Method of Moments

In this paper, we address the issue of estimating the parameters of general multivariate copulas, that is, copulas whose partial derivatives may not exist. To this aim, we consider a weighted least-squares estimator based on dependence coefficients, and establish its consistency and asymptotic normality. The estimator's performance on finite samples is illustrated on simulations and a real dataset.

Freezing is an important step in the manufacturing process of ice-cream and sorbet, since the operating conditions have a strong influence on the micro-structure, and consequently on the sensorial attributes of the final product. This steep of freezing is carried out by a scraped surface heat exchanger (SSHE) where the product quality is conditioned by process conditions as the evaporation temperature of a refrigerant fluid, the mix flow rate, the dasher speed and the cylinder pressure due to the air introduction. In order to study the relevance of a control system based on the influence of process variables on product quality, this paper presents a model for a continuous crystallization of a sorbet using the method of moments, which is validated by experimental data.The model created by this methodology has been able to represent the influence of the process conditions during the crystallization of the sorbet on the final product characteristics such as crystal size and the draw temperature in the outlet of the SSHE in absence of air. The model based in moments is studied as a reduced model of the population balance equation and includes the phenomena of heterogeneous nucleation and growth. This model developed represents minimal computational requirements and is highly adapted for optimization and/or process control tasks.

La etapa de precongelación es un importante paso en el proceso de manufactura de helados y sorbetes dado que las condiciones de operación tienen una fuerte influencia sobre la microestructura y por consecuencia sobre los atributos sensoriales del producto final. Esta etapa de precongelación es llevada a cabo en un intercambiador de calor de superficie raspada donde la calidad del producto es fuertemente influenciada por las condiciones de operación tales como la temperatura de evaporación de un refrigerante, el gasto másico de la alimentación, la velocidad del raspador y una presión provocada por la introducción de aire. Con la finalidad de estudiar la pertinencia de un sistema de control basado en la influencia de las variables del proceso sobre la calidad del producto, este trabajo presenta un modelo para una cristalización continua de un sorbete utilizando la metodología de momentos, el cual es validado con datos experimentales. El modelo realizado por esta metodología de momentos es capaz de representar la influencia de las condiciones de operación durante la cristalización de sorbete sobre las características finales del producto tales como el tama ño de cristal y la temperatura de salida del intercambiador de superficie raspada (ICSR) en ausencia de aire. El modelo basado en momentos se estudia, entonces, como la reducción del modelo de la ecuación de balance de población e incluye los fenómenos de nucleación heterogénea y crecimiento. De este modo, el modelo desarrollado representa requerimientos computacionales mínimos y está altamente adaptado para tareas de optimización y/o control del proceso.

Alle rechten voorbehouden. Niets uit deze uitgave mag worden vermenigvuldigd en/of openbaar gemaakt worden door middel van druk, fotokopie, microfilm, elektronisch of op welke andere wijze ook zonder voorafgaande schriftelijke toestemming van de uitgever. All rights reserved. No part of the publication may be reproduced in any form by print, photoprint, microfilm or any other means without written permission from the publisher. D/2013/7515/110 ISBN 978-94-6018-724-7 noodzakelijk zijn om de aanzet van ovaliserende trillingen in silogroepen realistisch te kunnen voorspellen met numerieke technieken.

In this paper, experimental and theoretical evaluation of coupling of electromagnetic radiation is reported. Validation of the results is obtained by comparing the experimental data with theoretical data both generated using CONCEPT Simulator and data from our hybrid MoM/FDTD formulation for the analysis of metallic enclosure with apertures. Both the CONCEPT Simulator and the hybrid MoM/FDTD formulation utilize the method of moments, however, the hybridization of the latter makes it more adaptive to the solutions of apertures of arbitrary shape within enclosures with inhomogeneous dielectrics. The problems analyzed are rectangular slot, cross-shaped aperture and diamondshaped aperture. The experimental results and MoM/FDTD results also agree fairly well with those available in the literature.

