Far-field Conditions Research Articles

A quasi-rigorous solution for focusing radially polarized vector beams by an arbitrary opening paraboloid mirror

For focusing of radially polarized vector beams using an arbitrary opening paraboloid mirror, a quasi-rigorous integral representation of light field is derived based on a rigorous vectorial diffraction theory of electromagnetic waves. Under far-field approximation conditions, the derived integrals reduce to the results from vectorial Debye-Wolf diffraction integral. Numerical calculations show that a marked deviation, as represented by evident focal shift, appears for low-aperture paraboloid mirrors, e.g. the maximum focusing semi-angle α below π/9 with the focal length f being 103λ, or below π/6 when f reduces to 102λ. The radial light spot sharpens to be 0.39λ (FWHM) and purely longitudinally polarized when α is close to 115°, while the axial light spot continuously sharpens to be about half wavelength with α approaching π. For an annular paraboloid mirror, it is possible to further compress the radial light spot down to 0.36λ (FWHM).

Numerical Validation of the Squire–Young Formula for Profile-Drag Prediction

The Squire–Young formula is widely used to calculate profile drag in two-dimensional airfoil analyses. Although experience shows that the formula provides reasonable and accurate predictions, full Navier–Stokes computational fluid dynamics allows for a numerical validation of the formula. A method is presented for evaluating the Squire–Young formula from a computational fluid dynamics solution, and demonstrated for several airfoils. The agreement between profile-drag coefficients determined using the Squire–Young formula and those calculated directly from the computational fluid dynamics solution using surface integration is typically within 2–3% in the low-drag range, with error increasing at higher lift coefficients. The applicability of the underlying assumptions is discussed, and the validity of the assumed variation of shape factor and edge velocity in the wake is investigated for a symmetric airfoil at zero lift. The formula is also demonstrated as being insensitive to spurious drag that may occur due to far-field boundary conditions. Finally, a derivation of the Squire–Young formula is included to further aid in understanding the influence of its assumptions on its predictions.

Intrinsic Modeling of Near-Field Electromagnetic Induction Antennas for Layered Medium Characterization

We present a closed-form equation for intrinsic modeling of near-field electromagnetic induction (EMI) antennas for planar layered media characterization. Resorting to a decomposition of the backscattered EM field into elementary distributions over the antenna aperture, the EMI transmitting and receiving antennas are modeled using infinitesimal magnetic dipoles and field points, and characteristic frequency-dependent global reflection and transmission coefficients. Low-frequency propagation of the EM fields in the medium is described using 3-D planar layered media Green's functions. We performed measurements with a loop antenna situated at different heights, ranging from near-field to far-field conditions, above water of known electrical conductivity to determine its intrinsic properties, and a range of salinity conditions was applied to subsequently validate the proposed model. The EMI system was set up using a vector network analyzer equipped with a prototype EMI antenna specifically designed for this application. The model showed good accuracy for reproducing the observed data, and model inversion provided good estimates of the medium electrical conductivity. Yet, insensitivity of the EMI signal to water electrical conductivity was encountered for low salinity due to the presence of a copper sheet as the bottom boundary condition of the experimental setup. Moreover, the efficiency of the antenna decreased rapidly as antenna height above water surface increases, leading to increasing discrepancies between estimated and measured water electrical conductivity values as the antenna moves away from the water surface. Although some technical improvements are still needed, the proposed approach is promising for quantitative estimation of soil electrical conductivity from EMI data.

