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A refined analytical model of spatially resolved diffuse reflectance with small source-detector separations (SDSs) for the in vivo skin studies is proposed. Compared to the conventional model developed by Farrell et al., it accounts for the limited acceptance angle of the detector fiber. The refined model is validated in the wide range of optical parameters by Monte Carlo simulations of skin diffuse reflectance at SDSs of units of mm. Cases of uniform dermis and two-layered epidermis-dermis structures are studied. Higher accuracy of the refined model compared to the conventional one is demonstrated in the separate, constraint-free reconstruction of absorption and reduced scattering spectra of uniform dermis from the Monte Carlo simulated data. In the case of epidermis-dermis geometry, the recovered values of reduced scattering in dermis are overestimated and the recovered values of absorption are underestimated for both analytical models. Presumably, in the presence of a thin mismatched topical layer, only the effective attenuation coefficient of the bottom layer can be accurately recovered using a diffusion theory-based analytical model while separate reconstruction of absorption and reduced scattering fails due to the inapplicability of the method of images. These findings require implementation of more sophisticated models of light transfer in inhomogeneous media in the recovery algorithms. [ABSTRACT FROM AUTHOR]

The capability of the in-house transient wave-multibody computational tool, ITU-WAVE, is extended to predict the wave power absorption with Wave Energy Converters (WECs) arrays placed in front of a vertical breakwater. The hydrodynamic forces are approximated by solving boundary integral equation at each time interval. The reflection of incoming waves due to a vertical wall is predicted with method of images. The constructive or destructive performance of WECs arrays with different array configurations is measured with mean interaction factor. The behaviour of the hydrodynamic forces of each WEC due to a vertical wall effect shows considerable differences than those of WECs arrays without a vertical wall. When the wave power absorption with WECs arrays with and without a vertical wall effect are compared, the numerical results show that WECs placed in front of a vertical wall have much greater effects on wave power absorption. This can be attributed to the hydrodynamic interaction, standing waves, and nearly trapped waves in the gap between a vertical wall and WECs arrays. The analytical and other numerical results are used for the validation of present ITU-WAVE computational results for exciting and radiation forces, and mean interaction factor of WECs arrays which show satisfactory agreements. [ABSTRACT FROM AUTHOR]

Diffraction radiation is widely used for the nondestructive diagnostics of charged particle beams. In the series of previous works, a method was developed for describing the diffraction radiation of a nonrelativistic particle on a perfectly conducting sphere, based on the method of images well-known from electrostatics. This method allows one to derive the analytic formulas for two main radiation characteristics, i.e., spectral angular density and polarization. The characteristic features of these values allow the possibility of developing, on their basis, new methods for monitoring the parameters of the trajectory of a moving particle in relation to the sphere center. In this work, formulas are obtained that describe the polarization of the coherent diffraction radiation on a metal sphere from a pancake-bunch of charged particles. It is shown that the polarization of the radiation in this case makes it possible to estimate the positions of bunch edges relative to the center of the sphere. This can be used for the nondestructive measurement of characteristic bunch dimensions. [ABSTRACT FROM AUTHOR]

The transition radiation of a charged particle in the simplest case of incidence on an infinitely conductive, ideal plane can be described based on the well-known method of images from electrostatics. This method also enables finding the distribution of fields in more complex cases, such as the field of a point particle in the presence of two intersecting conducting planes, the angle between which divides the angle 180° evenly. Based on the method of images, we describe the transition radiation that occurs when a fast charged particle strikes a target consisting of two conducting half-planes intersecting at right angles (from the inside of a dihedral angle). The characteristics of radiation emitted by fast and slow particles are qualitatively examined, and their visual interpretation is given. The possibility of using interference effects arising from radiation for monitoring beams of charged particles is discussed. [ABSTRACT FROM AUTHOR]

We propose a special variant of the inverse scattering transform method to construct and analyze soliton excitations in a semi-infinite sample of an easy-axis ferromagnet in the case of a partial pinning of spins at its surface. We consider the limit cases of free edge spins and spins that are fully pinned at the sample boundary. We find frequency and modulation characteristics of solitons localized near the sample surface. In the case of different degrees of edge spin pinning, we study changes in the cores of moving solitons as a result of their elastic reflection from the sample boundary. We obtain integrals of motion that control the dynamics of magnetic solitons in a semi-infinite sample. [ABSTRACT FROM AUTHOR]

