Arbitrary Number Of Layers Research Articles

Wideband Transition for Increased-Height Empty Substrate Integrated Waveguide

Recently, Empty Substrate Integrated Waveguide (ESIW) technology was proposed for embedding empty waveguides into planar substrates in order to improve their performance. A low-loss and narrow-band transition from microstrip to an increased height ESIW with 4 layers was presented in a previous work, and used to implement a very high-quality factor bandpass filter at Q-band. With such a narrow-band transition, based on a quarter-wavelength transformer, a very narrow-band filter response with resonators having a quality factor of 1000 was achieved. In this paper, in order to overcome the narrow-band and the 4-layers output restrictions, and extend the practical use of such increased height ESIWs beyond narrow-band filters, we present a novel wideband transition from microstrip to an increased height ESIW with an arbitrary number of layers. A full suite of wideband transitions to increased height ESIWs, built with different number of substrate layers ranging from 3 to 8, has been designed in this work to operate at Ka-band, though they can be easily transferred to other bands if the dimensions of the transition are properly scaled. To illustrate this, the original Ka-band transitions have been mapped to Ku-band, with excellent results. In order to test the proposed design method, a prototype of a 4-layer structure has been fabricated at Ka-band, achieving a good performance in the whole useful bandwidth of the ESIW.

Three-dimensional modeling of the static behavior of magneto-electro-elastic multilayer plates based on an elastic support

In this communication, the state space method is used to analyze the static behavior of laminated magneto-electro-elastic rectangular plates with simply supported boundary conditions based on an elastic support. The mathematical formulation is elaborated in a general form and an arbitrary number of layers as well as the orthotropic behavior can be considered. The methodology is based on the mixed formulation, in which basic unknowns are formed by collecting displacements, stresses, electrical displacements, electrical potential, magnetic induction and magnetic potential. As special case, multilayered rectangular plate is analyzed under the surface loading with simply supported boundary conditions based on an elastic support. The procedure of calculation shows that the formulation presented here is simple and direct.

Spectrum Concentration in Deep Residual Learning: A Free Probability Approach

We revisit the weight initialization of deep residual networks (ResNets) by introducing a novel analytical tool in free probability to the community of deep learning. This tool deals with the limiting spectral distribution of non-Hermitian random matrices, rather than their conventional Hermitian counterparts in the literature. This new tool enables us to evaluate the singular value spectrum of the input-output Jacobian of a fully connected deep ResNet in both linear and nonlinear cases. With the powerful tool of free probability, we conduct an asymptotic analysis of the (limiting) spectrum on the single-layer case, and then extend this analysis to the multi-layer case of an arbitrary number of layers. The asymptotic analysis illustrates the necessity and university of rescaling the classical random initialization by the number of residual units L, so that the squared singular value of the associated Jacobian remains of order O(1), when compared with the large width and depth of the network. We empirically demonstrate that the proposed initialization scheme learns at a speed of orders of magnitudes faster than the classical ones, and thus attests a strong practical relevance of this investigation.

Diffraction of Electromagnetic Waves by Nanoobjects With Internal Structure

This paper studies the problem of diffraction of electromagnetic waves on an object containing an arbitrary number of layers of materials with different permittivity and permeability. It is assumed that the typical size of the object is much smaller than the wavelength of the incident wave. In other words, we adopt long-wave approximation and the ratio of these values $k$ is considered a small parameter. In this case, the electromagnetic field can be described by an integral equation using the Stratton–Chu formula. The solution of this equation is sought in the form of a multipole expansion at large distances from the object and in the form of an expansion in the small parameter $k$ in the vicinity of the object. The coefficients in these expansions are determined by solving a recurrence system of electrostatic problems. To illustrate the approach, we consider diffraction of the electromagnetic wave on a cylinder whose cross section consists of two eccentric circles. The proposed scheme for solving diffraction problems is quite simple and does not impose any restrictions on the dielectric and magnetic permeability of the layers. It can be used in the calculation of the scattered electromagnetic field on metal structures as well as on nanoobjects containing layers of metamaterials.

