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A method of recursive images applicable to diffusion in multilayer materials, is extended to cases where there is convection at the outer faces. Therefore this old/new method is now applicable to a wider, more diverse and real life diffusion problems. This objective is reached using a result by Bryan [1] who established that the Green function at a convection boundary involves adding a mirror reflecting thermal wave while subtracting a one-sided convolution, of a decreasing exponential with that same reflected wave. This is verified in the case of convection of heat, for a slab with its back face insulated. This method was then applied to find temperature solution for the diffusion in a slab having convection both at the front and at the back face of the slab. Finally the same rationale, of the recently proposed method of generalized method of images, was used to find the temperature solution for a three layered material with radiation convection at its front face. An alternative method is suggested which minimizes computation errors when the convection coefficient becomes very large. Finally a relationship is found between the semi-infinite solutions with and without convection radiation.

In the paper, a mathematic model for determination of the resistivity of thin antistatic coatings is presented. The model is based on a hybrid of four-points method and the method of images. The parameters of measuring system and coating layer are described in terms of the ratios of characteristic dimensions of the system. Both 2D and 3D cases are taken into considerations. The limiting values for the application of simplified 2D descriptions are derived.

Microelectrode arrays (MEAs), substrate-integrated planar arrays of up to thousands of closely spaced metal electrode contacts, have long been used to record neuronal activity in in vitro brain slices with high spatial and temporal resolution. However, the analysis of the MEA potentials has generally been mainly qualitative. Here we use a biophysical forward-modelling formalism based on the finite element method (FEM) to establish quantitatively accurate links between neural activity in the slice and potentials recorded in the MEA set-up. Then we develop a simpler approach based on the method of images (MoI) from electrostatics, which allows for computation of MEA potentials by simple formulas similar to what is used for homogeneous volume conductors. As we find MoI to give accurate results in most situations of practical interest, including anisotropic slices covered with highly conductive saline and MEA-electrode contacts of sizable physical extensions, a Python software package (ViMEAPy) has been developed to facilitate forward-modelling of MEA potentials generated by biophysically detailed multicompartmental neurons. We apply our scheme to investigate the influence of the MEA set-up on single-neuron spikes as well as on potentials generated by a cortical network comprising more than 3000 model neurons. The generated MEA potentials are substantially affected by both the saline bath covering the brain slice and a (putative) inadvertent saline layer at the interface between the MEA chip and the brain slice. We further explore methods for estimation of current-source density (CSD) from MEA potentials, and find the results to be much less sensitive to the experimental set-up.

We derive a general system of images for regularized sources, Stokeslets, and other related elements starting from an arbitrary regularization kernel (blob) used in the simulation of Stokes flows in three dimensions bounded by a plane. This generalizes previous work in which the image system for a Stokeslet had been derived for one specific blob. The significance of this generalization is that recent work on regularization methods requires the use of blobs designed to satisfy certain properties, such as zero moment conditions and fast decay, and thus it is absolutely necessary to have the system of images starting from an arbitrary blob. The system of images for a regularized element consists of a set of several elements, usually of higher order, that produce a flow that is zero at the bounding plane. In order for the resultant flow to vanish analytically at the wall, two different but related blobs must be used. For any given blob, we provide the formula for the companion blob that accomplishes the cancellation and we derive a systematic way to compute the image system of regularized Stokeslets, sources and dipoles. Other elements can be derived from these. By taking the limit as the regularization parameter approaches zero, the system of images for the corresponding singular elements is found.

We study the asymptotic behavior of the free partition function in thet→0+limit for a diffusion process which consists ofd-independent, one-dimensional, symmetric,2s-stable processes in a hyperrectangular cavityK⊂Rdwith an absorbing boundary. Each term of the partition function for this polyhedron ind-dimensions can be represented by a quermassintegral and the geometrical information conveyed by the eigenvalues of the fractional Dirichlet Laplacian for this solvable model is now transparent. We also utilize the intriguing method of images to solve the same problem, in one and two dimensions, and recover identical results to those derived in the previous analysis.

We consider the problem of an arbitrary shaped rigid punch pressed against the boundary of a transversely isotropic half-space and interacting with an arbitrary flat crack or inclusion, located in the plane parallel to the boundary. The set of governing integral equations is derived for the most general conditions, namely the presence of both normal and tangential stresses under the punch, as well as general loading of the crack faces. In order to verify correctness of the derivations, two different methods were used to obtain governing integral equations: generalized method of images and utilization of the reciprocal theorem. Both methods gave the same results. Axisymmetric coaxial case of interaction between a rigid inclusion and a flat circular punch both centered along the z-axis is considered as an illustrative example. Most of the final results are presented in terms of elementary functions.