A refined analytical model of spatially resolved diffuse reflectance with small source-detector separations (SDSs) for the in vivo skin studies is proposed. Compared to the conventional model developed by Farrell et al., it accounts for the limited acceptance angle of the detector fiber. The refined model is validated in the wide range of optical parameters by Monte Carlo simulations of skin diffuse reflectance at SDSs of units of mm. Cases of uniform dermis and two-layered epidermis-dermis structures are studied. Higher accuracy of the refined model compared to the conventional one is demonstrated in the separate, constraint-free reconstruction of absorption and reduced scattering spectra of uniform dermis from the Monte Carlo simulated data. In the case of epidermis-dermis geometry, the recovered values of reduced scattering in dermis are overestimated and the recovered values of absorption are underestimated for both analytical models. Presumably, in the presence of a thin mismatched topical layer, only the effective attenuation coefficient of the bottom layer can be accurately recovered using a diffusion theory-based analytical model while separate reconstruction of absorption and reduced scattering fails due to the inapplicability of the method of images. These findings require implementation of more sophisticated models of light transfer in inhomogeneous media in the recovery algorithms.

This paper focuses on deriving new approximate analytical solutions in wedge‐shaped aquifers. The proposed methodology is applicable to any type of aquifer namely, leaky, confined and unconfined, under both steady state and transient flow conditions. By applying the method of images and separating the flow field into sections using physical arguments, approximate analytical expressions are obtained for the drawdown function, which in contrast to the conventional theory, are applicable to any arbitrary wedge angle. Moreover, the solutions fully observe the boundary conditions, while they preserve the continuity of the drawdown, which can be calculated directly at any point of the flow field. Nevertheless, comparison of the results of the new approximate analytical solutions to numerical ones, has been considered necessary to check their validity. MODFLOW, a well‐known numerical tool is used to calculate the numerical results. The discrepancies between the numerical results and those of the approximate analytical solution are negligible. The main advantages of the proposed methodology are the following: (a) The model needs only finite number of terms compared to conventional analytical and numerical solutions that involve infinite series, (b) The computational load is low, so it can be easily used in conjunction with meta‐heuristic algorithms to solve groundwater resources optimization problems, (c) Stream depletion rate can be calculated rather accurately and (d) The method is applicable to related flow problems. Key Points: New functions for drawdown calculation in wedge‐shaped aquifers are presentedThe proposed functions are suitable to be used in conjuction with meta‐heuristic algorithms to solve groundwater optimization problemsConvergence of the results obtained from the set of functions and numerical methods (MODFLOW) point out the validity of the proposed solutions [ABSTRACT FROM AUTHOR]

The capability of the in-house transient wave-multibody computational tool, ITU-WAVE, is extended to predict the wave power absorption with Wave Energy Converters (WECs) arrays placed in front of a vertical breakwater. The hydrodynamic forces are approximated by solving boundary integral equation at each time interval. The reflection of incoming waves due to a vertical wall is predicted with method of images. The constructive or destructive performance of WECs arrays with different array configurations is measured with mean interaction factor. The behaviour of the hydrodynamic forces of each WEC due to a vertical wall effect shows considerable differences than those of WECs arrays without a vertical wall. When the wave power absorption with WECs arrays with and without a vertical wall effect are compared, the numerical results show that WECs placed in front of a vertical wall have much greater effects on wave power absorption. This can be attributed to the hydrodynamic interaction, standing waves, and nearly trapped waves in the gap between a vertical wall and WECs arrays. The analytical and other numerical results are used for the validation of present ITU-WAVE computational results for exciting and radiation forces, and mean interaction factor of WECs arrays which show satisfactory agreements.