Remote Powered Medical Implants for Telemonitoring

Chronic diseases like diabetes mellitus often require a permanent monitoring of vital signs. Especially the use of telemedicine will increase the quality of life for affected patients. Therefore, novel systems are necessary which are able to permanently detect and provide health status information. But these systems must not control patient's life and should work autonomously. For this purpose, intelligent medical implants are well qualified. This work describes a system for wireless power supply and communication with medical implant applications. Monitoring vital signs will create a big amount of data. Therefore, high data rates are necessary provided by high operating frequencies which in turn lead to electromagnetic far-field conditions. In this case, high attenuation losses due to the permittivity of the human body ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> have to be considered. Hence, high frequencies are not suitable for the transfer of energy into the human body. The presented concept is based on two different frequencies for power supply and data transmission. An independent development of both blocks is thereby possible. The power supply operates at a frequency of 13.56 MHz, using inductive coupling. Consequently, the human body does not affect the energy transfer. In contrast, the data transmission is operated at a frequency of the medical implant communication service (MICS) band. The elaborated system consists of a power supply unit, a data transmission unit, and a control unit. The implementation of the power supply and data transmission as well as associated theoretical basics are presented. Performed measurements demonstrate that the realized system is qualified for the use on human beings.

Effect of interfacial slippage on the near-tip fields of an interface crack between a soft elastomer and a rigid substrate

We consider the role of interfacial slippage in the deformation and stress fields near the tip of a plane interface crack occurring between a compressible hyperelastic material and a rigid substrate. Specifically, we draw comparisons between the two limiting cases of ‘no-slip’ (infinitely high friction) and ‘frictionless’ (zero friction) surfaces by performing corresponding asymptotic analyses in the crack-tip region. Our results indicate that for the no-slip case, when the body is subjected to far-field loading, the crack deforms to a wedge-like shape consistent with experimental observations reported in the literature. Moreover, in this case, the wedge angle is shown to be directly related to ratios of various Cauchy stress components on the bonded surface in the near-tip region. Finite-element simulations reveal that the wedge angle also depends on material compressibility and the far-field loading conditions. By contrast, the analysis of the frictionless case reveals that the crack consistently opens into a smooth parabolic shape with a right wedge angle and near-tip stress field dominated by the normal stress at the surface. The results established here can be used as a basis for the understanding of the role of varying degrees of slippage on interfacial cracks.

Fingering phenomena in immiscible displacement in porous media flow

Pressure-driven displacement of one fluid by another in porous media has many applications, including oil production and the removal of soil contaminants. When the displacing fluid is less viscous, an idealized flat displacement front is ill-posed with respect to the growth of transverse perturbations (Taylor–Saffman instability). In models that include relative permeabilities, a macroscopic mixing of the fluids occurs in a rarefaction wave in a displacement region with a final discontinuity (shock wave) to the pure displaced fluid (Buckley–Leverett model). This discontinuity can also suffer from Taylor–Saffman instability. The instability is regularized by capillary effects, and a most unstable wavenumber can be found. Growth of these instabilities leads to fingering of the displacing fluid. In this work, we review the appropriate models and present a robust numerical approach to computing the most unstable wave numbers for given parameters (provided they lead to a non-degenerate parabolic problem). This approach to quantitatively accurate solutions will be of use in fitting experimental results and evaluating models used in a number of applications. We show that the Buckley–Leverett shock can be stabilized due to relative permeability effects in some cases. We give a clear presentation of asymptotic results in the limit of small capillarity for this problem. These asymptotic results lead to far-field pressure conditions that greatly simplify the numerical computations. They also highlight some open mathematical questions in this area.

Energy release rates for a misfitted spherical inclusion under far-field mechanical and uniform thermal loads

A misfitted spherical inclusion embedded in an infinite matrix under far-field triaxial mechanical and uniform thermal loads is analyzed in three-dimensional linear elasticity. Closed-form expressions for each loading case have been obtained separately utilizing proper continuity and far-field loading conditions. The principle of superposition has been utilized to obtain the complete solution from these three individual solutions. The solutions are discussed in terms of stress distribution, magnitude and locations of stress concentrations. Closed-form expressions for energy release rates have been derived based on the stress and strain solutions by employing the path-independent integrals, J, L and M considering the inclusion as a defect. The measure of self-similar expansion energy release rate provided by the M-integral brings some interesting insight which can be applicable to many practical cases such as phase transformations in metals and nanoscale defects. The fundamental work presented here will help to better understand the behavior of materials with a misfitted inclusion subjected to various loading environments.