This paper presents an analysis of radiation and absorption properties of cylindrical gold nanodipoles in the transmitting mode. The conventional antenna theory and the linear method of moments are used for the theoretical analysis of these antennas in the near-infrared and lower optical frequencies (100-500THz). Radiation and absorption parameters, such as input impedance, efficiency, radiation and loss resistance are calculated in function of frequency for different dipole's lengths and radii. The presented results can be useful to design efficient nanodipoles and to perform the input impedance matching of these antennas with plasmonic optical transmission lines.

A generalized three-dimensional computational numerical code is developed for Monolithic Microwave Integrated Circuit (MMIC) structures based on a full wave approach using integral equation techniques. The electromagnetic properties of the MMIC structures are calculated using a Method of Moments -Galerkin technique based on integral equations and the relevant Green function to obtain a rigorous formulation. The MMIC structures are assumed to have an arbitrary geometry involving orthogonal parallelepiped 'cells', each one of which is characterized with finite permittivity and conductivity values. A novel approach is proposed to treat the incident: reflected and transmitted waves at the two microstrip lines, which stand as input and output of the circuit. Their current distribution is also being taken into account in terms of incident, reflected and transferred waves. The derived matrix is being inverted and the obtained results are the unknown coefficients of the plane waves inside the 'cells' and also the reflection R and transfer T coefficients. The derived numerical results concern linear cases, while the examination of non-linear structures have been taken into account in the analytical formulation.

An efficient and accurate hybrid method, based on the combination of the method of moments (MoM) with a special Green's function in the space domain is presented to analyze antennas and array elements conformal to electrically large material coated circular cylinders. The efficiency and accuracy of the method depend strongly on the computation of the Green's function, which is the kernel of the integral equation that is solved via MoM for the unknown equivalent currents representing only the antenna elements. Three types of space-domain Green's function representations are used, each accurate and computationally efficient in a given region of space. Consequently, a computationally optimized analysis tool for conformal microstrip antennas is obtained. Input impedance of various microstrip antennas and mutual coupling between two identical antennas are calculated and compared with published results to assess the accuracy of this hybrid method.

In this paper an efficient method is proposed for computing electromagnetic wave propagation over terrain profiles. The paper extends the Tabulated Interaction Method (TIM) , applying it to the problem of 2D wave scattering from lossy surfaces using a coupled surface integral equation formulation. The proposed method is compared with the recently proposed Chacracteristic Basis Function Method (CBFM) [2], with which it shares several features. The numerical analysis demonstrates that TIM has a dramatically lower computational complexity and storage than CBFM.

Numerical modeling is now an essential part of undergraduate engineering education. This paper reviews the content and delivery of a course for undergraduate engineers, in computational and visual electromagnetics using the integrated programming language, Matlab. A number of numerical methods are discussed including FDM, FEM, MOM and BEM during class. Matlab is then used to implement these methods in a series of workshops, laboratories exercises and assignments.

In this paper, a new five-parameter lifetime distribution called beta generalized linear exponential distribution (BGLED) is introduced. It includes at least 17 popular sub-models as special cases such as the beta linear exponential, the beta generalized exponential, and the exponentiated generalized linear distributions. Mathematical and statistical properties of the proposed distribution are discussed in details. In particular, explicit expression for the density function, moments, asymptotics distributions for sample extreme statistics, and other statistical measures are obtained. The estimation of the parameters by the method of maximum-likelihood is discussed and the finite sample properties of the maximum-likelihood estimators (MLEs) are investigated numerically. A real data set is used to demonstrate its superior performance fit over several existing popular lifetime models.