A scaled boundary finite element method for static and dynamic analyses of cylindrical shells

A modeling technique based on the scaled boundary finite element method is developed for both static and dynamic analyses of cylindrical shells. A new scaling strategy is employed to ensure that the shell boundaries and the cross sections at the element inferfaces are accurately represented through the scaling process. The formulation starts directly from the three-dimensional linear elasticity theory for cylindrical shells. The principle of virtual work involving the inertial force is applied to derive the scaled boundary finite element equation. Only the in-plane dimensions of the structure are discretized with finite elements while the solution through the thickness is expressed analytically as a Padé expansion. A variable transformation procedure facilitates the development of the dynamic stiffness matrix, which leads to the static stiffness matrix and mass matrix naturally. A laminate model with arbitrary number of layers can readily be constructed. Numerical examples demonstrate the accuracy, applicability and efficiency of the two-layer model.

Surface plasmon sensing with broadband coherent laser pulses

A broadband detection method with coherent laser pulses exciting surface plasmons is investigated. The intensity and phase characteristics of the reflected light in Kretschmann configuration are calculated. It is shown that by mixing in-plane and out-of-plain polarization components of the incident light, the measurements of the changes of the refractive index of the adjacent media can be efficiently performed by observing the shift of the steep slope of the surface plasmon resonance (SPR) reflectance curve. We have demonstrated that such sensing can be performed by observing the angular shift of the SPR curve as well as the spectral shift. The developed model can account for an arbitrary number of layers and is used to simulate the response when an additional functionalizing layer adjacent to the gold film is used.

An Intuitive Equivalent Circuit Model for Multilayer Van Der Waals Heterostructures

Stacks of 2-D materials, known as van der Waals (vdW) heterostructures, have gained vast attention due to their interesting electrical and optoelectronic properties. This paper presents an intuitive circuit model for the out-of-plane electrostatics of a vdW heterostructure composed of an arbitrary number of layers of 2-D semiconductors, graphene, or metal. We explain the mapping between the out-of-plane energy band diagram and the elements of the equivalent circuit. Although the direct solution of the circuit model for an n-layer structure is not possible due to the variable, nonlinear quantum capacitance of each layer, this paper uses the intuition gained from the energy band picture to provide an efficient solution in terms of a single variable. Our method employs Fermi–Dirac statistics while properly modeling the finite density of states (DOS) of 2-D semiconductors and graphene. The approach circumvents difficulties that arise in commercial TCAD tools, such as the proper handling of the 2-D DOS and the simulation boundary conditions when the structure terminates with a nonmetallic material. Based on this methodology, we have developed 2dmatstacks , an open-source tool freely available on nanohub.org . Overall, this paper equips researchers to analyze, understand, and predict experimental results in complicated vdW stacks.

A software tool for simulating contaminant transport and remedial effectiveness in sediment environments

Sediments have often acted as sinks for contaminants that possess strong affinity for solids near historical pollution sources. Mathematical models describing the evolution of contaminant concentrations in sediment environments provide a scientific basis for decision support and remediation design. Herein, novel software (CapSim) is introduced including processes relevant to natural attenuation and in-situ treatment and containment (capping). The tool has been used as a basis for remedial design at a number of sites throughout the United States. CapSim is built on the concept of an arbitrary number of layers that each exhibit traditional porous media transport processes including sorption (linear and non-linear, transient or local equilibrium), advection, diffusion, dispersion, multicomponent linked reactions and, critically, processes specific to the sediment-water interface including bioturbation of both solids and porewater, deposition, consolidation, and interaction with the overlying surface water. A summary of recent applications and selected simulations of key features are presented.

Decoherence in neutrino propagation through matter, and bounds from IceCube/DeepCore

