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The method of images (MI) is an elementary concept in electromagnetism, which is a fundamental course in electrical engineering. In this work, the surface charge density of a conductive sphere in the inductive electrostatic field of a uniformly charged ring is analysed with MI. Meanwhile the surface charge distribution of this sphere is discussed when the sphere is at different positions of the axis of this ring. This work is aimed to help students understand MI and lay a solid foundation of electrical engineering learning. [ABSTRACT FROM AUTHOR]

Abstract: Conductivity of non-overlapping disks embedded in a two-dimensional background can be investigated by the method of images which is based on the successive application of the inversions with respect to circles. For closely placed disks, the classical method of images yields slowly convergent series. The method of images can be treated as an application of successive approximations to a system of functional equations. In this paper, modified functional equations are deduced to essentially accelerate the convergence. [Copyright &y& Elsevier]

In this paper, a new method for the calculation of leakage inductances between short-circuited windings is proposed. The main objective is to find an analytical alternative to the finite-element method (FEM) for the computation of short-circuit inductances in electromagnetic transients-type (EMT-type) programs. Typical EMT-type tools do not provide complex FEM-based computation engines for this sole purpose. The new approach is derived from the method of images and uses analytical formulations for magnetic vector potential and energy developed in this work. It is shown that the difference between the inductance calculated with the FEM in 2-D and that computed with the method of images decreases as the number of layers of images increases. Also, it is demonstrated that the classical approach, based on an axial flux distribution, can lead to considerable error if the windings have unequal heights and if they are located far from the core yokes. [ABSTRACT FROM AUTHOR]

The vibration motors for smart phones with haptic interfaces require higher reaction rate and longer service life than what a typical rotational motor with eccentric mass provides. In this paper, a new type of a linear vibration motor is proposed. A voice-coil actuator is employed for high reaction rate. Permanent magnets replace mechanical springs, which would help increase the service life. For analyzing and modeling the proposed vibration motor, we use the method of equivalent current sheet and the method of images. These methods are validated against finite element analyses and experiments. A prototype motor is designed and fabricated. Tests with the prototype show the feasibility of the proposed linear vibration motor. [ABSTRACT FROM PUBLISHER]

Abstract: As left-handed materials and metamaterials are becoming more prevalent, we examine the effect of negative permeability upon levitation force. We first consider two half spaces of differing permeability and a point magnetic source, so that the method of images may be employed. We determine that the resulting force may be larger than for conventional magnetic materials. We then illustrate the inclusion of a finite sample thickness. [Copyright &y& Elsevier]

Abstract: The Method of Images poses an important difficulty when used to solve the problem of a charge in the presence of a grounded conducting sphere. This arises from the fact that the sum of the inducing charge and the image charge is different from zero. As a consequence, there is a monopole field far from the system, and any ground wire physically connected to the sphere will carry an electric current, changing the initial balance of charges until a new equilibrium is reached. The approach taken in this paper assumed an infinite straight wire connecting the sphere to ground. The charge distribution over the surface of the conductors was calculated, and the results analyzed. It was shown that the thinner the wire, the lower will be its total charge, and the closer will be the calculated charge density at the surface of the sphere to the conventional solution by the Method of Images. [Copyright &y& Elsevier]

When a transformer is subjected to very fast front transients, the penetration of the magnetic flux into the core becomes, in general, negligible. To represent this phenomenon, it is common practice to compute the winding inductance matrix (turn-to-turn) at very high frequencies using the expressions for air-core inductors. However, since the core becomes a magnetic insulating wall at very high frequencies (MHz), the distribution of the magnetic field is altered because the field cannot enter the region occupied by the core. Therefore, the air-core approximation formulae overestimate the inductance at high frequencies. This is especially true in the region inside the core window. Large errors are found when the inductances are computed with the air-core approximation. This paper presents a technique, based on the application of a multilayer method of images, to take the presence of the core into consideration. The final expressions are very simple, yet they give remarkably accurate results. Comparisons with finite-element analyses prove the excellent accuracy of the technique. [ABSTRACT FROM AUTHOR]