Deflections and strains in an ice cover of a frozen channel caused by an underwater body moving under the ice with a constant speed along the channel are studied. The channel is of rectangular cross section, the fluid in the channel is inviscid and incompressible. The ice cover is clamped to the channel walls. The ice cover is modeled by a thin viscoelastic plate. The underwater body is modeled by a three-dimensional dipole. The intensity of the dipole is related to the speed and size of the underwater body. The problem is considered within the linear theory of hydroelasticity. For small deflections of the ice cover the velocity potential of the dipole in the channel is obtained by the method of images in leading order without account for the deflection of the ice cover. The problem of moving dipole in the channel with rigid walls provides the hydrodynamic pressure on the upper boundary of the channel, which corresponds to the ice cover. This pressure distribution does not depend on the deflection of the ice cover in the leading approximation. The deflections of the ice and strains in the ice plate are independent of time in the coordinate system moving together with the dipole. The problem is solved numerically using the Fourier transform, method of the normal modes and the truncation method for infinite systems of algebraic equations.

The approach that is based on the repeated use of the method of images is used to solve the problems of stationary acoustic, electromagnetic, and elastic wave scattering and diffraction by cylindrical and spherical obstacles in a semi-infinite domain. The solution is written in terms of an infinite series of multiply diffracted fields. Explicit approximate asymptotic solutions are found and investigated for the case of distant scattered fields in the longwave approximation. The known solutions for point obstacles are obtained as special cases described by the first terms of the series.

This paper presents an integrated algorithm for spinning mirror light field reconstruction displays in the field of volumetric three-dimensional display. The algorithm describes in detail the necessary data processing in the procedure of converting the computer three-dimensional model into an images sequence, which is required for light reconstruction 3D display. The influence of the designed angle between horizontal and mirror on the processing of securing image source, the adaptive transformation corresponding to rotated angles and the emendation of complex distorted images are described in this paper. Furthermore, we have discussed the binarization method of images sequence customized for the high speed projection kit and the construction of full color three-dimensional display sequence in detail. The experimental result shows that the proposed algorithm enables the acquisition and reconstruction of three-dimensional display images sequence in high-efficiency and high-quality.

Nowadays, there is a rising interest in studying the behavior of microbes and their interactions with flow and surfaces. In order to explore the velocity field, pressure and forces around the microbes, the solution of Stokes equations, which is called a Stokeslet, is used. This solution represents a singular velocity field due to a concentrated external force acting on fluid at a single point. This singularity could cause the expression of velocity not integrable. We use the Regularized Stokeslet Method and Method of Images to deal with this problem. The expression of force is replaced by a radially symmetric function, which distributes the force on a certain area rather than at a single point. We perform different numerical simulations to validate the code against analytical solution for flow around a sphere and a swimmer. The numerical results match well with the exact solutions. It can be concluded that the analytical solutions of microbes interacting with surfaces can be well simulated using the method of Regularized Stokeslet.

An analytical solution to leading-edge noise produced by a translating two-dimensional flat plate ingesting turbulence in proximity to a hard-wall is presented. This is a relevant problem to calculate the installation noise of open rotors and un-ducted fans. The analytical solution to the problem is given by using Amiet’s flat plate theory in conjunction with the Method Of Images (MOI) to include the effects of the wall. The low frequency, low Mach number limit of the analytical solution is investigated and it is shown that the flat plate in this limit behaves like a compact vertical dipole. The analytical solution is verified by a Computational AeroAcoustic (CAA) simulation that also uses the MOI to simulate a wall. While the MOI gives an approximation of the wall, it does not model all of the effects, such as diffraction from the edges of the flat plate and acoustic shielding due to the presence of the flat plate. These effects, which are ignored in the MOI are quantified using a CAA simulation that models the wall using a hard-slip-wall boundary condition. It is found that the analytical predictions and the CAA simulations using the MOI compare well. However, when the MOI is compared to the CAA simulation using a hard-slip-wall boundary condition, it is found that the MOI does not capture the effect of the shadow zone that is created due to the shielding effect of the aerofoil. The extent of the shadow zone is modified by changing the height of the aerofoil from the wall, and it shown that as the height of the aerofoil from the wall is increased, the shielding effect decreases.