We revisit neutrino oscillations in matter considering the open quantum system framework, which allows to introduce possible decoherence effects generated by New Physics in a phenomenological manner. We assume that the decoherence parameters gamma _{ij} may depend on the neutrino energy, as gamma _{ij}=gamma _{ij}^{0}(E/text {GeV})^n (n = 0,pm 1,pm 2) . The case of non-uniform matter is studied in detail and, in particular, we develop a consistent formalism to study the non-adiabatic case dividing the matter profile into an arbitrary number of layers of constant densities. This formalism is then applied to explore the sensitivity of IceCube and DeepCore to this type of effects. Our study is the first atmospheric neutrino analysis where a consistent treatment of the matter effects in the three-neutrino case is performed in presence of decoherence. We show that matter effects are indeed extremely relevant in this context. We find that IceCube is able to considerably improve over current bounds in the solar sector (gamma _{21}) and in the atmospheric sector (gamma _{31} and gamma _{32}) for n=0,1,2 and, in particular, by several orders of magnitude (between 3 and 9) for the n=1,2 cases. For n=0 we find gamma _{32},gamma _{31}< 4.0times 10^{-24}, (1.3times 10^{-24}) hbox {GeV} and gamma _{21}<1.3times 10^{-24}, (4.1times 10^{-24}) hbox {GeV} at the 95% CL, for normal (inverted) mass ordering.

Versatile Transition for Multilayer Compact Devices in Empty Substrate Integrated Waveguide

Empty substrate integrated waveguide (ESIW) devices can provide high quality and completely integrated devices, but they are usually larger than the same ones implemented with alternative technologies. One of the most extended strategies to compact electronic devices is the use of multilayer technology. Nevertheless, to perform multilayer devices in ESIW, a versatile and efficient transition between the guides in different layers is needed. Currently, only one multilayer device is known in this ESIW technology, which is a transition between a pair of guides built in contiguous layers that requires complex and nonstandard 3-D manufacturing processes. In this letter, a multilayer transition to connect a pair of guides separated by an arbitrary number of layers is successfully designed and experimentally validated without 3-D manufacturing processes. This novel and versatile transition opens the way to further develop multilayer compact devices in the ESIW technology such as compact filters.

Actuation of Piezoelectric Layered Beams With and Coupling.

In this paper, we derive and compare the linear static bending of piezoelectric actuators with transversal ( ) and longitudinal ( ) coupling. The transducers are, respectively, structures utilizing top and bottom electrodes (TBEs) and interdigitated electrodes (IDEs). While the theory is well developed for the TBE beam, governing equations for the bending of the piezoelectric beams with IDEs are far less developed. We improve on this by deriving the governing equation for the IDE beam with an arbitrary number of layers and with coupling consistently included. In addition, we introduce a phenomenological quadratic form for the nonuniform field that lets us derive a deflection formula with nontrivial effects of the field accounted for. The theory is applied to derive deflection formulas for both cantilever and clamped-clamped beams. All analytic results are validated with numerical simulations. From the analytic models, two different figures of merit (FOMs) are derived. We show that these FOMs are the same for cantilevers and doubly clamped beams. The analysis indicates the optimal transducer length for clamped-clamped beams and gives a criterion that can be used to determine which design concept ( or ) gives the largest deflection.

Fracture Analysis of a Three-Dimensional Functionally Graded Multilayered Beam

Delamination fracture behavior of the three-dimensional functionally graded multilayered crack lap shear (CLS) beam configuration was studied analytically in terms of the strain energy release rate with linear-elastic fracture mechanics methods. The CLS under consideration can consist of an arbitrary number of layers, each having different thickness and material properties. The material of each layer is functionally graded along its width, thickness, and length. A delamination crack is arbitrarily located along the beam height. The strain energy release rate was derived by analyzing its density in the beam cross section ahead and behind the crack front. It was additionally analyzed using the strain energy release rate was performed by using the beam strain energy for verification. The effect of the material gradient and crack location along the beam height on the delamination fracture behavior was evaluated.

A Design Technique Based on Equivalent Circuit and Coupler Theory for Broadband Linear to Circular Polarization Converters in Reflection or Transmission Mode

A new approach to designing frequency selective surface (FSS)-based linear to circular polarization (LP–CP) converters is presented. It is based on the use of FSSs which exhibit dual diagonal symmetry, and a novel four-port equivalent circuit able to describe the electrical behavior of the cells for the two linear incident polarizations at the same time. The equivalent circuit allows the use of standardized branch line coupler theory to design LP–CP converters comprising a cascade of an arbitrary number of layers, whose synthesis includes the phase and makes it possible to achieve prescribed electrical conditions systematically. A full design procedure has been developed using the new approach and several designs in both transmission and reflection modes are presented and evaluated. It has been proven that single layer reflective converters exhibit large bandwidths as the two reflected field components are in quadrature independently of the frequency. One of these devices was designed and showed an axial ratio <0.2 dB within the band from 21.5 to 28.5 GHz. The reflective LP–CP converters designed was also manufactured and tested, and the measurements were used to validate the design procedure.