This paper considers the pricing of European options on assets that follow a stochastic differential equation with a quadratic volatility term. We correct several errors in the existing literature, extend the pricing formulas to arbitrary root configurations, and list alternative representations of option pricing formulas to improve computational performance. Our exposition is based entirely on probabilistic arguments, adding a fresh perspective and new intuition to the existing PDE-dominated literature on the subject. Our main tools are martingale methods and shifts of probability measures; the fact that the underlying process is typically a strict local martingale is carefully considered throughout the paper. [ABSTRACT FROM AUTHOR]

Left-right symmetry breaking is critical to vertebrate embryonic development; in many species this process begins with cilia-driven flow in a structure termed the 'node'. Primary 'whirling' cilia, tilted towards the posterior, transport morphogen-containing vesicles towards the left, initiating left-right asymmetric development. Recent theoretical models based on the point-force stokeslet and point-torque rotlet singularities, explaining how rotation and surface-tilt produce directional flow are reviewed. Analysis of image-singularity systems enforcing the no-slip condition shows how tilted rotation produces a far-field 'stresslet' directional flow, and how time-dependent point-force and time-independent point-torque models are in this respect equivalent. Associated slender-body-theory analysis is reviewed; this approach enables efficient and accurate simulation of three-dimensional time-dependent flow, time-dependence being essential in predicting features of the flow such as chaotic advection, which have subsequently been determined experimentally. A new model for the nodal flow utilising the regularized stokeslet method is developed, to model the effect of the overlying Reichert's membrane. Velocity fields and particle paths within the enclosed domain are computed and compared with the flow profiles predicted by previous 'membrane-less' models. Computations confirm that the presence of the membrane produces flow-reversal in the upper region, but no continuous region of reverse flow close to the epithelium. The stresslet far-field is no longer evident in the membrane model, due to the depth of the cavity being of similar magnitude to the cilium length. Simulations predict that vesicles released within one cilium length of the epithelium are generally transported to the left via a 'loopy drift' motion, sometimes involving highly unpredictable detours around leftward cilia. Particles released just above the cilia tips were not predicted to reach to the extreme edges of the node, but rather are returned to the right by the counterflow. Flow to the right and left of the cilia array is of very small magnitude, suggesting that effective transport of particles to the extremities of the node requires cilia to be distributed all the way to the edges. There is no continuous layer of rightward flow close to the epithelium, except for a region close to the posterior edge of the node. Future work will involve investigating issues such as the precise shape of the node and cilia distribution and the effect of advection and diffusion on morphogens, hence explaining more fully the role of fluid mechanics in this vital developmental process. [ABSTRACT FROM AUTHOR]

Abstract: The problem of computing the capacitance coupling in Very Large Scale Integrated (VLSI) circuits is studied in this work. The proposed method is an approximate extended version of the method of images. The initial problem is formulated here as an optimization problem for the solution of which a genetic algorithm (GA) is employed. The proposed method is fast, general, does not rely on fitting techniques and is applicable to an arbitrary 2D or 3D geometry configuration of conductors. Extensive simulation results are presented for several practical case studies. Comparative results are given with other methods from literature and a commercial tool employing the Finite Element Method (FEM). The results show that the capacitance value computed by our method is in close agreement to the value obtained by the other methods from literature and also by the commercial tool with the average difference ranging between 2% and 5% while demonstrating better scalability as the problem complexity rises. [Copyright &y& Elsevier]

We show that Lord Kelvin's method of images is a way to prove generation theorems for semigroups of operators. To this end we exhibit three examples: a more direct semigroup-theoretic treatment of abstract delay differential equations, a new derivation of the form of the McKendrick semigroup, and a generation theorem for a semigroup describing kinase activity in the recent model of Kaźmierczak and Lipniacki (J. Theor. Biol. 259:291-296, ). [ABSTRACT FROM AUTHOR]

Abstract: In celebration of the Sixth International Conference on Lattice Path Counting and Applications, it is befitting to review the history of lattice path enumeration and to survey how the topic has progressed thus far. We start the history with early games of chance specifically the ruin problem which later appears as the ballot problem. We discuss André''s Reflection Principle and its misnomer, its relation with the method of images and possible origins from physics and Brownian motion, and the earliest evidence of lattice path techniques and solutions. In the survey, we give representative articles on lattice path enumeration found in the literature in the last 35 years by the lattice, step set, boundary, characteristics counted, and solution method. Some of this work appears in the author''s 2005 dissertation. [Copyright &y& Elsevier]