Increasing the collection efficiency from solid-state emitters is an important step towards achieving robust single photon sources, as well as optically connecting different nodes of quantum hardware. A metallic substrate may be the most basic method of improving the collection of photons from quantum dots, with predicted collection efficiency increases of up to 50%. The established 'method-of-images' approach models the effects of a reflective surface for atomic and molecular emitters by replacing the metal surface with a second fictitious emitter which ensures appropriate electromagnetic boundary conditions. Here, we extend the approach to the case of driven solid-state emitters, where exciton-phonon interactions play a key role in determining the optical properties of the system. We derive an intuitive polaron master equation and demonstrate its agreement with the complementary half-sided cavity formulation of the same problem. Our extended image approach offers a straightforward route towards studying the dynamics of multiple solid-state emitters near a metallic surface.

© 2016 Elsevier B.V. This paper presents a simulation-based analysis of the effect of a reflecting surface on aeroacoustic Time-Reversal (TR) source localization/characterization and compares the results of TR with those obtained using cross-spectral Conventional Beamforming (CB). The TR technique is shown to require the use of at least two line arrays of microphones to accurately characterize the nature of aeroacoustic sources. This work, however, shows that in the presence of a rigid surface, only one line array of microphones is sufficient to accurately localize and characterize idealized aeroacoustic sources. Forward simulations were carried out using the 2-D Linearized Euler Equations on a rectangular domain with a rigid bottom boundary (modeling a 2-D semi-infinite space) for the test-cases of stationary idealized tonal aeroacoustic (monopole, dipole and lateral quadrupole) sources located in a fully-developed mean shear flow field wherein the acoustic pressure time–history was stored at the computational boundaries. A set of TR simulations are implemented that show for each test-case that only the top line array is required to accurately characterize the idealized aeroacoustic sources in the presence of a reflecting bottom boundary, thereby suggesting the redundancy of acoustic pressure measurement at the rigid surface. The test-case of convecting (moving) idealized aeroacoustic source was also considered and the TR simulation using only the top line array in the presence of reflecting bottom boundary was able to accurately retrieve the source trajectory and simultaneously characterize its nature. This numerical experiment demonstrates in principle that when a rigid surface is mounted on the floor of an Anechoic Wind Tunnel, the use of only one (top) line array of microphones should be sufficient to characterize the nature and location of experimental flow-induced noise source. Acoustic source maps were also obtained using the CB method based on the Method of Images (to model the reflecting surface) and incorporation of the Ray-Tracing algorithm necessary to account for the effect of mean flow. The CB results were found to be highly comparable to those obtained using TR for the test-cases of non-convecting sources; thereby demonstrating the conceptual equivalence of the Method of Images and directly implementing the rigid-wall condition during TR for source localization/characterization.

The extrema of Wiener processes are relevant to the pricing of so-called exotic options, which have many financial applications. The probability den-sities of such extrema are well known for one dimensional Wiener processes. We employ elementary methods to derive analytical expressions for the den-sities for multidimensional Wiener processes, with multiple extrema. These take the form of (possibly infinite) series expansions of Gaussian densities. This is undertaken using the characterization of the Wiener process by the heat equation, a well known connection in mathematical physics.

This paper is devoted to application of the fast algorithm to determine the flux around closely spaced non-overlapping disks on the conductive plane. This method is based on successive approximations applied to functional equations. When the distances between the disks are sufficiently small, convergence of the classical method of images fails numerically. In this talk, the limitations on geometric parameters are described.

We study $N$ noninteracting fermions in a domain bounded by a hard wall potential in $d \geq 1$ dimensions. We show that for large $N$, the correlations at the edge of the Fermi gas (near the wall) at zero temperature are described by a universal kernel, different from the universal edge kernel valid for smooth potentials. We compute this $d$ dimensional hard edge kernel exactly for a spherical domain and argue, using a generalized method of images, that it holds close to any sufficiently smooth boundary. As an application we compute the quantum statistics of the position of the fermion closest to the wall. Our results are then extended in several directions, including non-smooth boundaries such as a wedge, and also to finite temperature., 5 pages + 14 pages (Supp. Mat.), 6 figures

Near-field acoustic holography (NAH) is the process of reconstructing the vibrational behaviour of a structure from measurements of the acoustic field generated by these vibrations. Traditionally NAH was applied to planar regions where Fourier methods can be used to reconstruct the structural vibrations, even at frequencies beyond the sampling resolution limit. The Method of Superposition (MoS) is a relatively simple method for reconstructing the vibrational properties of structures with more general geometries. Recent work has shown that the MoS can also be effectively combined with sparse l1 regularisation to generate solutions from only a small number of terms in the superposition. In this work we discuss a reformulation of the MoS for NAH experiments in a semi-anechoic chamber; experiments in fully anechoic chambers can often prove impractical. In particular, we propose a modified Green’s function approach for a semi-infinite domain with a hard reflecting boundary using the Method of Images and present the results of some supporting numerical experiments.