Numerical simulation of the far-field boundaries onto a microdisc electrode by using the infinite element

The numerical simulation of the diffusion problem onto a microdisc electrode is made difficult by the presence of a boundary singularity at the electrode edge (edge effect) and the truncated far-field boundary conditions. In general, the far-field distance is several orders larger than the radius of the microelectrode. Simulating in such a large domain is time-consuming so the far-field distance is often truncated. The accuracy of the simulated current depends on how far of the truncated far-field boundary conditions. An approximated function is obtained to estimate the sufficient distance for a given accuracy of the current calculation and vice-versa. We also introduce the use of infinite elements at far-field boundary which is proved as an optimal approach to deal with boundary conditions at semi-infinite distance.

Simulation of charge packet formation in layered polymer film

Purpose – The purpose of this paper is to describe a rapid and robust axisymmetric hybrid algorithm to create dynamic temporal and spatial charge distributions, or charge map, in the simulation of bipolar charge injection using Schottky emission and Fowler-Nordheim tunneling, field-dependent transport, recombination, and bulk and interfacial trapping/de-trapping for layered polymer films spanning the range from initial injection to near breakdown. Design/methodology/approach – This hybrid algorithm uses a source distribution technique based on an axisymmetric boundary integral equation method (BIEM) to solve the Poisson equation and a fourth-order Runge-Kutta (RK4) method with an upwind scheme for time integration. Iterative stability is assured by satisfying the Courant-Friedrichs-Levy (CFL) stability criterion. Dynamic charge mapping is achieved by allowing conducting and insulating boundaries and material interfaces to be intuitively represented by equivalent free and bound charge distributions that collectively satisfy all local and far-field conditions. Findings – Charge packets cause substantial increase of electric stress and could accelerate the breakdown of polymeric capacitors. Conditions for the creation of charge packets are identified and numerically demonstrated for a combination of impulsive step excitation, high charge injection, and discontinuous interface. Originality/value – Metallized bi-axially oriented polypropylene (BOPP) dielectric thin film capacitor with self-clearing and enhanced current carrying capability offer an inexpensive and lightweight alternative for efficient power conditioning, energy storage, energy conversion, and pulsed power. The originality is the comprehensive physics and multi-dimensional modeling which span the dynamic range from initial injection to near breakdown. This model has been validated against some empirical data and may be used to identify failure mechanisms such as charge packets, gaseous voids, and electroluminescence. The value lies in the use of this model to develop mitigation strategies, including re-designs and materials matching, to avoid these failure mechanisms.

Dynamic charge mapping in layered polymer films

This paper describes a hybrid algorithm for the solution of the drift-diffusion equations for bipolar charge transport in layered polymer films. Dynamic charge mapping is achieved using a source distribution technique for the solution of the Poisson equation and time-integration using a fourth order total variation diminishing Runge-Kutta scheme that satisfies the Courant-Friedrichs-Levy stability criterion. An integral equation formulation allow conducting and insulating boundaries and material interfaces to be represented by equivalent free and bound charge distributions that collectively satisfy all local and far-field boundary conditions. This hybrid technique solves the drift-diffusion equations that simulate charge injection, field-dependent mobility transport, recombination, and trapping/de-trapping in the bulk and at material and physical interfaces. The resulting charge map is the taxonomy of the different charge types and their abundance; presenting a dynamic view of the temporal and spatial distributions. Results are discussed for single-layer and multi-layered samples with physical and material interfaces. Conditions for creation of charge packets and electroluminescence due to recombination are computed and discussed.