The transient response of thin-wire structures in the presence of a multilayer medium is investigated by means of a new formulation of the method of moments in the time domain (MoM-TD). The proposed mathematical model is based on a novel representation of the time-domain mixed potential integral equation (TD-MPIE) for thin-wire structures located above a multilayer medium through recently developed closed-form time-domain Green's functions called complex-time Green's functions. The time-domain integral equation is solved by using MoM-TD along with marching-on-in-time (MOT) procedure resulting in the space -time current distribution on the thin-wire structure being stimulated by an arbitrary time-varying source. The numerical results are verified by comparison with other known methods. Accuracy, stability and numerical efficiency are the main advantages of the developed method. In this paper, we utilise newly developed time-domain Green's functions for multilayer media called complex-time

An accurate and efficient technique is developed to calculate the current distribution over the cross-section and close to the corners of a high-temperature superconducting (WTS) strip in a stripline structure. The problem is formulated in terms of a set of coupled integral equations for the axial electric field inside and outside of the strip. An accurate and fast converging complex images Green's function is derived for the exterior region. Numerical results are presented for a typical HTS stripline. Non-singular behaviour of the current density distribution close to the corners is demonstrated.

A new and efficient differential global surface impedance (DGSI) model has been developed for the analysis of periodic structures. The proposed rigorous model makes use of the equivalence principle to relate the surface electric current and the tangential electric field on the boundary of the object made of a general medium. This approach not only enables one to limit the discretization to the surface of the object located in one unit cell of the periodic structure but also eliminates the need for equivalent surface magnetic current in applying the equivalence principle. These advantages result in a great reduction in the need for computational resources and time. The use of an efficient periodic Green's function by employing the complex images technique combined with the proposed DGSI model has increased the numerical efficiency of the proposed method. A number of dielectric periodic structures made of an array of cylinders with circular or square cross sections have been analyzed by this method. Accuracy of the proposed method as well as its numerical efficiency have been demonstrated by comparing its results with other methods in the literature employing surface and volume integral equations. © 2017 Optical Society of America OCIS codes: (050.1755) Computational electromagnetic methods; (050.2770) Gratings; (000.3860) Mathematical methods in physics; (000.4430) Numerical approximation and analysis.

An integral equation method employing complex images Green's functions is developed for analyzing different devices fabricated in 2-D dielectric photonic crystals. The integral equation is written in terms of the unknown equivalent current sources flowing on the surfaces of the periodic 2-D cylinders. The method of moments is then employed to solve for the unknown current distributions. The required Green's function of the problem is represented in terms of a finite summation of complex images instead of the conventional slowly converging infinite series. It is shown that when the field-point is far from the periodic sources, it is just sufficient to consider the contribution of the propagating poles in the structure. This will result in a summation of plane waves that has an even smaller size compared with the conventional complex images Green's function. This will enable us to analyze the dielectric periodic structures efficiently and accurately. The method is applied to a number of waveguide structures and its results are compared with the existing literature. Terms-Complex images, integral equation method, method of moments (MoM), periodic Green's function, photonic crystal devices. I. INTRODUCTION P HOTONIC crystals, proposed by Yablonovitch [1] and John [2], are now a popular subject of photonic researches. Photonic crystal, a periodic material with a photonic band gap, has a potential capability in manipulating and controlling light. It leads to design of applications to the bandgap devices [3], including optical waveguides, couplers, and high-quality resonant cavities [4]. Many numerical techniques have been developed and used for investigating the wave propagation behavior of different photonic crystal structures. Plane wave expansion method [5], transmission line method [6], finite difference [7] and finite-element [8] methods, the pseudospectral method [9], and time-domain techniques including the most popular finite-difference time domain [10], [11] and integral equation techniques [12] have been presented capable of analyzing these structures. The Floquet-Bloch theorem limits the analysis to a unit cell. When applying integral equation techniques to this cell, it is nec-

The transient scattering of a thin wire buried in a halfspace is calculated by a novel Time-Domain Mixed Potential Integral Equation (TD-MPIE), using complex-time Green's functions. The TD-MPIE is solved by MoM in time domain along with a Marching-On-in-Time (MOT) procedure. The excitation is a Gaussian plane wave and Band-Limited Second-Order Lagrange (BL-2L) functions are used as Temporal Basis Functions (TBFs). Numerical results show that the solution using BL-2L TBFs is stable and accurate, without late-time instabilities, and efficient in computation.

