Transmission Boundary Research Articles

Acoustic nonreciprocity in a lattice incorporating nonlinearity, asymmetry, and internal scale hierarchy: Experimental study.

In linear time-invariant systems acoustic reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and it can be broken only by odd external biases, nonlinearities, or time-dependent properties. Recently it was shown that one-dimensional lattices composed of a finite number of identical nonlinear cells with internal scale hierarchy and asymmetry exhibit nonreciprocity both locally and globally. Considering a single cell composed of a large scale nonlinearly coupled to a small scale, local dynamic nonreciprocity corresponds to vibration energy transfer from the large to the small scale, but absence of energy transfer (and localization) from the small to the large scale. This has been recently proven both theoretically and experimentally. Then, considering the entire lattice, global acoustic nonreciprocity has been recently proven theoretically, corresponding to preferential energy transfer within the lattice under transient excitation applied at one of its boundaries, and absence of similar energy transfer (and localization) when the excitation is applied at its other boundary. This work provides experimental validation of the global acoustic nonreciprocity with a one-dimensional asymmetric lattice composed of three cells, with each cell incorporating nonlinearly coupled large and small scales. Due to the intentional asymmetry of the lattice, low impulsive excitations applied to one of its boundaries result in wave transmission through the lattice, whereas when the same excitations are applied to the other end, they lead in energy localization at the boundary and absence of wave transmission. This global nonreciprocity depends critically on energy (i.e., the intensity of the applied impulses), and reduced-order models recover the nonreciprocal acoustics and clarify the nonlinear mechanism generating nonreciprocity in this system.

Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium

We present a general derivation of the frequency-domain volume integral equation (VIE) for the electric field inside a non-magnetic scattering object from the differential Maxwell equations, transmission boundary conditions, radiation condition at infinity, and locally-finite-energy condition. The derivation applies to an arbitrary spatially finite group of particles made of isotropic materials and embedded in a passive host medium, including those with edges, corners, and intersecting internal interfaces. This is a substantially more general type of scatterer than in all previous derivations. We explicitly treat the strong singularity of the integral kernel, but keep the entire discussion accessible to the applied scattering community. We also consider the known results on the existence and uniqueness of VIE solution and conjecture a general sufficient condition for that. Finally, we discuss an alternative way of deriving the VIE for an arbitrary object by means of a continuous transformation of the everywhere smooth refractive-index function into a discontinuous one. Overall, the paper examines and pushes forward the state-of-the-art understanding of various analytical aspects of the VIE.

Combining Solar Energy Harvesting with Wireless Charging for Hybrid Wireless Sensor Networks

The application of wireless charging technology in traditional battery-powered wireless sensor networks (WSNs) grows rapidly recently. Although previous studies indicate that the technology can deliver energy reliably, it still faces regulatory mandate to provide high power density without incurring health risks. In particular, in clustered WSNs there exists a mismatch between the high energy demands from cluster heads and the relatively low energy supplies from wireless chargers. Fortunately, solar energy harvesting can provide high power density without health risks. However, its reliability is subject to weather dynamics. In this paper, we propose a hybrid framework that combines the two technologies - cluster heads are equipped with solar panels to scavenge solar energy and the rest of nodes are powered by wireless charging. We divide the network into three hierarchical levels. On the first level, we study a discrete placement problem of how to deploy solar-powered cluster heads that can minimize overall cost and propose a distributed 1:61(1+ϵ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -approximation algorithm for the placement. Then, we extend the discrete problem into continuous space and develop an iterative algorithm based on the Weiszfeld algorithm. On the second level, we establish an energy balance in the network and explore how to maintain such balance for wireless-powered nodes when sunlight is unavailable. We also propose a distributed cluster head re-selection algorithm. On the third level, we first consider the tour planning problem by combining wireless charging with mobile data gathering in a joint tour. We then propose a polynomial-time scheduling algorithm to find appropriate hitting points on sensors' transmission boundaries for data gathering. For wireless charging, we give the mobile chargers more flexibility by allowing partial recharge when energy demands are high. The problem turns out to be a Linear Program. By exploiting its particular structure, we propose an efficient algorithm that can achieve near-optimal solutions. Our extensive simulation results demonstrate that the hybrid framework can reduce battery depletion by 20 percent and save vehicles' moving cost by 25 percent compared to previous works. By allowing partial recharge, battery depletion can be further reduced at a slightly increased cost. The results also suggest that we can reduce the number of high-cost mobile chargers by deploying more low-cost solar-powered sensors.