Fuzzy logic control of a stiffness-adaptable seismic isolation system

SUMMARY Traditional passive isolation systems have been shown to provide satisfactory seismic mitigation performance under typical far-field earthquake conditions. However, because of the untunable designated isolation period, the performance of these systems is still strongly affected by the low-frequency resonance phenomenon observed during near-fault earthquakes, which are usually dominated by a long-duration impulse. The use of semi-active isolation systems with variable stiffness, which are usually equipped with a customized control algorithm to determine the isolation stiffness or period in real time, could be a promising solution to overcome this problem. To realize this technology, this study develops a smart isolation system that combines the leverage-type stiffness-controllable isolation system (LSCIS) with a simple fuzzy logic control (FLC). Because the proposed FLC merely requires feedback from the velocity and displacement responses of the isolation base, it is quite easily implemented. Theoretical analysis shows that the extreme displacement of the isolation level caused by near-fault seismic waves can be mitigated by the proposed system with tolerable acceleration response variations compared with that of the traditional passive isolation system. The movement of the pivot point of the LSCIS can also be adjusted to address the inherent hardware constraint that limits its practical application. Experimental verification conducted on a shake table further demonstrates the feasibility of integrating the LSCIS system with FLC after proper consideration of the friction effect generated by the leverage mechanism and the inevitable time delay effect. Copyright © 2014 John Wiley & Sons, Ltd.

Specific absorption rate (SAR) revisited for the ellipsoidal model of a human body

An unexplored procedure leading to a unified formulation of the average whole-body SAR, thus entirely covering the frequency spectrum of technical interest, is here described. The explanatory and referential example of an ellipsoid mimicking exposition of a standing man on a ground plane is adopted and an approximate closed form for the SAR is provided. In spite of the far-field condition which in principle applies to this investigation, the analysis starts from rigorously recognizing the near-field performances of the time average Poynting vector and goes on accordingly in modeling the induction mechanism. Therefore, the external dosimetry is preliminary assessed by using a quasistatic approach. This step is rather to be intended as an intermediate one with the aim of evaluating the SAR which, as a consequence, results subject to the same quasistatic conditions. Indeed, the approximation error affecting the calculation especially depends on the fact that the adopted biological model behaves as a perfect conductor externally to its boundary and internally as a dissipating dielectric body. On the whole, the continuous curves obtained in function of frequency are in fairly good agreement with available counterparts which, do not forget, are rather constructed by interpolation of discontinuous databases given using different models and spanning restricted frequency ranges. The only striking departure consists in the smoothed appearance of the curves related to this method against the presence of a resonance sharp peak arising elsewhere under specialized exposure conditions. In the light of this theory, the peak in question is hard to explain, except when the adopted corpulent ellipsoid is replaced with a more refined model.

Acoustical characterization of polysaccharide polymers tissue-mimicking materials

Tissue-mimicking phantoms play a crucial role in medical ultrasound research because they can simulate biological soft tissues. In last years, many types of polymeric tissues have been proposed and characterized from an acoustical and a thermal point of view, but, rarely, a deep discussion about the quality of the measurements, in terms of the uncertainty evaluation, has been reported. In this work, considering the necessity to develop laboratory standards for the measurement of ultrasonic exposure and dose quantities, a detailed description of the experimental apparatuses for the sound speed and the attenuation coefficient measurements is given, focusing the attention on the uncertainty evaluation both of the results and analysis algorithms. In particular, this algorithm reveals a novel empirical relation, fixing a limit to the energy content (therefore limits the number of cycles) of the three parts in which the authors have proposed to divide the acoustical signal.Furthermore, the realisation of multi-components phantoms, Agar and Phytagel based tissue-mimicking gels along with others long chain molecules (dextrane or polyvinyl alcohol) and scattering materials (silicon carbide and kieselguhr) are investigated.This paper reports accurate speed of sound and attenuation coefficient measurements. Speed of sound is measured by a pulse-echo technique in far-field condition, using an optical glass buffer rod; while attenuation coefficient is determined by an insertion technique, using demineralized water as reference material.The experimental sound speed results are subjected to an overall estimated relative uncertainty of about 1.5% and the attenuation coefficient uncertainty is less than 2.5%.For the development of laboratory standards, a detailed analysis of the measurement uncertainty is fundamental to make sample properties comparable. The authors believe this study could represent the right direction to make phantoms characterizations referable and traceable.