To reduce the risk of damage due to lightning for electrical and electronic systems within a structure, lightning protection system have to be properly designed. This paper illustrate the influence of the main factors and parameters which affect the selection and installation of surge protective device (SPD) in protecting against surge on power line. The two types of SPD are manufactured according to the most typical technology are considered, namely Metal Oxide Varistor (MOV) and Triggered Spark Gap (TSG). From there, the basic recommendations are given in the effective selection SPD in protecting against surge on power line.

By combining the work of J. R. Wait on a periodically loaded vertical wire grid and the work of D. A. Hill and J. R. Wait on a wire mesh, a novel generalized formulation, the Wait-Hill formulation, is obtained for the analysis of lumped-element periodically-loaded orthogonal wire grid generic frequency selective surfaces. The Wait-Hill formulation is simple and not restricted by the miniaturization assumption of current approximate simple methods for the analysis of loaded and unloaded wire grids. The results of the Wait-Hill formulation are shown to agree well with those of a commercial software.

The presented method can be adapted easily for the calculation of other characteristics of inhomogeneous DRs such as field distributions inside or radiation patterns. REFERENCES 1. A.A. Kucharski, Resonances in inhomogeneous dielectric bodies of revolution placed in the multilayered mediaᎏTE modes, Ž . Microwave Opt Technol Lett 21 1999 1᎐4. 2. A.A. Kucharski, Resonances in inhomogeneous dielectric bodies of revolution placed in the multilayered mediaᎏHEM modes, Ž .

The radial stub as a key microstrip structure to provide low impedance levels with a well‐defined insertion point is proposed. Its characterization through a planar approach provides a superior accuracy, as compared with the simulations attainable from presently available CAD packages. Some experiments have fully confirmed the design. Furthermore, the flexibility of radial lines in replacing both open and shorted straight stubs is demonstrated together with some successful results, achieved through their use in practical applications.

In this article, a novel hybrid method of multilevel kernel degeneration and adaptive cross approximation (MLKD-ACA) algorithm with integral kernel truncations is proposed to accelerate solving integral equations using method of moments (MoM), and to simulate the 3D eddy current nondestructive evaluation (NDE) problems efficiently. The MLKD-ACA algorithm with an integral kernel-truncations-based fast solver is symmetrical in the sense that: (1) the impedance matrix, which is generated by the MoM representing the interactions among the field and source basis functions, is symmetrical; (2) the factorized form of the integral kernel (Green's function) resulted from degenerating it by the Lagrange polynomial interpolation is symmetrical; (3) the structure of the truncated integral kernel for the interactions among the blocks, which ignores the trivial ones of the far block pairs, is symmetrical using the integral kernel truncations technique. The impedance variations predicted by the proposed symmetrical eddy current NDE solver are compared with other methods in benchmarks to show the remarkable accuracy and efficiency.

In this article, a novel hybrid method of multilevel kernel degeneration and adaptive cross approximation (MLKD-ACA) algorithm with integral kernel truncations is proposed to accelerate solving integral equations using method of moments (MoM), and to simulate the 3D eddy current nondestructive evaluation (NDE) problems efficiently. The MLKD-ACA algorithm with an integral kernel-truncations-based fast solver is symmetrical in the sense that: (1) the impedance matrix, which is generated by the MoM representing the interactions among the field and source basis functions, is symmetrical; (2) the factorized form of the integral kernel (Green’s function) resulted from degenerating it by the Lagrange polynomial interpolation is symmetrical; (3) the structure of the truncated integral kernel for the interactions among the blocks, which ignores the trivial ones of the far block pairs, is symmetrical using the integral kernel truncations technique. The impedance variations predicted by the pr...