Systematic design of broadband path-coiling acoustic metamaterials

A design approach for acoustic metamaterial unit cells based on a coiled path with impedance matching layers (IMLs) is proposed in this paper. A theoretical approach is developed to calculate the transmission of the labyrinthine unit cells with different effective refractive indices. The IML is introduced to broaden the transmission bandwidth and produce a lower envelope boundary of transmission for unit cells of different effective refractive indices. According to the theory, cells of all effective refractive indices can be built to achieve unitary transmission at center working frequencies. The working frequency can be tuned by adjusting the length of the IML. Numerical simulations based on finite element analysis are used to validate the theoretical predictions. The high transmission and low dispersive index nature of our designs are further verified by experiments within a broad frequency band of over 1.4 kHz centered at 2.86 kHz. Our design approach can be useful in various wavefront engineering applications.

Elliptic equations with transmission and Wentzell boundary conditions and an application to steady water waves in the presence of wind

In this paper, we present results about the existence and uniqueness of solutions of elliptic equations with transmission and Wentzell boundary conditions. We provide Schauder estimates and existence results in Hölder spaces. As an application, we develop an existence theory for small-amplitude two-dimensional traveling waves in an air-water system with surface tension. The water region is assumed to be irrotational and of finite depth, and we permit a general distribution of vorticity in the atmosphere.

A hybrid numerical–asymptotic boundary element method for high frequency scattering by penetrable convex polygons

We present a novel hybrid numerical–asymptotic boundary element method for high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. Our method is based on a standard reformulation of the associated transmission boundary value problem as a direct boundary integral equation for the unknown Cauchy data, but with a nonstandard numerical discretization which efficiently captures the high frequency oscillatory behaviour. The Cauchy data is represented as a sum of the classical geometrical optics approximation, computed by a beam tracing algorithm, plus a contribution due to diffraction, computed by a Galerkin boundary element method using oscillatory basis functions chosen according to the principles of the Geometrical Theory of Diffraction. We demonstrate with a range of numerical experiments that our boundary element method can achieve a fixed accuracy of approximation using only a relatively small, frequency-independent number of degrees of freedom. Moreover, for the scattering scenarios we consider, the inclusion of the diffraction term provides an order of magnitude improvement in accuracy over the geometrical optics approximation alone.

Trade-off between accuracy, cost, and QoS using a beacon-on-demand strategy and Kalman filtering over a VANET

Vehicular Ad-hoc Networks (VANETs) have been suggested as an active and powerful field of research to mitigate environmental problems and challenges. The main challenge in a VANET is to ensure routing with a good Quality of Service (QoS). The Greedy Perimeter Stateless Routing (GPSR) protocol is one of the most promising position-based routing mechanisms used to overcome this challenge. Its effectiveness depends entirely on the information on a node's mobility and the precision of this information. By broadcasting periodic beaconing within transmission boundary ranges, GPSR can manage neighbors' mobility information and maintain up-to-date lists of neighbours. Nevertheless, information on the position of a neighboring vehicle quickly becomes outdated, which negatively influences the efficiency of the routing. In order to monitor information mobility and to increase the QoS in this challenging area, position estimation needs to be considered.Thus, in this study, we examine the position estimation problem, and propose an improvement to the GPSR protocol, named KF-GPSR, where each vehicle estimates in real time the position of its neighbors using the Kalman filter algorithm. Indeed, by employing this strong estimation technique, it is possible to reduce considerably the frequency of exchanged beacon packets, while maintaining high position accuracy. For greater reliability, we also propose an extension to KF-GPSR, called BOD-KF-GPSR, that uses the “beacon-on-demand” process only if a node needs to rediscover its neighborhood. Simulation experiments using the network simulator NS-2 are presented to demonstrate the ability and usefulness of our two proposals. Here, we compare the proposed protocols against diverse common protocols: GPSR, AODV, DSR, and ZRP. The results show that BOD-KF-GPSR achieves a significant enhancement in terms of its packet delivery ratio, routing cost, normalized routing load, end-to-end delay, and throughput.