Near-field and far-field goniophotometry of narrow-beam LED arrays

In lighting calculations and simulations, the emission of a light source is conventionally modeled using the far-field luminous intensity distribution. However, the advent of luminaires including large arrays of LEDs with focusing optics creating narrow beams has made the traditional limiting photometric distance to reach far-field conditions less easy to determine. Furthermore, even correct far-field data can lead to erroneous predictions when illuminances are determined on a task surface which is positioned within the near-field region. A near-field representation could overcome these problems, but experimental validation for such LED arrays is lacking. This paper reports on near-field and far-field laboratory experiments using an array of two and five narrow-beam LEDs. A near-field approach makes discussions to determine the far-field photometric distance superfluous and leads to correct illuminances at any location with respect to the array, irrespective of the dimensions of the array and the beam angle of the individual components. Introducing the near-field representation of light sources in lighting design offers more accurate predictions when luminaires based on LED arrays with focusing optics are involved.

Antiplane scattering of SH waves by a circular cavity in an exponentially graded half space

In this study, an analytical solution of antiplane scattering of plane SH waves by a circular cavity in an exponentially graded material is obtained via the complex variable method and image technique, and dynamic response of the interface and the cavity is investigated. The medium is a bimaterial with a semi-infinite homogeneous part and an exponentially graded half space containing a circular cavity. The study provides a treatment to the orthogonality of boundary conditions along the half surface and the cavity periphery. Based on Helmholtz decomposition, the stress and displacement components are expressed by complex variables. The scattered waves by the interface surface are regarded as transmitting from the origin of the cavity and its image. These waves can be also satisfy the far-field radiation conditions. The boundary value problem results in a set of infinite algebraic equations which can be solved straightforwardly. Finally, parametric study shows that the inhomogeneous parameter, the dimensionless frequency of the incident waves and the distance-radius ratio of the cavity have significant effect on dynamic response of the medium.

Olfactory source localization in the open field using one or both nostrils

This study aims to examine humans &#769; abilities to localize odorants within the open field. Young participants were tested on a localization task using a relatively selective olfactory stimulus (2-phenylethyl-alcohol, PEA) and cineol, an odorant with a strong trigeminal component. Participants were blindfolded and had to localize an odorant source at 2 m distance (far-field condition) and a 0.4 m distance (near-field condition) with either two nostrils open or only one open nostril. For the odorant with trigeminal properties, the number of correct trials did not differ when one or both nostrils were used, while more PEA localization trials were correctly completed with both rather than one nostril. In the near-field condition, correct localization was possible in 72-80% of the trials, irrespective of the odorant and the number of nostrils used. Localization accuracy, measured as spatial deviation from the olfactory source, was significantly higher in the near-field compared to the far-field condition, but independent of the odorant being localized. Odorant localization within the open field is difficult, but possible. In contrast to the general view, humans seem to be able to exploit the two-nostril advantage with increasing task difficulty.

Reduction of the stress concentration factor in a homogeneous panel with hole by using a functionally graded layer

This work aims at understanding the effect of a radially heterogeneous layer around the hole in a homogeneous plate on the stress concentration factor. The problem concerns a single hole in a plate under different far-field in-plane loading conditions. By assuming a radial power law variation of Young’s modulus and constant value for Poisson’s ratio, the governing differential equations for plane stress conditions, and general in-plane loading conditions are studied. The elastic solutions are obtained in closed form and, in order to describe localized interface damage between the ring and the plate, two different interface conditions (perfectly bonded and frictionless contact) are studied. The formulae for the stress concentration factors are explicitly given for uniaxial, biaxial and shear in-plane loading conditions and comparisons with interface hoop stress values are performed. The solutions are investigated to understand the role played by the geometric and graded constitutive parameters. The results are validated with numerical finite element simulations in which some simplified hypotheses assumed in the analytical model, are relaxed to explore the range of validity of the elastic solution presented. In this way the results obtained are useful in tailoring the parameters for specific applications.