A new technique for two-dimensional vortex methods is presented. The vorticity field is discretized and represented by vortex blobs. Viscosity and roughness are incorporated into vortex simulations by means of the corrected core-spreading method with LES theory. A deterministic and efficient grid-free method simulates viscous effects by maintaining small vortex core sizes through a splitting algorithm that controls the consistency error. The LES theory also enables the implementation of the roughness model. The effectiveness of this method is shown in calculating vortex interactions and decay in aircraft wakes with crosswind near a rough ground plane. The numerical results of the trajectory of primary vortical structures are compared with experimental data (when possible), suggesting the validity of the method. In general, the control of the roughness height size appears as an important factor to interfere on the trajectory of primary vortical structures in the ground effect with crosswind. The effect of the relative roughness height of ε/Δs = 0.001 shows that the primary vortical structures survive the interaction with the ground plane and can attain a maximum height in the order of 0.95 h (h is the release height of the primary vortical structures) during the loop for crosswind velocity of U∞ = 0.02 at Re = 7650. On the other hand, the combined effects of roughness ε/Δs = 0.001 and of crosswind U∞ = 0.04 at Re = 75,000 indicate that the primary vortical structures attain a maximum height about 0.83 h during the loop, tending to leave the runway faster, with sufficient intensity to disturb a smaller aircraft operating on a parallel runway. [ABSTRACT FROM AUTHOR]

External barrier options are financial securities that have two assets for stochastic variables, where the payoff depends on one underlying asset and the barrier depends on another state variable such that it determines whether the option is knocked in or out. In this study, considering the financial derivatives subject to the default risks of the option writer in over-the-counter markets since the global financial crisis of 2007–2008, we study vulnerable external barrier option prices by utilizing multivariate Mellin transforms and the method of images and then examine the behaviors and sensitivities of the vulnerable external barrier option prices in terms of the model parameters. Based on the results obtained, our study has two main contributions. First, by using multivariate Mellin transform approaches, we can find an explicit-form pricing formula for the option prices more effectively and easily, resolving the complexity of calculation of the option prices by using probabilistic or other methods. Second, we verify that our closed-form solution has been accurately and efficiently obtained by comparing the closed-form solution with the Monte Carlo simulation solution. [ABSTRACT FROM AUTHOR]

We study Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half spaces. First, we provide explicit density formulas, hinted by the method of images. These explicit expressions rely on infinite oscillating sums of Bessel functions and may demand computationally costly procedures. We propose suitable recursive algorithms for the simulation of the laws of reflected and stopped Brownian motion which are based on generalizations of the reflection principle in two dimensions. We study and give bounds for the complexity of the proposed algorithms. • Explicit density formula for the reflected Brownian motion in two dimensional wedges • Monte Carlo simulation algorithms for the reflected or stopped Brownian motion • Estimates on the computation time and adaptations to other reflected processes [ABSTRACT FROM AUTHOR]

Flow around, and hydrodynamic forces on, moving objects can be determined for low Reynolds numbers by superposing elemental Stokeslets to enforce velocity boundary conditions. The method of regularised Stokeslets provides a computationally-practical approach, replacing a sum over singular point elements by one over finite distributed sources. Flow disturbances extend a considerable distance in low-Re flow (typically falling off in magnitude as the reciprocal of distance) and the presence and nature of a nearby boundary cause a profound change to forces on moving objects. Representing boundaries by additional Stokeslets requires significantly more computational resources, so it is common to represent single planar boundaries by the method of images. Here we formally state the image systems for regularised Stokeslets in the case of plane no-slip walls and free surfaces in a form that is independent of orientation and in canonical six-term forms (for velocity) and three-term forms (for pressure) that are convenient for computation. We validate our implementation using exact solutions (sphere moving in unbounded flow and parallel or perpendicular to slip or no-slip boundaries) and previous simulations (translating and rotating helical filament). We then present new comparisons with experimental data for velocity profiles and forces on objects translating (towed cube in a confined tank) and rotating (helical micro-robot). Our simulations illustrate competing physical effects near a boundary. For an object moving, or propelling fluid, toward or away from a boundary, whether slip or no-slip, an increase in thrust is required to redirect fluid through 90°; viscous drag on a no-slip boundary increases the resistance coefficient further. For an object moving parallel to a boundary, however, opposing effects with different range come into play: the absence of fluid above the boundary reduces the required overall thrust on the fluid over a wide range of gap sizes, but enhanced viscous drag near a no-slip wall exceeds this at small gap sizes. • Orientation-independent canonical forms for regularised Stokeslet image systems. • Low-Re regularised Stokeslet solutions for velocity and pressure. • Forces due to translating/rotating bodies near no-slip walls and free surfaces. • Validation for exact solutions (sphere), previous calculations and new experiments. • Nearby boundaries may reduce resistance coefficient due to less fluid mobilised. • Nearby no-slip boundaries may increase resistance coefficient to overcome viscous drag. [ABSTRACT FROM AUTHOR]