Multitrace/singletrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers

We present Nyström discretizations of multitrace/singletrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material properties. We investigate the performance of DDM with both classical Robin and optimized transmission boundary conditions. The optimized transmission boundary conditions incorporate square root Fourier multiplier approximations of Dirichlet to Neumann operators. While the multitrace/singletrace formulations as well as the DDM that use classical Robin transmission conditions are not particularly well suited for Krylov subspace iterative solutions of high-contrast high-frequency Helmholtz transmission problems, we provide ample numerical evidence that DDM with optimized transmission conditions constitute efficient computational alternatives for these type of applications. In the case of large numbers of subdomains with different material properties, we show that the associated DDM linear system can be efficiently solved via hierarchical Schur complements elimination.

Nanocross: A Highly Tunable Plasmonic System

With the help of electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) and boundary element method (BEM) simulations, we have shown that silver nanocross can be used to tune the plasmon modes and especially the higher order modes in a very controlled manner. Morphing a nanorod to a nanocross by growing another arm along the perpendicular bisector of a nanorod can lead to a spectacular evolution of various order modes in the EEL spectra. One can keep a mode fixed in energy while bringing the next higher order mode close to it, or even make it cross. This allows one to control the relative separation of energy of the plasmon modes. Hybridization of individual nanocross plasmon modes have also been studied by bringing two nanocrosses close together along one of their arms. An analytical approach based on first order perturbation theory and symmetry arguments based on group theory aptly fits the experimental observations.

Modeling the response of small myelinated axons in a compound nerve to kilohertz frequency signals

Objective. There is growing interest in electrical neuromodulation of peripheral nerves, particularly autonomic nerves, to treat various diseases. Electrical signals in the kilohertz frequency (KHF) range can produce different responses, including conduction block. For example, EnteroMedics’ vBloc® therapy for obesity delivers 5 kHz stimulation to block the abdominal vagus nerves, but the mechanisms of action are unclear. Approach. We developed a two-part computational model, coupling a 3D finite element model of a cuff electrode around the human abdominal vagus nerve with biophysically-realistic electrical circuit equivalent (cable) model axons (1, 2, and 5.7 µm in diameter). We developed an automated algorithm to classify conduction responses as subthreshold (transmission), KHF-evoked activity (excitation), or block. We quantified neural responses across kilohertz frequencies (5–20 kHz), amplitudes (1–8 mA), and electrode designs. Main results. We found heterogeneous conduction responses across the modeled nerve trunk, both for a given parameter set and across parameter sets, although most suprathreshold responses were excitation, rather than block. The firing patterns were irregular near transmission and block boundaries, but otherwise regular, and mean firing rates varied with electrode-fibre distance. Further, we identified excitation responses at amplitudes above block threshold, termed ‘re-excitation’, arising from action potentials initiated at virtual cathodes. Excitation and block thresholds decreased with smaller electrode-fibre distances, larger fibre diameters, and lower kilohertz frequencies. A point source model predicted a larger fraction of blocked fibres and greater change of threshold with distance as compared to the realistic cuff and nerve model. Significance. Our findings of widespread asynchronous KHF-evoked activity suggest that conduction block in the abdominal vagus nerves is unlikely with current clinical parameters. Our results indicate that compound neural or downstream muscle force recordings may be unreliable as quantitative measures of neural activity for in vivo studies or as biomarkers in closed-loop clinical devices.

Stabilization of the transmission wave/plate equation with variable coefficients

We consider the stabilization of the transmission wave/plate equation with variable coefficients and a general transmission boundary. By virtue of the Riemannian geometric approach, we obtain some stability results for nonlinear feedbacks acting on the regions under suitable geometric conditions.