The radiation resulting from the uniform motion of a charged particle near a hemispheric bulge in a metal plane is considered. The description of the radiation process based on the method of images is developed for the case of non-relativistic particle and perfectly conducting target. The spectral-angular and spectral densities of the diffraction radiation on the single bulge (as well as the Smith-Purcell radiation on the periodic string of bulges) are computed. The possibility of application of the developed approach to the case of relativistic incident particle is discussed., Comment: presented at RREPS-17, September 18-22, 2017, Hamburg, Germany

In this communication, based upon the stochastic Gompertz law of population growth, we have reformulated the Leaky Competing Accumulator (LCA) model with multiple alternatives such that the positive-definiteness of evidence accumulation is automatically satisfied. By exploiting the Lie symmetry of the backward Kolmogorov equation (or Fokker-Planck equation) assoicated with the model and applying the Wei-Norman theorem, we have succeeded to derive the N-dimensional joint probability density function (p.d.f.) and marginal p.d.f. for each alternative in closed form. With this p.d.f., a likelihood function can be constructed and thus model-fitting procedures become feasible. Moreover, by the method of images the closed-form first-passage-time distribution function across a parametric time-varying evidence boundary for each alternative has been obtained. The first-passage-time distribution function is useful for the study of response times in decision making as well as the investigation on how the evidence boundary can influence decision performance. Lastly, it should be noted that the proposed Lie-algebraic approach can also be applied to tackle the LCA model with time-varying parameters.

Aquitards can serve as long-term contaminant sources to aquifers when contaminant mass diffuses from the aquitard following aquifer source mass depletion. This study describes analytical and experimental approaches to understand reactive and nonreactive solute transport in a thin aquitard bounded by an adjacent aquifer. A series of well-controlled laboratory experiments were conducted in a two-dimensional flow chamber to quantify solute diffusion from a high-permeability sand into and subsequently out of kaolinite clay layers of vertical thickness 15 mm, 20 mm, and 60 mm. One-dimensional analytical solutions were developed for diffusion in a finite aquitard with mass exchange with an adjacent aquifer using the method of images. The analytical solutions showed very good agreement with measured breakthrough curves and aquitard concentration distributions measured in situ by light reflection visualization. Solutes with low retardation accumulated more stored mass with greater penetration distance in the aquitard compared to high-retardation solutes. However, because the duration of aquitard mass release was much longer, high-retardation solutes have a greater long-term back diffusion risk. The error associated with applying a semi-infinite domain analytical solution to a finite diffusion domain increases as a function of the system relative diffusion length scale, suggesting that the solutions using image sources should be applied in cases with rapid solute diffusion and/or thin clay layers. The solutions presented here can be extended to multilayer aquifer/low-permeability systems to assess the significance of back diffusion from thin layers.

Thermal analysis is essential in 3D-IC technology due to the reduced footprint and higher power densities compared to conventional 2D packaging. Computationally fast thermal models (FTMs) are being developed for fast evaluation of the temperature distribution in 3D packages. The steady state FTM discussed in this paper is based on Green's function theory and exploits convolution and the fast Fourier transform to compute the temperature profiles starting from matrices storing the power dissipation densities (power maps) and the temperature responses to hot spots. However, this methodology is not directly applicable for finite dimensional structures. The method of images is exploited to include the effect of insulating lateral boundary conditions. The number of images needed to ensure accurate results depends on the specific structure of the stack. A fast method to compute it is proposed together with a short analysis of its dependence on some system parameters. A two dies stack case study is thermally analyzed showing good agreement with the finite element method (FEM) results (errors less than 0.5%). The computational time is also discussed indicating a O ( N log N ) behavior, where N is the number of elements in the extended power maps, which include images, as well as a 70 times speed up with respect to FEM. Finally, since in the FTM the package is implicitly included in the boundary conditions, the thermal impact of its real configuration is investigated.

International audience; In the presence of a nearby highly reflecting dielectric substrate the optical response of a metal nanoparticle exhibits a rich multipolar plasmonic structure. For interpreting and quantifying the spectral patterns, the quasistatic hydrodynamic plasmon hybridization (PH) method developed by the Nordlander group has been applied to the particle/interface system in the simple generic case of a jellium sphere (PI–PH model). In the quasistatic limit, the method of images allows the PI–PH model to be tightly related to the two-sphere dimer PH model (D–PH model). However, because the dynamics of the electron fluid in the mirror particle is enslaved to that of the particle above the interface, strong differences between both PH models result from the reduction by a factor two of the number of dynamical variables describing the electron fluids. In particular the PI–PH model involves only bonding bright modes, whereas bonding and antibonding, bright and dark modes are involved in the homodimer case. A very detailed description of both PH models is provided, with particular emphasis on the coupling with an external field and the transfer of the oscillator strength of the dipole excitations of the isolated particle(s) to high-order plasmon modes of the particle/interface or dimer systems. The predictions of both PH models are also compared, through absorption and extinction cross-section spectra, to exact results computed in the frame of the multipole expansion method, allowing the range of applicability and limits of both models to be determined. Some comments about heterodimers are also provided.