The inapplicability of the method of images to partial inductance calculation within the magneto-quasi-static approximation has been shown by the authors in previous works. This concept is restated in this paper, and some correction terms for the application of the method of images are proposed. A partial inductance calculation technique based on potential theory is also proposed, which does not require the calculation of the current distribution, and is limited at present to infinite perfectly conducting planes. The proposed correction terms are verified with simple structures at first, and later with the calculation of the partial inductance matrix of a quad flat package. [ABSTRACT FROM AUTHOR]

Abstract: We present a mathematical model for maternal blood flow in a placental circulatory unit (a placentone), describing flow of maternal blood via Darcy''s law and steady advective transport of a dissolved nutrient. The method of images and computational integration along streamlines are employed to find flow and solute concentration distributions, which are illustrated for a range of governing system parameters. The model shows how the calibre of the basal vessels can be a dominant determinant of the maternal blood flow rate through the placentone, given a driving pressure difference between the spiral arteries and decidual veins. The model supports the hypothesis that basal veins are located on the periphery of the placentone in order to optimise delivery of nutrients and suggests the existence of an optimal volume fraction of villous tissue. [Copyright &y& Elsevier]

The paper presents a computational model for acoustic scattering of a near-the-ground sound source around a body moving in a uniform flow. Using the method of images and the concept of reflection coefficient, the half space Green's function in a uniform flow is derived in the framework of the boundary element method (BEM). The method is validated against analytical solutions and is further applied in the case of acoustic scattering around an airfoil moving in the vicinity of the ground both for rigid and soft ground conditions. The results show the importance of ground impedance in the attenuation of sound. [ABSTRACT FROM AUTHOR]

We consider in this article the arbitrage free pricing of double knock-out barrier options with payoffs that are arbitrary functions of the underlying asset, where we allow exponentially time-varying barrier levels in an otherwise standard Black-Scholes model. Our approach, reminiscent of the method of images of electromagnetics, considerably simplifies the derivation of analytical formulae for this class of exotics by reducing the pricing of any double-barrier problem to that of pricing a related European option. We illustrate the method by reproducing the well-known formulae of Kunitomo and Ikeda (1992) for the standard knock-out double-barrier call and put options. We give an explanation for the rapid rate of convergence of the doubly infinite sums for affine payoffs in the stock price, as encountered in the pricing of double-barrier call and put options first observed by Kunitomo and Ikeda (1992). [ABSTRACT FROM AUTHOR]

Summary: In this paper we study minimization of pumping cost of a given total flow rate from any number and layout of wells. Building on previously published results, we have considered steady state flow in aquifers with two zones of different transmissivities, to which the method of images applies. Moreover, we have taken into account additional regional flow, which results in different hydraulic head values at the location of the wells, independent of their operation. We prove analytically that in this general case, pumping cost is minimized, when final differences between hydraulic head values at the locations of the wells, resulting from superposition of the regional flow and the operation of the system of the wells, are equal to the half of those, which are due to the regional flow only. Finally we present the analytical calculation procedure of the optimal distribution of the required total flow rate to the individual wells and we provide illustrative examples. [Copyright &y& Elsevier]

Abstract: In this paper, we report a new development of image charge approximations of reaction fields for a charge inside a dielectric spherical cavity immersed in an ionic solvent with arbitrary ionic strength. This new development removes the requirement of low ionic strength of the solvent in a previous result [S. Deng, W. Cai, Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: high-order image approximations for reaction fields, J. Comput. Phys. 227 (2007) 1246–1266], thus extending the applicability of the image charge approximations of reaction fields in the modeling of biomolecular solvation. [Copyright &y& Elsevier]

This paper formally analyses two exotic options with lookback features, referred to as extreme spread lookback options and look-barrier options, first introduced by Bermin. The holder of such options receives partial protection from large price movements in the underlying, but at roughly the cost of a plain vanilla contract. This is achieved by increasing the leverage through either floating the strike price (for the case of extreme spread options) or introducing a partial barrier window (for the case of look-barrier options). We show how to statically replicate the prices of these hybrid exotic derivatives with more elementary European binary options and their images, using new methods first introduced by Buchen and Konstandatos. These methods allow considerable simplification in the analysis, leading to closed-form representations in the Black-Scholes framework. [ABSTRACT FROM AUTHOR]