A discrete Fourier transform (DFT)-based iterative method of moments (IMoM) algorithm is developed to provide an O(N tot ) computational complexity and memory storages for the efficient analysis of electromagnetic radiation/scattering from large phased arrays. Here, N tot is the total number of unknowns. Numerical results for both printed and free-standing dipole arrays are presented to validate the algorithm's efficiency and accuracy.

Recently a discrete Fourier transform–method of moments (DFT‐MoM) scheme was developed for fast analysis of electrically large rectangular planar dipole arrays, which has been shown to be very efficient in terms of number reduction of unknown variables and computational complexity. The applications of this DFT‐MoM to treat dipole arrays printed on a grounded dielectric substrate are examined in this Letter. Numerical results are presented to validate its efficiency and accuracy. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 203–207, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10417

The purpose of this paper is to investigate the model of the static tool influence function (sTIF) of bonnet polishing (BP). Three kinds of sTIF are mathematically modeled, which are static tool influence function of tilted polishing (sTIF t ), static tool influence function of discrete precession polishing (sTIF d ), and static tool influence function of continuous precession (sTIF c ), respectively. Pressure distribution in the contact area is confirmed based on finite element analysis (FEA) technology. A group of experiments to extract the polishing spots have been conducted to verify the accuracy of the sTIF model. Meanwhile, the difference between sTIF d and sTIF c is studied. It turns out that the removal depths of sTIF d and sTIF c are almost the same, and the continuous precession polishing can be replaced by discrete precession polishing to ease control in practical polishing process especially for the aspheric surfaces polishing.

Approved for public release; distribution unlimited. This work was supported in part by the National Science Foundation under Grant ECS-7921354 19. KEY WORDS (Continue on r9V0Tam mid* U necmmamry and IdmntUy by block numbmr) capacitive posts Obstacles in waveguides diaphragms Waveguide discontinuities inductive posts Waveguide junctions method of moments i 1 ( \ c 1 20. ABSTRACT (Conlinu* on rtvf tid* H nmcfary and Idtntlty by block numbtr) Three systems of waveguide discontinuities are considered. The first 3ystem is that of multiple apertures of arbitrary shape in the transverse plane Detween two cylindrical waveguides. The second system consists of metallic obstacles in a rectangular waveguide that are uniform along the narrow side of «?aveguide but are otherwise of arbitrary shape and thickness, i.e., a system 3f inductive posts. The third system consists of metallic obstacles in a rec-;anguar waveguide that are uniform along the broad side of the waveguide, but (cont'd) DD ,^ FORM 1^7, AN 73 14/J EDITION OF

The latest specifications detailing the test waveforms for indirect Ligbttransients as applied to aircraft Wtia systems speCiry very high voltages and currents. Althougb considerable data exists for measca 6 le screen leakage usingsuch metbods as Surface Transfer lm@anct and Bulk cable Injection there is lrttle data on the likely core transient level that u likely to be rnduced from tbcse threats. In particular the new Waveform 5 at very high current levels (1OkA) IS reputed to cause seyere cable damqe. A range of represemtative cables were made with various screen termmation techniques and screening levels. These were tested first to determine their relative screening performance and then they were subected to lightning transient testing to all the specified waveforms. Core voltages were measured for Testswere also performed on bundles with fewer wires to determine the failure criteria with waveforn 5 and these tests also mcluded Flat Conductor Cables. The test showed that correctl...

To obtain the moments estimates we would have the relationship n a, / Za = ,. Since there is no constraint on the a, 's , we need an extra equation There is no unique criteria to detcrmine this extra equation and therefore can be considered an ad hoc choice.

Using the Wiener-Hopf-technique, we compute the electrostatic field distribution of interdigital transducers at the plane interface of two dielectric media sandwiched between two grounded metallic plates and neighbored by two grounded semiinfinite plates at the interface. To this end, we compute, for the first time, the associated Green's function, which already satisfies the boundary conditions at all the grounded plates. Consecutively, the Green's function is used to derive the elements of the charge-potential-interrelation matrix for various basis-and testing functions for a method-of-moments application. Examples demonstrate that the new method has considerable advantages with respect to accuracy and computer-memory requirements.