For quantitative analysis of impact of grounding capacitance on the traction power supply system, in this paper, two wires system as an example with the mirror image method concluded the calculation formula of two wires system to ground capacitance and partial capacitance. At last, the influence of grounding capacitance on the traction power supply system is given quantitatively to provide the more accurate basis for engineering calculation.

This paper concerns the modeling of an eddy current damper with a finite conducting plate. In the eddy current damper, a finite rectangular conducting plate is moving between cuboidal magnets. The first step of the modeling method is based on an infinite conducting plate. For this infinite conducting plate, the eddy current density is derived using two different methods, the scalar potential method and the vector potential method. The finite boundaries of the conducting plate are included by means of the method of images in two dimensions and, therewith, complete the model. By applying the method of images, the accuracy of the models for calculating the damping coefficient is significantly improved. The assumption of an infinite conducting plate gives less than 15% error for a conducting plate with at least twice the dimensions of the permanent magnet. Applying the method of images reduces the modeling error for a conducting plate with two times the permanent-magnet dimensions to less than 3% in respect to a finite-element model. For the verification of the semianalytical model, measurements are performed. For a variation of the plate width, the presented semianalytical model has less than 5% discrepancy with respect to the measurements.

SUMMARY An analysis method for transient groundwater flow during slug tests performed in vertical cutoff walls is presented. The analytical solution for evaluating hydraulic conductivity of vertical cutoff walls is derived by applying the method of images to the previously developed analytical solution that is exclusively applicable to an infinite aquifer. Two distinct boundary conditions are considered to account for the configuration of the vertical cutoff wall: the wall-soil formation interfaces with or without the existence of filter cakes, that is, constant-head boundary and no-flux boundary conditions. A series of type curves is constructed from the analytical solution and compared with those of a partially penetrated well within an aquifer. The constant-head boundary condition provides faster hydraulic head recovery than the aquifer case. On the other hand, the no-flux boundary condition leads to a delayed hydraulic head recovery. The greater the shape factor and well offset from the center of the cutoff wall, and the smaller the width of the cutoff wall, the greater the effect of the boundary condition observed in the type curves. This result shows the significance of considering proper boundary conditions at the vertical cutoff wall in analyzing slug tests. Copyright © 2014 John Wiley & Sons, Ltd.

We present an algorithm for finding the electromagnetic field produced by an antenna located near a semiconducting plane by the method of images. The results of calculating the radiation pattern of an X-shaped antenna system with four inclined beams, which is located in immediate proximity of the Earth’s surface, are presented.

We use Kelvin’s method of images (Bobrowski in J. Evol. Equ. 10(3):663–675, 2010; Semigroup Forum 81(3):435–445, 2010) to show that given two non-negative integers $i\not= j$ there exists a unique cosine family generated by a restriction of the Laplace operator in C[0,1], that preserves the moments of order i and j about 0, if and only if precisely one of these integers is zero.

The two-dimensional scattering and diffraction of plane SH waves by a symmetrical V-shaped canyon with a circular underground structure in a half-space is studied by using the wavefunction expansion method. The underground structure involved covers three common types: a cavity, a lined tunnel and a geological inclusion. By combining a domain decomposition strategy and the method of images, the wavefields in corresponding subregions are constructed in terms of infinite series of wavefunctions with unknown complex coefficients. The unknown coefficients are obtained by applying the Graf's addition formula and solving a matrix that represents the boundary conditions along subregion interfaces. To show effects of the surficial canyon and underground structure combined irregularity on ground motions, a parametric study is executed in both the frequency and time domain. A zone of ground motion amplification is found at the vicinity of the corner of the canyon with a lined tunnel buried nearby.