A Reduced-Order Model of the Mean Properties of a Turbulent Wall Boundary Layer at a Zero Pressure Gradient

A novel two-equations model for computing the flow properties of a spatially-developing, incompressible, zero-pressure-gradient, turbulent boundary layer over a smooth, flat wall is developed. The mean streamwise velocity component inside the boundary layer is described by the Reynolds-averaged Navier–Stokes equation where the Reynolds shear stress is given by an extended mixing-length model. The nondimensional form of the mixing length is described by a polynomial function in terms of the nondimensional wall normal coordinate. Moreover, a stream function approach is applied with a leading-order term described by a similarity function. Two ordinary differential equations are derived for the solution of the similarity function along the wall normal coordinate and for its streamwise location. A numerical integration scheme of the model equations is developed and enables the solution of flow properties. The coefficients of the mixing-length polynomial function are modified at each streamwise location as part of solution iterations to satisfy the wall and far-field boundary conditions and adjust the local boundary layer thickness, δ99.4, to a location where streamwise speed is 99.4% of the far-field streamwise velocity. The elegance of the present approach is established through the successful solution of the various flow properties across the boundary layer (i.e., mean streamwise velocity, viscous stress, Reynolds shear stress, skin friction coefficient, and growth rate of boundary layer among others) from the laminar regime all the way to the fully turbulent regime. It is found that results agree with much available experimental data and direct numerical simulations for a wide range of Reθ based on the momentum thickness (Reθ) from 15 up to 106, except for the transition region from laminar to turbulent flow. Furthermore, results shed light on the von Kármán constant as a function of Reθ, the possible four-layer nature of the mean streamwise velocity profile, the universal profiles of the streamwise velocity and the Reynolds shear stress at high Reθ, and the scaling laws at the outer region.

Effect of gaseous void on bipolar charge transport in layered polymer film

This paper describes a hybrid algorithm to study the effect of a gaseous void on bipolar charge transport in layered polymer film. This hybrid algorithm uses a source distribution technique based on an axisymmetric boundary integral equation method to solve the Poisson equation and a fourth order Runge–Kutta (RK4) method with an upwind scheme for time integration. Iterative stability is assured by satisfying the Courant–Friedrichs–Levy stability criterion. Dynamic charge mapping is achieved by allowing conducting and insulating boundaries and material interfaces to be represented by equivalent free and bound charge distributions that collectively satisfy all local and far-field conditions. This hybrid technique caters to bipolar charge injection, field-dependent mobility transport, recombination, and trapping/de-trapping in the bulk and at material and physical interfaces. The resulting charge map is the taxonomy of the different charge types and their abundance, and presents a dynamic view of the temporal and spatial distributions. The paper is motivated by images of breakdown experiments that point to the role of gaseous void in delamination growth. For the test configuration, the high field at the edge of the gaseous void act as a sink first for positive and then negative charge. The net effect is to increase delamination stress at the edge leading to further growth of the defect and increasing the potential for partial discharge within the void.

Efficient and non-reflecting far-field boundary conditions for incompressible flow calculations

Traditionally, the artificial compressibility (AC) method of Chorin is used for simulation of low-speed and incompressible flows. In this method, the difficulty of continuity and momentum equations decoupling is removed by adding an artificial time derivative of pressure to the continuity equation. For the first time, a fully two-dimensional upwind scheme was presented for AC equations by using characteristic structure of equations by the authors. In this paper, a new remote boundary calculation method is presented by using the idea of characteristics for these equations. Instead of simple boundary conditions which usually are employed for incompressible flows, the flow quantities at the far-field boundaries are evaluated by compatibility relations of characteristic equations. This is implemented by assuming a row of ghost cells outside of the far-field boundary and using the flux calculation method based on characteristics similar to the inside of computational domain. The idea in conjunction with multidimensional characteristic based scheme was tested for incompressible flow around circular cylinder in comparison with conventional far-field boundary condition and showed good improvements in the terms of accuracy and convergence speed.