A new technique for two-dimensional vortex methods is presented. The vorticity field is discretized and represented by vortex blobs. Viscosity and roughness are incorporated into vortex simulations by means of the corrected core-spreading method with LES theory. A deterministic and efficient grid-free method simulates viscous effects by maintaining small vortex core sizes through a splitting algorithm that controls the consistency error. The LES theory also enables the implementation of the roughness model. The effectiveness of this method is shown in calculating vortex interactions and decay in aircraft wakes with crosswind near a rough ground plane. The numerical results of the trajectory of primary vortical structures are compared with experimental data (when possible), suggesting the validity of the method. In general, the control of the roughness height size appears as an important factor to interfere on the trajectory of primary vortical structures in the ground effect with crosswind. The effect of the relative roughness height of ε/Δs = 0.001 shows that the primary vortical structures survive the interaction with the ground plane and can attain a maximum height in the order of 0.95 h (h is the release height of the primary vortical structures) during the loop for crosswind velocity of U∞ = 0.02 at Re = 7650. On the other hand, the combined effects of roughness ε/Δs = 0.001 and of crosswind U∞ = 0.04 at Re = 75,000 indicate that the primary vortical structures attain a maximum height about 0.83 h during the loop, tending to leave the runway faster, with sufficient intensity to disturb a smaller aircraft operating on a parallel runway.

The interaction between spherical cavitation bubble and flat wall is transformed into that between the real bubble and imaging bubble by the method of images. Firstly, we investigate the dynamics of real bubble and matched, inversed or mis-matched imaging bubble driven by a small amplitude ultrasound, revealing the characteristics of the interaction between cavitation bubble and rigid, soft and impedance walls. Then, we emphatically study the dynamics of real bubble and mis-matched imaging bubble driven by a finite amplitude ultrasound, and the interaction characteristics between cavitation bubble and real impedance wall are revealed. The results show that the cavitation bubble is always close to the rigid wall and far away from the soft wall; For the impedance wall, whether the cavitation bubble is far away or close depends on the specific wall parameters. Moreover, the direction and magnitude of bubble's translation velocity can be changed by adjusting the driving parameters. Understanding the interaction between cavitation bubble and impedance wall is of great significance for efficient application of ultrasonic cavitation.

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We discuss reachable states for the Hermite heat equation on a segment with boundary L²-control. The Hermite heat equation corresponds to the heat equation to which the quadratic potential x² is added. We will discuss two situations: when one endpoint of the segment is the origin and when the segment is symmetric with respect to the origin. One of the main results is that reachable states extend to functions in a Bergman space on a square one diagonal of which is the segment under consideration, and that functions holomorphic in a neighborhood of this square are reachable. [ABSTRACT FROM AUTHOR]

Since the initial isolation of few-layer graphene, a plethora of two-dimensional atomic crystals has become available, covering almost all known materials types including metals, semiconductors, superconductors, ferro- and antiferromagnets. These advances have augmented the already existing variety of two-dimensional materials that are routinely realized by quantum confinement in bulk-semiconductor heterostructures. This review focuses on the type of material for which two-dimensional realizations are still being actively sought: magnetoelectrics. We present an overview of current theoretical expectation and experimental progress towards fabricating low-dimensional versions of such materials that can be magnetized by electric charges and polarized electrically by an applied magnetic field – unusual electromagnetic properties that could be the basis for various useful applications. The interplay between spatial confinement and magnetoelectricity is illustrated using the paradigmatic example of magnetic-monopole fields generated by electric charges in or near magnetoelectric media. For the purpose of this discussion, the image-charge method familiar from electrostatics is extended to solve the boundary-value problem for a magnetoelectric medium in the finite-width slab geometry using image dyons, i.e. point objects having both electric and magnetic charges. We discuss salient features of the magnetoelectrically induced fields arising in the thin-width limit.