Рассматривается способ сортировки изображений пыльцевых зерен на этапе предобработки для формирования выборки для обучения сверточной нейронной сети LeNet. На python разработана программа кадрирования изображения пыльцы, полученного с помощью оптического микроскопа, ImageSplitter, с помощью которой было кадрировано изображение полифлорного меда на 1131 изображение размером 128 ´ 128 пикселей при шаге скользящего окна 32 пикселя. На python разработана программа первичной классификации, позволяющая отсортировывать пустые изображения от непустых посредством задачи условий и интервалов степени заполненности черным. Проведено исследование на возможность сортировки непустых изображений на три класса по проценту заполненности черным. Вычисляется доля черных точек среди всех Perimeter total (т. е. критерий занятой зерном площади кадра), доля черных точек среди точек на границах – критерий занятого зерном периметра кадра – Perimeter black и в процентном соотношении Perimeter percentage. Осуществлялась инвертированная пороговая бинаризация для выделения объектов. Были получены следующие результаты: в промежутке от 0 до 30 программа не вывела никаких изображений, т. е. папка output_result_0-30 оказалась пустой; в промежутке от 31–60 программа классифицировала 4 изображения, т. е. в папке output_result_31-60 оказалось 4 изображения; в промежутке 61–99 программа классифицировала 130 изображений.

Strains in the ice cover of a frozen channel, which are caused by a body moving under the ice at a constant speed along the channel, are studied. The channel is of rectangular cross section, the fluid in the channel is inviscid and incompressible. The ice cover is modeled by a thin viscoelastic plate clamped to the channel walls. The underwater body is modeled by a three-dimensional dipole. The intensity of the dipole is related to the speed and size of the underwater body. The problem is considered within the linear theory of hydroelasticity. For small deflections of the ice cover the velocity potential of the dipole in the channel is obtained by the method of images without account for ice deflection in the leading order. The problem of a dipole moving in the channel with rigid walls provides the hydrodynamic pressure on the upper boundary of the channel, which corresponds to the ice cover. This pressure distribution does not depend on the deflection of the ice cover in the leading approximation. The deflections of ice and the strains in the ice cover are independent of time in the coordinate system moving together with the dipole. The problem is solved numerically using the Fourier transform along the channel, the method of normal modes across the channel, and the truncation method for resulting infinite systems of linear equations. It was revealed that the strains in the ice strongly depend on the speed of the dipole with respect to the critical speeds of the hydroelastic waves propagating along the frozen channel. The width of the channel matters even it is much larger than the characteristic length of the ice cover.

In the present paper, the hydrodynamic performance of a linear array of truncated circular cylinders in front of a bottom–mounted vertical wall is analysed in the frequency domain in order to investigate the effect of the wave reflections combined with the disturbances induced by the bodies themselves. Infinite and finite-length wall cases are examined and compared. The former case is formulated and solved using the matched eigenfunction expansion technique and the “direct” solution methodology for the numerical implementation. The existence of a “pure” wave-reflecting wall of infinite length is considered by utilizing the method of images. For the finite-length wall cases the conventional Boundary Integral Equation (BIE) formulation is employed. Emphasis is given on: (a) revealing the limitations of the “infinite wall” concept on the calculation of the exciting forces acting on the cylinders of the array and (b) investigating the effect of the length of the wall on the aforementioned physical quantities. The results demonstrate that the “infinite wall” concept leads to under- or over-estimation of the heave exciting forces at small wave numbers, while this concept seems not to be adequate for the accurate calculation of the horizontal exciting forces in cases of small outer cylinder's center–to–wall's edge distance. The change of the wall's length affects the surge and the heave exciting forces, while, the presence of the wall, contrary to the case of the isolated array, leads to an intense variation pattern of the cylinders' sway exciting forces. This pattern is characterized by successive local minima, which can be related to the existence of a symmetrical wave field in the seaward and leeward sides of the cylinders.

The solution of the elastic field for inclusions in an elastic half space has been applied widely in many contact analyses and engineering designs. A popular method to solve the half-space inclusion problem resorts to the method of images, where the solution is decomposed into 3 components consisting of the full space inclusion, mirrored inclusion, and the surface traction cancellation. In the process of cancelling the redundant surface tractions determined from a full space inclusion problem, the computation domain is supposed to be limited in a finite size and there is inevitably truncation error. It has not been quantitatively investigated how the truncation error will influence the accuracy of the numerical computations based on the method of images. This work studies the deflection of the boundary surface of a half-space containing an Eshelby inclusion. Errors due to mesh refinement and domain truncation are quantitatively analyzed. Parametric studies are performed for a systematic examination of surface redundant tractions and their influences.

