics. Therefore, it can be recommended as a method of choice. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1515,1521, 2004 [source]

Generalization and numerical investigation of QMOM

AICHE JOURNAL, Issue 1 2007
R. Grosch
Abstract A generalized framework is developed for the quadrature method of moments (QMOM), which is a solution method for population balance models. It further evaluates the applicability of this method to industrial suspension crystallization processes. The framework is based on the concepts of generalized moments and coordinate transformations, which have been used already in earlier solution approaches. It is shown how existing approaches to QMOM are derived from the suggested unified framework. Thus, similarities and differences between the various QMOM methods are uncovered. Further, potential error sources involved in the different approaches to QMOM are discussed and assessed by means of a series of test cases. The test cases are selected to be challenging. The error in the QMOM solution is evaluated by comparison to an adaptive, error controlled solution of the population balance. The behavior of a range of different QMOM formulations is analyzed by means of numerical quadrature, dynamic simulation, as well as numerical continuation and bifurcation analysis. As a result of this detailed analysis, some general limitations of the method are detected and guidelines for its application are developed. This article is limited to lumped population balance models with one internal coordinate. © 2006 American Institute of Chemical Engineers AIChE J, 2007 [source]

Multipolar Ordering in Electro- and Magnetostatic Coupled Nanosystems

CHEMPHYSCHEM, Issue 9 2008
Elena Y. Vedmedenko Dr. habil.
Abstract Electric and magnetic multipole moments and polarizabilities are important quantities in studies of intermolecular forces, non-linear optical phenomena, electrostatic, magnetostatic or gravitational potentials and electron scattering. The experimental determination of multipole moments is difficult and therefore the theoretical prediction of these quantities is important. Depending on purposes of the investigation several different definitions of multipole moments and multipole,multipole interactions are used in the literature. Because of this variety of methods it is often difficult to use published results and, therefore, even more new definitions appear. The first goal of this review is to give an overview of mathematical definitions of multipole expansion and relations between different formulations. The second aim is to present a general theoretical description of multipolar ordering on periodic two-dimensional lattices. After a historical introduction in the first part of this manuscript the static multipole expansion in cartesian and spherical coordinates as well as existing coordinate transformations are reviewed. On the basis of the presented mathematical description multipole moments of several symmetric charge distributions are summarized. Next, the established numerical approach for the calculation of multipolar ground states, namely Monte Carlo simulations, are reviewed. Special emphasis is put on the review of ground states in multipolar systems consisting of moments of odd or even order. The last section is devoted to the magnetization reversal in dense packed nanomagnetic arrays, where the magnetic multipole,multipole interactions play an important role. Comparison between the theory and recent experimental results is given. [source]

An algorithm for the structural analysis of state space: synthesis of nonlinear observers

Virgilio López-Moralès
Abstract The problem addressed is the linearization of multi-input multi-output (MIMO) nonlinear systems by a generalized state coordinates transformation and generalized input,output injection, in order to design an observer. This observer will have linear error dynamics. The goal is to bring together two observers design approaches: a structural one and a numerical one. Necessary and sufficient conditions for the existence of a linearizing generalized state transformation are obtained by an algebraic way and without computing the input,output differential equations. The main result tests integrability conditions of differential one-forms derived from the state space representation and is applicable to a large subclass of nonlinear systems. Copyright © 2001 John Wiley & Sons, Ltd. [source]