This paper considers method for parametric analysis of the theoretical apparent soil resistivity profiles over spherical ore deposit, or metallic object in the form of sphere buried in a uniform or a two-layer soil using the Wenner four-point method. The apparent soil resistivity is calculated by means of complex image method using optical analogy and analogy with electrostatic fields. Comprehensive equations for calculating apparent soil resistivity using the Wenner method across perfectly conducting sphere are readily available. Several synoptic image location maps are introduced to explain this method of images as it is applied to the calculation of the apparent soil resistivity. The main application of proposed model is the estimation of the influence of spherical buried metallic objects when using the Wenner method. [ABSTRACT FROM AUTHOR]

Abstract: The image system for the method of regularized Stokeslets is developed and implemented. The method uses smooth localized functions to approximate a delta distribution in the derivation of the fluid flow due to a concentrated force. In order to satisfy zero-flow boundary conditions at a plane wall, the method of images derived for a standard (singular) Stokeslet is extended to give exact cancellation of the regularized flow at the wall. As the regularization parameter vanishes, the expressions reduce to the known images for singular Stokeslets. The advantage of the regularized method is that it gives bounded velocity fields even for isolated forces or for distributions of forces along curves. These are useful in the simulation of ciliary beats, flagellar motion, and particle suspensions. The expression relating force and velocity can be inverted to find the forces that generate a given velocity boundary condition. The latter is exemplified by modeling a cilium as a filament moving in a three-dimensional flow. The cilium velocity at various times is constructed from known data and used to determine the force field along the filament. Those forces can then reproduce the flow everywhere. The validity of the method is evaluated by computing the drag on a sphere moving near a wall. Comparisons with known expressions for the drag show that the method gives accurate results for spheres even within a distance from the wall equal to the surface discretization size. [Copyright &y& Elsevier]

London and Maxwell equations are used in order to derive an exact and universal expression for the force and torque between a magnetic field (eventually a magnet) and a superconductor. This expression is useful for any shape and size of both magnet and superconductor and is suitable for finite elements calculations in the static limit. Furthermore, the equivalence of our general purpose expression with the well-known method of images is demonstrated for the case of a semi-infinite plane superconductor. [ABSTRACT FROM AUTHOR]

Abstract: As a sequel to our previous paper on extending the Fast Multipole Method (FMM) for charges inside a dielectric sphere [J. Comput. Phys. 223 (2007) 846–864], this paper further extends the FMM to the electrostatic calculation for charges inside a dielectric sphere immersed in an ionic solvent, a scenery with more relevance in biological applications. The key findings include two fourth-order multiple discrete image approximations in terms of u = λa to the reaction field induced by the ionic solvent, provided that u = λa <1 where λ is the inverse Debye screening length of the ionic solvent and a is the radius of the dielectric sphere. A 10−4 relative accuracy in the reaction field of a source charge within the sphere can be achieved with only 3–4 point image charges. Together with the image charges, the FMM can be used to speed up the calculation of electrostatic interactions of charges in a dielectric sphere immersed in an ionic solvent. [Copyright &y& Elsevier]

Abstract: Among different papers devoted to superconducting levitation of a permanent magnet over a superconductor using the method of images, there is a discrepancy of a factor of two when estimating the lift force. This is not a minor matter but an interesting fundamental question that contributes to understanding the physical phenomena of “imaging” on a superconductor surface. We solve it, make clear the physical behavior underlying it, and suggest the reinterpretation of some previous experiments. [Copyright &y& Elsevier]

Abstract: In this paper we use the method of images to derive the closed-form formula for the first passage time density of a time-dependent Ornstein–Uhlenbeck process to a parametric class of moving boundaries. The results are then applied to develop a simple, efficient and systematic approximation scheme to compute tight upper and lower bounds of the first passage time density through a fixed boundary. [Copyright &y& Elsevier]