In this paper, we investigate the fundamental linkage between underwater electric potential (UEP) signatures and their related electric fields above the waterline, which are introduced as above water electric potential (AEP) signatures. As a first step, the field distribution for an underwater point source excitation (fundamental solution) is derived analytically, using an adjusted method of images. Subsequently a numerical approach is introduced, whereby the calculation of the stationary current density distribution and electrostatic fields are coupled within an FEM simulation. Simulation results are presented for the aforementioned point source, as well as for a submarine model, where the latter includes considering non-linear polarization curves to model the electrochemical behavior at the metal&ndash, seawater interface. Finally, the relevance of AEP signatures in the context of anti-submarine warfare (ASW) is discussed. Our results show that AEP signatures inevitably occur along with UEP signatures, and could therefore in principal be used to detect submerged submarines via airborne sensors. However, an estimation of the expectable signal-to-noise-ratio (SNR) suggests that AEP signatures are difficult to exploit and therefore entail a much lower risk compared to other signatures.

Insulation level of power equipment is always dependent on the electric field intensity (EFI) on the electrode surface and in internal dielectric of power equipment. However, as we know, the EFI on the electrode surface cannot be measured so far. The method for electronic EFI measurement is proposed in this article. The physical model for the experiment with an analytical solution to EFI is designed. The EFI measurement is conducted at many different points on the metal surface of high-voltage conductor of the physical model. Combined the method of images with the electric axis method, the analytical solution of the electric field at different positions on the surface of a high-voltage conductor is obtained. Comparison between measurement results and computation results of the EFI is made. The relative error between them is less than 5%. The proposed method is verified. The proposed method of EFI in this article can be used in study of compact power equipment, online detection, state evaluation, and the study on safety and stability of power grid.

This paper presents the electrostatic analysis of a conducting prolate spheroid under an external electric field in axisymmetric configurations. The configurations consist of a conducting spheroid which is in contact with or separated from a grounded plane. We apply the method of images using multipoles to the electric field calculation. The calculation uses the multipole re-expansion formulae and the equivalent image charges of a prolate conducting spheroid. The induced charge and force are determined from the multipole images. For a spheroid on the grounded plane, the calculation results show that the maximal field increases nonlinearly with the major-to-minor axis ratio of the spheroid. The charge and the force are compared between the spheroids of the same major axis or the same surface area. We propose empirical formulae for approximating the maximal field, charge and force with the errors smaller than 2% for the axis ratio between 1 and 32. We examine the propriety of the approximation of the electric field, charge and force based on a hemispheroidal model. For an uncharged spheroid separated from the grounded plane, we clarify the relationship between the separation and the field intensification at the bottom pole of the spheroid. Based on the critical field strength of a background medium, the position of the spheroid where the partial discharge takes place is estimated. For a charged spheroid, we found that the maximal electric field hardly depends on the separation from the plane.

For the relative motion between an imaging system and its objects, it results in motion-blurred images in acquiring images. The physical theory of motion-blurred images for moving objects are analyzed in this paper, then the motion-blurred process is researched to establish blurring-model and the essential elements of the process are extracted to form the expressions. The every grey scale value of images pixels is computed and processed to form the motion-blurred images, then based on the contradictorily computing analysis, the restoring model of blurring imaging is established and the restoring expressions are gained. The processing courses of motion-blurred and restoring images are achieved by computing program VC++. The simulation experiments show that the method of images process can be used to make motion-blurred images and restoring images when the objects motion is two dimensions uniform velocity rectilinear motion effectively.

This paper explores the advantages of pricing American options using the first-passage density of a Brownian motion to a curved barrier. First, we demonstrate that, under this approach, the exact computation of the optimal boundary becomes secondary. Consequently, a simple approximation to the optimal boundary suffices to obtain accurate prices. Moreover, the first-passage approach tends to give more accurate prices than the early-exercise-premium integral representation. We present two ways of implementing the approach. The first is based on an exact representation of the first-passage density. The second exploits the method of images, which gives us a family of barriers with first-passage densities given in closed form. Both methods are very easy to implement and give accurate prices. In particular, the images-based method is extremely accurate.

Knowledge of the end winding inductance of electrical machines is decisive for calculating their operating performance. In this article, two different approaches to analytically calculate the stator end winding inductance of large induction machines are discussed. The first method is based on the exact replication of the 3D conductor geometry using serially connected straight filaments, where the inductances are calculated by solving Neumann's integral. In the second method, the end winding flux is resolved into components excited by the axial and circumferential end winding magnetomotive force, resulting in a far simpler geometrical model. In both cases, end face effects are taken into account by adopting the method of images. The analytical approaches are compared to the known analytical calculation method proposed by Alger [1]. In addition, the stator end winding inductance is computed by means of 3D finite-element analysis. Using experimental validation, it is shown that both the analytical a...