2D Numerical Simulation of Improving Wellbore Stability in Shale Using Nanoparticles Based Drilling Fluid

The past decade has seen increased focus on nanoparticle (NP) based drilling fluid to promote wellbore stability in shales. With the plugging of NP into shale pores, the fluid pressure transmission can be retarded and wellbore stability can be improved. For better understanding of the interaction between shale and NP based drilling fluid based on previous pressure transmission tests (PTTs) on Atoka shale samples, this paper reports the numerical simulation findings of wellbore stability in the presence of NP based drilling fluid, using the 2D fluid-solid coupling model in FLAC3D™ software. The results of previous PTT are discussed first, where the steps of numerical simulation, the simulation on pore fluid pressure transmission, the distribution of stress and the deformation of surrounding rock are presented. The mechanisms of NP in reducing permeability and stabilizing shale are also discussed. Results showed that fluid filtrate from water-based drilling fluid had a strong tendency to invade the shale matrix and increase the likelihood of wellbore instability in shales. However, the pore fluid pressure near wellbore areas could be minimized by plugging silica NP into the nanoscale pores of shales, which is consistent with previous PTT. Pore pressure transmission boundaries could also be restricted with silica NP. Furthermore, the stress differential and shear stress of surrounding rock near the wellbore was reduced in the presence of NP. The plastic yield zone was minimized to improve wellbore stability. The plugging mechanism of NP may be attributed to the electrostatic and electrodynamic interactions between NP and shale surfaces that are governed by Derjaguin-Landau-Verwey-Overbeek (DLVO) forces, which allowed NP to approach shale surfaces and adhere to them. We also found that discretization of the simulation model was beneficial in distinguishing the yield zone distribution of the surrounding rock in shales. The combination of PTT and the 2D numerical simulation offers a better understanding of how NP-based drilling fluid can be developed to address wellbore stability issues in shales.

Homogenization of parabolic problem with nonlinear transmission condition

In this paper, we investigate the periodic homogenization of nonlinear parabolic equation arising from heat exchange in composite material problems. This problem, defined in periodical domain, is nonlinear at the interface. This nonlinearity models the heat radiation on the interface, which constitutes the transmission boundary conditions, between the two components of the material. The main challenge is, first, to show the well-posedness of the microscopic problem using the topological degree of Leray–Schauder tools. Then, we apply the two scale convergence to identify the equivalent macroscopic model using homogenization techniques. Finally, in order to confirm the efficiency of the homogenization process, we present some numerical results obtained via finite element approximation.

Optimized interface conditions in domain decomposition methods to solve reaction–diffusion problems with strong heterogeneity in the coefficients in a sectorial domain

The aim of this paper is to derive appropriate second order transmission boundary conditions near the corner used in domain decomposition methods to study the reaction–diffusion problems (“−∇.(ν(x)∇.)+η(x).”) with strong heterogeneity in the coefficients in a singular non-convex domain with Neumann and Dirichlet boundary condition. These transmission conditions will be tested and compared numerically with other approaches.

Numerical analysis of multicomponent responses of surface-hole transient electromagnetic method

We calculate the multicomponent responses of surface-hole transient electromagnetic method. The methods and models are unsuitable as geoelectric models of conductive surrounding rocks because they are based on regular local targets. We also propose a calculation and analysis scheme based on numerical simulations of the subsurface transient electromagnetic fields. In the modeling of the electromagnetic fields, the forward modeling simulations are performed by using the finite-difference time-domain method and the discrete image method, which combines the Gaver–Stehfest inverse Laplace transform with the Prony method to solve the initial electromagnetic fields. The precision in the iterative computations is ensured by using the transmission boundary conditions. For the response analysis, we customize geoelectric models consisting of near-borehole targets and conductive wall rocks and implement forward modeling simulations. The observed electric fields are converted into induced electromotive force responses using multicomponent observation devices. By comparing the transient electric fields and multicomponent responses under different conditions, we suggest that the multicomponent-induced electromotive force responses are related to the horizontal and vertical gradient variations of the transient electric field at different times. The characteristics of the response are determined by the varying the subsurface transient electromagnetic fields, i.e., diffusion, attenuation and distortion, under different conditions as well as the electromagnetic fields at the observation positions. The calculation and analysis scheme of the response consider the surrounding rocks and the anomalous field of the local targets. It therefore can account for the geological data better than conventional transient field response analysis of local targets.