In this article, we illustrate some examples of how using spheres for computational electromagnetics (CEM) validation provides a range of challenges and broadly meaningful results. We show how complications that arise with validating using spheres can be representative of the issues that occur when modeling more complex objects. However, using spheres makes it easier to identify and understand these issues and discrepancies. We also describe how spheres present demanding problems for the CEM validation and benchmarking of both small-and large-size problems.

Lightning surges induced on subscriber lines in Kuala Lumpur, Malaysia, which is located in a tropical region, were observed at telecommunication centers. More than 100 surges per line were observed during a three-month period. Peak values, observed using a lightning surge counter, show that lightning surge current occurrences normalized by the number of thunderstorm days and number of subscriber lines closely agreed with data observed in temperate areas, e.g., Japan. Surge waveforms appearing at several points ranging from underground cable ducts to exchange equipment were observed using a wave memory system. The results show that lightning surge currents on the cables were larger thanthose on a wire, but the correlation between them was weak. Common and differential mode surge waveforms observed using the wave memory system were almost the same. These results will be useful in designing protection circuits for equipment used in tropical areas.

Microstrip antennas are becoming increasingly popular are widely used in microwave and millimeter-wave circuits. Owing to the implementation of the electronic device only on the PCB, the microstrip antenna has received a great deal of attention. In this paper we present some practical design considerations for the 3-band microstrip antennas. In our work, after the theoretical foundations are defined, the characteristics of the microstrip antenna is experimentally studied. It is not very convenient to analytically design these types of antennas therefore most of the work in this field is implemented by computational electromagnetics methods or hardware experiments. The E.M. analysis is implemented by the Full-Wave EM Analysis Method. In this method, the Method of Moments (MoM) is involved along with the Geometrical and Physical Theory of Diffraction. The selection of mentioned methods depends on the ratio of the structure (antenna) size to the wavelength. Therefore, when used togethe...

Solution to high-frequency electromagnetic problems require increased computational resources if "exact" numerical techniques such as Finite Difference Time Domain (FDTD), Finite Element Methods (FEM), or, the Method of Moments (MoM) with free-space Green's function, are used. These approaches require discretization of the entire structure into cubic cells of sizes between fa and fa, with still finer gridding near source and material interface regions. This process yields accurate results, but consumes computational resources directly proportional to the electrical size of the problem. An alternative to such exact approaches is the access to, and application of, analytical techniques that have the potential to generate better-than-acceptable answers in these high frequency regions. These special class of techniques, developed from the principles of quasior ray-optics and their sophisticated extensions, have found extensive applications for a wide variety of problems. Notable amongst a class of ray-optic analysis methods are: Uniform Theory of Diffraction (UTD), Physical Theory of Diffraction (PTD) and the Spectral Theory of Diffraction (STD). A common interesting feature is that the computation time is inversely proportional to the electrical size of the problem and thus serves to complement the exact approaches. Additionally, due to the nature of these quasior ray-optic methods, the dominant contributors to the complete solution can be realized in terms of "rays" that provide deeper physical insight into the various electromagnetic interaction mechanisms. In this exposition, the early experimental work on light scattering by perfectly conducting circular cylinders, and mathematical foundations of the state-of-art rayoptic methodologies are comprehensively reviewed. The versatility of the high-frequency, ray-optic techniques will be exemplified through some select numerical examples from the NEC-BSC version 4.2 (Numerical Electromagnetics Code -Basic Scattering Code), that employs the UTD formulations. Recent research topics associated with the present high-frequency methods, such as the Stokes phenomenon, complex rays, hybrid ray-mode methods are discussed, followed by an extensive list of references.