Groundwater studies face computational limitations when providing local detail (such as well drawdown) within regional models. We adapt the Analytic Element Method (AEM) to extend separation of variable solutions for a rectangle to domains composed of multiple interconnected rectangular elements. Each rectangle contains a series solution that satisfies the governing equations and coefficients are adjusted to match boundary conditions at the edge of the domain and continuity conditions across adjacent rectangles. A complete mathematical implementation is presented including matrices to solve boundary and continuity conditions. This approach gathers the mathematical functions associated with head and velocity within a small set of functions for each rectangle, enabling fast computation of these variables. Benchmark studies verify that conservation of mass and energy conditions are accurately satisfied using a method of images solution, and also develop a solution for heterogeneous hydraulic conductivity with log normal distribution. A case study illustrates that the methods are capable of modeling local detail within a large-scale regional model of the High Plains Aquifer in the central USA and reports the numerical costs associated with increasing resolution, where use is made of GIS datasets for thousands of rectangular elements each with unique geologic and hydrologic properties, Methods are applicable to interconnected rectangular domains in other fields of study such as heat conduction, electrical conduction, and unsaturated groundwater flow.

The acoustic field radiation from an impulsive source located in a discretely layered and laterally bounded fluid is investigated with the aid of the generalized-ray theory. The main ingredient of the presented approach is the Cagniard–de Hoop technique in combination with the method of images that provide exact space–time expressions for the activated acoustic wavefield components. Illustrative numerical examples are presented.

Some characteristics of interior explosions within a cabin structure with a venting hole are investigated. It may simulate a warhead explosion inside a cabin following its penetration through the cabin wall. The study includes both experimental and theoretical analyses of the problem. The experimental investigation comprises of two types of explosives at the center of the cabin. The pressure distributions at different locations on the cabin wall are obtained. The effect of internal shock reflection is analyzed by using the method of images (MOI). It is found that the geometric symmetries can cause the multiple reflected shocks to converge with strength comparable to the initial free shock.

This paper extends the image charge solvation model (ICSM) [J. Chem. Phys. 131, 154103 (2009)], a hybrid explicit/implicit method to treat electrostatic interactions in computer simulations of biomolecules formulated for spherical cavities, to prolate spheroidal and triaxial ellipsoidal cavities, designed to better accommodate non-spherical solutes in molecular dynamics (MD) simulations. In addition to the utilization of a general truncated octahedron as the MD simulation box, central to the proposed extension is an image approximation method to compute the reaction field for a point charge placed inside such a non-spherical cavity by using a single image charge located outside the cavity. The resulting generalized image charge solvation model (GICSM) is tested in simulations of liquid water, and the results are analyzed in comparison with those obtained from the ICSM simulations as a reference. We find that, for improved computational efficiency due to smaller simulation cells and consequently a less number of explicit solvent molecules, the generalized model can still faithfully reproduce known static and dynamic properties of liquid water at least for systems considered in the present paper, indicating its great potential to become an accurate but more efficient alternative to the ICSM when bio-macromolecules of irregular shapes are to be simulated.

In radar cross section (RCS) calculation of a rough surface, the model can be simplified into the scattering of geometrically idealized bosses on a surface. Thus the problem of the RCS calculation of a rough surface is changed to the RCS calculation of the semicircular boss. The RCS measurement of scale model can help save time and money. The utilization of terahertz in RCS is attractive because of its special properties: the wavelength of the terahertz wave can help limit the size of the model in a suitable range in the measurement of the scale model and get more detailed data in the measurement of the real object. However, usually the incident beam of a terahertz source is a Gaussian beam; in the theoretical RCS estimation, usually a plane wave is assumed as the incident beam for sake of simplicity which may lead to an error between the measurement and calculation results. In this paper, the method of images is used to calculate the RCS of a semicircular boss at 2.52 THz and the results are compared to the one calculated when the incident beam is a plane wave.

Cylindrical and prismatic nano-structures (nano-wires and pores) with circular and hexagonal cross-section are studied using mirror boundary conditions to solve the Schrodinger equation in effective mass approximation. In comparison with “quantum billiard” problem, the solution using mirror boundary conditions allows to obtain the results in a much simpler way. It is possible to use even and odd mirror boundary conditions depending on the sign of the wave-function equated in the original and the image points, respectively. The even mirror boundary conditions provides non-vanishing wave-function at the boundary, corresponding to weak confinement allowing quantum tunneling. The odd mirror boundary conditions set wave-function to zero at the boundary, corresponding to a strong confinement. We report on spatial distributions of probability density in cross-section of a cylindrical and prismatic nano-structures, presenting the formulas for the energy of the corresponding quantum states.