Adequate knowledge of physical phenomena has been shown to be essential for the development of new technologies. Such knowledge allows several engineering problems to be studied and solutions to be found. More and more complex problems have been studied and solved, especially in recent centuries. Infinite and semi-infinite spaces presented great discretization difficulty due to the scarcity of resources for this. With the emergence of numerical methods, these problems had their closest possible solution to being found. The present work presents the formulation and mathematical principles that comprise the Boundary Element Method model to approach twodimensional problems with infinite and semi-infinite domains. The particulars regarding the definition of the relevant variables, the characteristics of the fundamental solutions in these cases, and the behavior of primal variables at infinitely distant points are discussed. Aspects related to the discretization and numerical issues are also addressed by solving two particular semi-plane problems. The numerical results obtained showed satisfactory accuracy, confirming that the Boundary Element Method is the most adequate technique even today to solve such problems. [ABSTRACT FROM AUTHOR]

The application of in-house transient wave-body interaction ITU-WAVE computational tool is extended to predict the wave power absorption with Wave Energy Converters (WECs) arrays in front of a vertical wall using time dependent boundary integral equation method. The vertical wall effect is taken into account with method of images which considers the perfect reflection of incident waves from a vertical wall. The effects of separation distance between WECs as well as a vertical wall and WECs, and heading angles are studied to predict wave power absorption, mean and individual interaction factors which determine the performances of WECs arrays. The numerical results of WECs arrays in front of vertical wall show that both radiation and exciting force parameters are quite different from those of without a vertical wall. The numerical investigations also demonstrate that wave power absorption with an array system in front of a vertical wall are significantly greater than those of without a vertical wall. This is due to nearly trapped and standing waves between a vertical wall and WECs. The prediction of hydrodynamic parameters in front of a vertical wall with present ITU-WAVE are validated against other published numerical, analytical, and experimental results which show satisfactory agreements. [ABSTRACT FROM AUTHOR]

The behavior of spins undergoing Larmor precession in the presence of time varying fields is of interest to many research fields. The frequency shifts and relaxation resulting from these fields are related to their power spectrum, determined from the Fourier Transform of the auto-correlation functions of the time varying field. Using the method of images C. M. Swank, A. K. Petukhov, and R. Golub (2012 and 2016) calculated the position-position auto-correlation function for particles moving in a rectangular cell with specular scattering walls. In this work we present a heuristic model that applies the method of images to the case of Lambert scattering walls. The results of this model are compared to simulation and show remarkably good agreement from the ballistic to diffusive regime of gas collisions, for both square and general rectangular cells. • Method of images used to calculate correlation functions in the case of Lambert scattering walls. • Resulting model is valid from ballistic to diffusive regime of gas collisions. • Model is valid for square and rectangular cells. • Model shows good agreement with simulations. • Application to gradient induced relaxation and frequency shifts in NMR. [ABSTRACT FROM AUTHOR]

Method of images is used in many fields like electrostatics, fluid dynamics, etc. It requires many different formulae. This article aims to help the students comprehend these formulae and highlight the relation between electrostatic images with the results of optics. [ABSTRACT FROM AUTHOR]

Planar mirrored-coil structures are often used in the field of biomedicine as a sensor to measure physiological signals wirelessly. Although there are many studies on interrogation methodologies, research on the sensor itself remains understudied. In this article, we report an analytical formulation and a data-fitted formula to calculate the resonant frequency for a planar mirrored-coil sensor. Compared to the measured results, our analytical formula and data-fitted formula deviate by 13% and 9% median errors, respectively, which is much more accurate than the conventional one, 23%. It shows that both methods provide a way to quickly evaluate and design a planar mirrored-coil structure with high precision. [ABSTRACT FROM AUTHOR]