The method of moments (MoM) analysis of probe-fed rectangular microstrip patches requires the inclusion of a probe-to-patch attachment mode-expansion function when the substrate thickness 0 02 , where is the free-space wavelength. The results for the input impedance showed increased divergence with measurements when the attachment mode was omitted from the full-wave analysis. The attachment mode can be expressed as an infinite eigenfunction series that increases the fill time of the impedance matrix in an MoM analysis. In an earlier investigation, the infinite eigenfunction series was reduced to a residue series that required one or two terms compared to about 55 terms for the eigenfunction series. In this paper, the convergence properties of the eigenfunction and residue series are investigated in view of rigorous MoM analysis. The relative errors resulting from replacing the eigenfunction by the residue series for the attachment mode, are compared by numerically evaluating a class of two-dimensional (2-D) spatial integrals shown to be closely related to the elements of an MoM impedance matrix. Additionally, the computation times for the evaluation of these integrals for the two forms of the attachment mode-expansion function are also included. Based on the superior convergence properties of the residue series for the attachment mode-expansion function, it is mathematically justified that this form can readily be used for analytic reduction of the spatial, reaction integrals from four to 2-D forms. This feature allows further reduction of the fill time of the MoM impedance matrix, suggesting the possibility of developing an efficient space-domain MoM technique for modeling of wide-band microstrip antennas. Index Terms-Method of moments, microstrip antennas. U SE of small microstrip antennas with probe feeds is becoming increasingly popular for handheld personal communication systems (PCS) cellphones . Broad-band antennas are desired [2] and computer-aided design tools for broad-band probe-fed patches are thus attracting attention [3], . The effect of the probe location (at the high-frequency end of the stipulated bandwidth) on the input impedance is thus critical. The input impedance variation with frequency dictates the wide-band properties of such microstrip antennas for PCS applications ([1, fig. 2]). While approximate modeling Manuscript

The use of moment method with curved segments for numerically modeling helical antennas has been the scope of many papers, it is mainly used to solve for the current distribution on the helix contour with high accuracy at a reduced number of segments. It is often very challenging to use the resulting electrical current distribution to evaluate the far field expressions. This paper is intended to cover the development of the far field expressions for a helix antenna analyzed using moment method under curved basis and testing functions. The electric field is expressed in unified expressions based on the antenna current distribution. The validity of the obtained expressions is verified through the analysis of commonly known operation modes by choosing different geometries for the Helical Antenna.

In this paper we propose a new Eulerian model and related accurate and robust numerical methods, describing polydisperse evaporating sprays, based on high order moment methods in size. The main novelty of this model relies on the use of fractional droplet surface moments and their ability to predict some geometrical variables of the droplet-gas interface, by analogy with the liquid-gas interface in interfacial flows. Evaporation is evaluated by using a Maximum Entropy (ME) reconstruction. The use of fractional moments introduces some theoretical and numerical difficulties. First, relying on a study of the moment space, we extend the ME reconstruction to the case of fractional moments. Then, we propose a new high order and robust algorithm to solve the moment evolution due to evaporation, which preserves the structure of the moment space. It involves some negative order fractional moments for which a novel treatment is introduced. The present model and numerical schemes yield an accurate and stable evaluation of the moment dynamics with minimal number of variables, as well as computational cost, but also provides an additional capacity of coupling with diffuse interface model and transport equation of averaged geometrical interface variables, which are essential in order to describe atomization.

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Liquid fuel injection modeling and simulation in automotive engines face new challenges related to the need for predictive simulations of combustion regimes. Recently, derived from a statistical approach at mesoscopic level, a high order method of moments coupled to realizable, robust and accurate numerical methods [1], has been obtained and shown to describe properly the dynamics of polydisperse evaporating sprays and its coupling to a turbulent gaseous flow field [2]. However, building up a global multi-scale model with the capability to resolve the whole injection process requires a major breakthrough in terms of both modeling and numerical methods. A new model for evaporating polydisperse sprays with easy coupling capabilities to the separated phases zone is proposed in the present contribution, as well as specific numerical methods and implementation in the p4est library [3] for adaptive mesh refinement and massively parallel computing. The key ingredient is a good choice of va...