Abstract: This paper presents the method of images for calculating electric field in two-dimensional arrangements. The method utilizes multipoles as the images to satisfy boundary conditions. The images are given for planar or cylindrical boundaries between two dielectrics and for those between a dielectric and a conductor. We introduce the use of three kinds of multipole re-expansions, which enables the calculation of images in complicated arrangements. The method has a clear advantage over using only line charges or line dipoles when the arrangement under consideration consists of more than two objects. Calculation examples are given to demonstrate the application of the method. The calculation results show that in an arrangement where the field is highly non-uniform, high accuracy can be attained by using the method. [Copyright &y& Elsevier]

Abstract: This paper presents the analysis of electric field and force on a conducting sphere lying on a dielectric solid under a uniform field. To achieve high accuracy, we have applied the analytical method of successively placing three infinite sequences of point and dipole charges (zero- or first-order multipoles). The electric field is highest at the contact point, called the triple junction, where the conductor, the dielectric solid, and the surrounding medium (gas or vacuum) meet together. Both the contact-point field and the force increase with the permittivity ratio of the solid to that of the surrounding medium. The resulting force always attracts the sphere to the solid, in contrast to the repulsive force in the case of a conducting sphere lying on a plane conductor under an external field. We have given very simple formulae for approximating the contact-point field and the force which agree with the precise values within a difference of 3% for permittivity ratios up to 32 and 64, respectively. [Copyright &y& Elsevier]

A new method for pricing lookback options (a.k.a.hindsightoptions) is presented, which simplifies the derivation of analytical formulas for this class of exotics in the Black-Scholes framework. Underlying the method is the observation that a lookback option can be considered as an integrated form of a related barrier option. The integrations with respect to the barrier price are evaluated at the expiry date to derive the payoff of an equivalent portfolio of European-type binary options. The arbitrage-free price of the lookback option can then be evaluated by static replication as the present value of this portfolio. We illustrate the method by deriving expressions for generic, standard floating-, fixed-, and reverse-strike lookbacks, and then show how the method can be used to price the more complex partial-price and partial-time lookback options. The method is in principle applicable to frameworks with alternative asset-price dynamics to the Black-Scholes world. [ABSTRACT FROM AUTHOR]

A new method for predicting the scattered acoustic field due to a plane wave incident upon an infinitely long cylinder lying near an penetrable plane interface is presented. The method generalizes the method of images which is restricted to rigid and soft plane interfaces. Validity domains, physical interpretations, simulations and numerical results are described for sedimentary medium-fluid plane interfaces. And, they are well compared with high frequency asymptotic results based on the Geometrical Theory of Diffraction(G.T.D.). [ABSTRACT FROM AUTHOR]

A procedure is described that permits a derivation of Cottrell’s equation without explicitly solving Fick’s second law. The procedure, which is based on a Green’s function approach is shown to successfully treat several other electrochemical situations. Unfortunately, however, the method is not universally valid. It is demonstrated that success is dependent on strict geometric conditions being met. [Copyright &y& Elsevier]

An analytic framework is developed to model the three-dimensional steady flow generated by wells placed at general nonvertical orientations within a horizontal aquifer. This framework uses closed-form solutions for a distribution of point sinks and point doublets along the centerline of the well and semi-infinite panel elements, each with piecewise linearly varying strengths. This extends previously published implementations and enables a boundary condition of uniform head along the cylindrical face of the well to be accurately matched. The resulting model is used to examine the drawdown and capture zone topology for wells spanning orientations ranging from vertical to horizontal. Scaling relationships are developed for wells perpendicular to flow that are invariant with respect to drawdown and to the strength of elements. The capture zone geometry for such wells is variant with respect to a dimensionless pumping rate, going through transition from two-dimensional flow in a plane perpendicular to the well to two-dimensional flow in a horizontal plane. [ABSTRACT FROM AUTHOR]

An image dipole method is employed to calculate the induced dipole moments of a pair of unequal-size conducting spheres subjected to a uniform electric field. Expressions for the dipole moments are given, involving the size ratio and separation of the spheres. Two typical cases are analyzed; two similar conducting spheres and two unequal conducting spheres with remarkable difference in size. [Copyright &y& Elsevier]