The evaluation of the tunnel correction remains an actual problem, especially for the effect of tunnel walls. Even if the experimental campaign meets the basic similitude criteria (Mach, Reynolds etc.), the wall effect on the measured data is always present. Consequently, the flow correction due the limited by walls must be evaluated. Solid wall corrections refer to the aerodynamic interference between the experimental model and the walls of the wind tunnel. This interaction affects the measured forces and implicitly the angle of attack. Usually, these effects are introduced through semi-empirical correction factors which change the global measured forces. The present paper refers to the mathematical and numerical modeling of aerodynamic interferences between the experimental model and the solid walls based on the potential flow model. The main goal is to asses a method allowing an estimate of the corrections for each configuration with a minimum computational resource.

Three dimensional dielectric systems are simulated to obtain the relaxational polarization responses. The dielectric system consists of randomly distributed permanent dipoles that fluctuate due to thermal activation in double well potentials between two plane-parallel electrodes. The barrier height between the wells is assumed to be proportional to the dipole length. The electrodes' effect is considered with the method of images. The relaxational phenomena of two dielectric systems, one with fixed and the other with distributed dipole lengths having single and distributed relaxation times, respectively, are calculated with a Monte-Carlo simulation method. The local field at every dipole and consequently the transition probabilities are computed to determine the transient polarization response iteratively. Both dielectric systems are simulated over a wide range of temperatures for interacting and non-interacting cases. The mean relaxation times exhibit a Vogel-Fulcher law for interacting systems and an Arrhenius law for non-interacting systems. [ABSTRACT FROM AUTHOR]

Mechanics of defects in solids across a wide span of length scales is commonly formulated using the dislocations theory. This paper revisits the classical problem of interaction between an elastic edge dislocation and a circular cavity. A heuristic, yet, mechanistic approach is taken to obtain the stress solution to this problem. The approach uses complex variable theory of elasticity, along with method of images. For this purpose, a definition and formulation of elastic dipole singularities similar to dipole charges in electrostatics is developed. It is shown that an image dislocation with Burger's vector of the same strength as the real dislocation but in opposite direction, as well as a set of four singularities including a dislocation dipole, a moment-dilatation dipole, and two centers of dilatation would establish a circular, traction-free boundary in an infinite elastic medium. Adding a Volterra dislocation to the finite-length edge dislocation from this study would recover the related problem of interaction between an infinite-length edge dislocation and circular cavity. The interesting analogy between the considered elastic problem and the electrostatic problem of interaction between a line electric charge and a cylindrical conductor is discussed. [ABSTRACT FROM AUTHOR]

We calculate exact two-dimensional analytic expressions for the electric and magnetic fields and their potentials generated by a linear beam of relativistic charged particles between infinite ideally conducting planes and ferromagnetic poles. We use the method of summing an infinite sequence of fields of linear image charges and image currents to obtain solutions and also calculate the density distribution of the electric charge on the conductor surface induced by the charged particle beam. We obtain new formulas for the linear approximation of the fields near the beam and discuss the mathematical features of the exact solutions and the applicability constraints for the linear approximations. [ABSTRACT FROM AUTHOR]

It is well known that long-term water injection may induce fractured channel(s), and that the fracture geometry would change with the decrease of bottom-hole pressure (BHP) during shut-in. This results in difficulties in modelling BHP behavior. This paper presents a pressure-transient procedure to analyze the BHP performance of water injectors by taking the dynamic behavior of the water injection fractured channel into consideration. Perturbation theory is adopted to solve the non-linear equations caused by decreasing fracture conductivity, while the finite-difference method is used to include the shrinking conductive fracture length during the shut-in period. Then, Duhamel's principle is deployed to characterize the bi-storage effect; that is, fracture-storage caused by fracture closure and wellbore storage because of wellbore after-flow. Since the mobility outside of channel walls are much poorer than that in the channel, the walls are modeled as two parallel sealed boundaries. Therefore, the method of images is lastly applied to obtain the BHP response. The bi-storage phenomenon is characterized by two unit slopes in the pressure-derivative curve, and the variable fracture-storage is identified as a new flow regime in water injectors that is caused by fracture shrinkage. The interpreted storage coefficient will be much larger than the true value if the fracture-storage flow is mistakenly regarded as wellbore-storage flow. Because of the fractured channel walls and decreasing fracture conductivity, the pressure-derivative curve would increase in late time. Finally, two cases from the Changqing Oilfield are discussed to demonstrate the capabilities of the proposed approach. [ABSTRACT FROM AUTHOR]