High fidelity modeling and simulation of turbulent dispersed two-phase flows is still a major challenge for many applications. Eulerian approaches are well suited for high performance computations of such flows. Recently, hybrid Eulerian methods that combine the multi-fluid approach-where the size is discretized-and the moment method were developed. On the one hand, in order to capture efficiently the size-polydispersion, two size moments were used on each interval of the size discretization (Two Size Moment method). On the other hand, the Anisotropic Gaussian (AG) velocity closure has been introduced as a relevant model to describe velocity dispersion occurring when the particles from the disperse phase have a significant inertia compared to the time scales of the flow, leading to particle trajectory crossings. The purpose of this contribution is to develop a model able to describe size and velocity dispersion, coupling the two-size moment Eulerian multi-fluid method and the anisot...

In this work, we investigate an original strategy in order to derive a statistical modeling of the interface in gas-liquid two-phase flows through geometrical variables. The contribution is two-fold. First it participates in the theoretical design of a unified reduced-order model for the description of two regimes: a disperse phase in a carrier fluid and two separated phases. The first idea is to propose a statistical description of the interface relying on geometrical properties, such as the mean and Gauss curvatures, and to define an associated Surface Density Function (SDF). The second main idea consists in using such a formalism in the disperse case, where a clear link is proposed between local statistics of the interface and the statistics of countable objects, such as a number density function. To this end we make essential the use of topological invariants in geometry through the Gauss-Bonnet formula. This strategy strictly includes the works conducted on sprays of spherical droplets, but it also yields a statistical treatment of populations of non-spherical objects, such as ligaments, as long as they are homeomorphic to a sphere. Second, we propose an original statistical post-processing of DNS data of interfacial flows. Starting from the proposed theoretical approach, we identify a kernel for the spatial averaging of geometrical quantities which preserves the topological invariants. Coupled to a new algorithm for the evaluation of the surface and its curvatures, that also preserves these invariants, we analyze two sets of DNS results obtained with the ARCHER code from CORIA, with and without topological changes, and assess the approach. Indeed, this procedure allows us to transform the interfacial information provided by a Level-Set function into a number distribution of a collection of objects in the proper geometrical phase space.

The objectives of this thesis are learning and combining inverse model with method of moments (MOM) for obtaining accurate and realistic oil saturation estimates. The streamline-based inverse model developed in Texas A&M University coupled with the finite-difference ECLIPSE simulator was used to calculate the oil saturation distribution from partitioning interwell tracer test (PITT) data. Inverse model was tested for both single-phase at residual oil saturation and then for two-phase flow simulations during a waterflood. First sensitivity tests were performed. Then, the MOM and inverse modeling techniques were applied to PITTs at various tracer detection limits and their accuracy compared. Furthermore, these methods are used in a complementary way by using the saturation from the MOM as the initial guess for the inverse model calculation. In two-phase flow simulations, the sensitivity of inverse modeling to relative permeability, injection rate, cross-flow and to different partition...

In many studies concerning wire heating during MR imaging, a "resonant wire length" that maximizes RF heating is determined. This may lead to the nonintuitive conclusion that adding more wire, so as to avoid this resonant length, will actually improve heating safety. Through a theoretical analysis using the method of moments, we show that this behavior depends on the phase distribution of the RF transmit field. If the RF transmit field has linear phase, with slope equal to the real part of the wavenumber in the tissue, long wires always heat more than short wires. In order to characterize the intrinsic safety of a device without reference to a specific body coil design, this maximum-tip heating phase distribution must be considered. Finally, adjusting the phase distribution of the electric field generated by an RF transmit coil may lead to an "implantfriendly" coil design. Magn Reson Med 48:1096 -1098, 2002.