A simple optical system for miniature spindle runout monitoring

Abstract We proposed a novel optical technique to monitor miniature spindle runout in a simple manner. Miniature spindles are commonly used in many machining applications, for example: micro-milling and micro-grinding. However, the capacitive sensors (CS) or eddy current sensors typically used for spindle runout measurements cannot be used for miniature spindle systems. This is due to the nonlinearity of the charge between a curved surface and a flat plate (sensing area) and a curved surface (measuring target area) and the effective sensing area being larger than the measuring target area. The proposed sensor utilizes curved-edge diffraction (CED), which uses the effect of the cylindrical surface curvature on the diffraction phenomenon in the transition regions adjacent to shadow, transmission, and reflection boundaries. The laser beam is incident to the spindle shaft edges along the Y and Z axes, four photodetectors then collect the total fields produced by the interference created by the waves due to CED around the spindle shaft edges. Two CS were used as a baseline comparison with the proposed sensor’s performance. A spindle with a shaft diameter of ϕ 5.0 mm (same as CS effective sensing area) was selected to compare the results of the curved-edge sensor (CES) with the results of the CS. The spindle runout was measured and the following results were found: CES-CS calibration nonlinearity (Z 0.35% and Y 0.40%) and resolution (Z 20.1 nm and Y 26.0 nm for CS and Z 20.3 nm and Y 15.9 nm for CES). The fundamental sensing limit of CES was estimated to be: Z 0.52 nm / Hz and Y 0.41 nm / Hz for a working range of approximately 100 μm, respectively.

The Complex Airy Operator on the Line with a Semipermeable Barrier

We consider a suitable extension of the complex Airy operator, $-d^2/dx^2 + ix$, on the real line with a transmission boundary condition at the origin. We provide a rigorous definition of this operator and study its spectral properties. In particular, we show that the spectrum is discrete, the space generated by the generalized eigenfunctions is dense in $L^2$ (completeness), and we analyze the decay of the associated semi-group. We also present explicit formulas for the integral kernel of the resolvent in terms of Airy functions, investigate its poles, and derive the resolvent estimates.

A Double Scale Fast Algorithm for the Transient Evolution of a Resonant Tunneling Diode

A fast algorithm is proposed for the simulation of the transient evolution of a resonant tunneling diode by a multiscale approach. The problem is modeled by the time-dependent Schrodinger--Poisson system. By decomposing the wave function into a nonresonant part and a resonant part, the fast algorithm is designed by combining a standard finite difference method for the Schrodinger--Poisson equation with proper time-dependent and/or nonlinear transmission boundary conditions. In addition, with a suitable interpolation of the nonresonant part, an accurate and fast algorithm is presented for the computation of the resonant part via the projection method. With this two scale decomposition, the new numerical method can save computational time significantly.

Iterative Tikhonov regularization for the Cauchy problem for the Helmholtz equation

The Cauchy problem for the Helmholtz equation appears in various applications. The problem is severely ill-posed and regularization is needed to obtain accurate solutions. We start from a formulation of this problem as an operator equation on the boundary of the domain and consider the equation in (H1/2)∗ spaces. By introducing an artificial boundary in the interior of the domain we obtain an inner product for this Hilbert space in terms of a quadratic form associated with the Helmholtz equation; perturbed by an integral over the artificial boundary. The perturbation guarantees positivity property of the quadratic form. This inner product allows an efficient evaluation of the adjoint operator in terms of solution of a well-posed boundary value problem for the Helmholtz equation with transmission boundary conditions on the artificial boundary.In an earlier paper we showed how to take advantage of this framework to implement the conjugate gradient method for solving the Cauchy problem. In this work we instead use the Conjugate gradient method for minimizing a Tikhonov functional. The added penalty term regularizes the problem and gives us a regularization parameter that can be used to easily control the stability of the numerical solution with respect to measurement errors in the data. Numerical tests show that the proposed algorithm works well.

The Efficient Mixed FEM With the Impedance Transmission Boundary Condition for Graphene Plasmonic Waveguides

A mixed finite-element method with an impedance transmission boundary condition (ITBC) is proposed to solve the graphene plasmonic modes. The new variational formulation combines the Gauss’ law with the transverse components of vectorial Helmholtz equation and models the field penetration through a thin graphene sheet by ITBC. The second-order edge-based vector LT/QN basis functions are applied to expand the transverse components of the electric field, and the nodal-based scalar basis functions are employed to discretize its longitudinal component. Numerical results on some designed graphene-based waveguides clearly demonstrate that the proposed method is efficient and accurate for the determination of graphene plasmonic modes.