In the present study, the problems of diffraction and radiation of water waves by a cylindrical heaving wave energy converter (WEC) placed in front of a reflecting V-shaped vertical breakwater are formulated. The idea conceived is based on the possible exploitation of amplified scattered and reflected wave potentials originating from the presence of V-shaped breakwater, towards increasing the WEC’s wave power absorption due to the wave reflections. An analytical solution based on the method of images is developed in the context of linear water wave theory, taking into account the hydrodynamic interaction phenomena between the converter and the vertical wall. Numerical results are presented and discussed concerning the hydrodynamic forces on the absorber and its wave power efficiency for various examined parameters, namely, the breakwaters’ forming angle, the distance between the converter and the vertical walls and the wave heading angle. The results show that the amount of the harvested wave power by the WEC in front of the walls is amplified compared to the wave power absorbed by the same WEC in the open sea.

The one‐dimensional advection‐dispersion equation with streamwise boundaries has been used to model a wide range of real‐world processes including groundwater contaminant transport, atmospheric plume deposition, and the movement of planktonic organisms and migratory animals through riverine systems. Imposing boundary conditions at upstream and downstream locations complicates the analysis of this equation, and processes that require such boundary conditions are, therefore, typically modeled using approximations that are valid only under certain conditions. Approximations typically involve a simplification of the mass influx into the system, require a large separation between source and boundary, or work only in either strongly advection‐ or strongly dispersion‐dominated systems. Here, we circumvent these limitations by providing an analytical solution to a class of advection‐dispersion equations that are broadly applicable to the processes described above as well as many other physical and biological problems. Our solution makes it possible to relax the assumptions required under previous analytic approximations, making it a more flexible approach for modeling advection‐dispersion processes under realistic field conditions. We show that the solution is in good agreement with random walk simulations. To illustrate the broad utility of the method, we also apply it to an empirical data set from a population of migratory fish moving through a river system in the California Central Valley and demonstrate that it describes the data more accurately than do existing methods. Key Points: We provide an analytical solution of the advection‐dispersion equation with complex boundary conditionsOur solution Applies to environmental and ecological problems such as transport and fate of pollutants and aquatic organismsOur solution is a scalable and fast scoping tool for water resources and operations management [ABSTRACT FROM AUTHOR]

The polarization characteristics of diffraction radiation appearing during the uniform motion of a nonrelativistic charged particle near an ideally conducting sphere and also a hemispherical bulge in a conducting plane are calculated. Our previously developed approach based on the method of images, which is known in electrostatics, is used. It is shown that, in the low-frequency range, radiation at a hemisphere is always linearly polarized, while radiation at a sphere is generally characterized by elliptical polarization. [ABSTRACT FROM AUTHOR]

The radiation resulting from the uniform motion of a charged particle near (or through) a perfectly conducting sphere as well as near a hemispheric bulge on a metal plane has been considered previously using the method of images known from electrostatics. Here we discuss three topics: polarization of the diffraction radiation on the sphere as well as on the hemispherical bulge, transition radiation on the hemispherical bulge, and the coherent diffraction radiation from a bunch of charged particles. [ABSTRACT FROM AUTHOR]

Highlights • Method of images is successfully adopted to predict the LVG vortex dynamics. • A mixed LVG configuration is suggested to enhance the heat transfer performance. • LVG aspect ratio and channel height are very critical to the LVG effectiveness. Abstract This paper reports a numerical investigation of fluid flow and heat transfer in a rectangular channel with delta-shaped winglet longitudinal vortex generators (LVGs) under different configurations. In addition to the conventional common-flow-down configuration and the common-flow-up configuration, a unique mixed configuration is suggested. The "method of images" is successfully adopted to analyze the dynamics of the longitudinal vortices due to wall interference. The Nusselt number, friction factor and overall performance coefficient for the three configurations are compared at various Reynolds numbers (all less than 2200), LVG row numbers, channel heights, and LVG aspect ratios. It is found that the channel height and LVG aspect ratio are the two most critical factors influencing the effectiveness of the different LVG configurations, which may explain why inconsistent conclusions have been presented by previous studies comparing the performance of the common-flow-down and common-flow-up configurations. When the channel height is relatively small, the unique mixed configuration is found to be the most effective at enhancing fluid mixing (and therefore improving heat transfer) at streamwise cross sections. When the LVG aspect ratio becomes large, the common-flow-down configuration outperforms the common-flow-up configuration. This paper sheds some insight on how to design the optimal LVG configuration for enhancing heat transfer performance. [ABSTRACT FROM AUTHOR]

Far-field patterns of wire antennas on a PEC sphere are calculated from quasi-static near fields using spherical harmonic expansion. Three cases of the wire antennas—F-antenna, dipole, and resonant loop on the PEC sphere—are considered. With the assumed sinusoidal current distribution on the antenna, the method of images is employed to obtain currents and charges on the antenna's image against the sphere. Only from the charge density and current distributions of the wire antenna and its image, ignoring the sphere, the quasi-static near fields are calculated using Coulomb's and Biot–Savart's laws. The fields in a source-free region are expressed in spherical harmonic expansion with the coefficients obtained from the radial components of the calculated quasi-static electric and magnetic near fields. The far fields thus obtained from the expansion match well with that of the simulated patterns. Deviations between simulation and theory are discussed and explained. [ABSTRACT FROM AUTHOR]

The diffraction and transition radiation of a nonrelativistic charged particle on a perfectly conducting sphere is described using the method of image charges known from electrostatics. Asymptotic formulas that describe the characteristics of the radiation in the low- and high-frequency regions are constructed. It is shown that this approach in the high-frequency limit can be extended to the case of a relativistic incident particle. [ABSTRACT FROM AUTHOR]

The evaluation of the tunnel correction remains an actual problem, especially for the effect of tunnel walls. Even if the experimental campaign meets the basic similitude criteria (Mach, Reynolds etc.), the wall effect on the measured data is always present. Consequently, the flow correction due the limited by walls must be evaluated. Solid wall corrections refer to the aerodynamic interference between the experimental model and the walls of the wind tunnel. This interaction affects the measured forces and implicitly the angle of attack. Usually, these effects are introduced through semi-empirical correction factors which change the global measured forces. The present paper refers to the mathematical and numerical modeling of aerodynamic interferences between the experimental model and the solid walls based on the potential flow model. The main goal is to asses a method allowing an estimate of the corrections for each configuration with a minimum computational resource. [ABSTRACT FROM AUTHOR]

Forward modeling of seismic waves using physics-informed neural networks (PINNs) has attracted much attention. However, a notable challenge arises when modeling seismic wave propagation in large domains (i.e., a half-space), PINNs may encounter the issue of "soft constraint failure". To address this problem, we propose a novel framework called physics-constrained neural networks (PCNNs) specifically designed for modeling seismic wave propagation in a half-space. The method of images is incorporated to effectively implement the free stress boundary conditions of the Earth's surface, leading to the successful propagation of plane waves and cylindrical waves in a half-space. We analyze the training dynamics of neural networks when solving two-dimensional (2D) wave equations from the neural tangent kernel (NTK) perspective. An adaptive training algorithm is introduced to mitigate the unbalanced gradient flow dynamics of the different components of the loss function of PINNs/PCNNs. Furthermore, to tackle the complex behavior of seismic waves in layered media, a sequential training strategy is considered to enhance network scalability and solution accuracy. The results of numerical experiments demonstrate the accuracy and effectiveness of our approach. • Propose a novel framework called physics-constrained neural networks (PCNNs) to model seismic wave propagation in half-space. • An adaptive training algorithm is introduced for solving two-dimensional wave equations using PINNs/PCNNs. • The method of images is introduced to PINNs to hard-constraint the surface traction-free condition. [ABSTRACT FROM AUTHOR]