High thermoelectric power factor from multilayer solution-processed organic films

We investigate the suitability of the “sequential doping” method of organic semiconductors for thermoelectric applications. The method consists of depositing a dopant (F4TCNQ) containing solution on a previously cast semiconductor (P3HT) thin film to achieve high conductivity, while preserving the morphology. For very thin films (∼25 nm), we achieve a high power factor around 8 μW/mK−2 with a conductivity over 500 S/m. For the increasing film thickness, conductivity and power factor show a decreasing trend, which we attribute to the inability to dope the deeper parts of the film. Since thick films are required to extract significant power from thermoelectric generators, we developed a simple additive technique that allows the deposition of an arbitrary number of layers without significant loss in conductivity or power factor that, for 5 subsequent layers, remain at ∼300 S/m and ∼5 μW/mK−2, respectively, whereas the power output increases almost one order of magnitude as compared to a single layer. The efficient doping in multilayers is further confirmed by an increased intensity of (bi)polaronic features in the UV-Vis spectra.

Dynamic and static behaviors of multilayered angle-ply magnetoelectroelastic laminates with viscoelastic interfaces

In this paper, the state space method is used to analyze the static and dynamic behaviors of laminated magneto-electro-elastic rectangular plates with simply supported boundary conditions. Multilayers are considered as well as viscoelastic interfaces. The Kelvin-Voigt model is used to take into accounted the viscoelastic interface effects. The mathematical formulation is elaborated in a general form and an arbitrary number of layers as well as the orthotropic behavior can be considered. The coupling time and thickness variables formalism is presented in an elegant matrix way allowing a versatility and capability of the formalism to handle more general multilayered plates. The solution procedure is based on the transfer relationships coupled with the Lagrange polynomials in discretised time intervals. The static behavior of multilayered magneto-electro-elastic rectangular plates is analyzed and the main results are the viscoelastic interface effect on the dynamic behavior of multifunctional structures. New results have been obtained by this coupling state space-Lagrange polynomial methodology. The mathematical procedure, elaborated in this paper, is original and allows the numerical study of the effects of the viscoelastic interfaces. The effectiveness of the proposed methods has been demonstrated by performing variant numerical tests.

Elastic-plastic delamination of multilayered graded four-point bending beam

PurposeThis paper aims to analyze the elastic-plastic delamination fracture behaviour of multilayered functionally graded four-point bending beam configuration.Design/methodology/approachThe mechanical response of beam is described by a power-law stress-strain relation. The fracture is studied analytically in terms of the strain energy release rate by considering the beam complimentary strain energy. The beam can have an arbitrary number of layers. Besides, each layer may have different thickness and material properties. Also, in each layer, the material is functionally graded along the beam width. A delamination crack is located arbitrary between layers. Thus, the crack arms have different thickness.FindingsThe analysis developed is used to elucidate the effects of crack location, material gradient and non-linear behaviour of material on the delamination fracture. It is found that the material non-linearity leads to increase in the strain energy release rate. Therefore, the non-linear behaviour of material should be taken into account in fracture mechanics-based safety design of structural members and components made of multilayered functionally graded materials. The analysis revealed that the strain energy release rate can be effectively regulated by using appropriate material gradients in the design stage of multilayered functionally graded constructions.Originality/valueDelamination fracture behaviour of multilayered functionally graded four-point bending beam configuration is studied in terms of the strain energy release rate by taking into account the material non-linearity.

Free vibration of cross-ply laminated plates based on higher-order shear deformation theory

Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

Interlaminar shear stress function for adhesively bonded multi-layer metal laminates

A new analytical model is proposed for the estimation of interlaminar shear stress in adhesively bonded metal laminates consisting of an arbitrary number of layers. The interface shear stress in the laminates is related to the difference in average axial strain and elongation between adjoining layers through a newly proposed interlaminar shear stress function (ILSSF). The parameters of the ILSSF are determined from finite element simulations using a data fitting procedure. The accuracy of the model is investigated by comparing experimental measurements of average elongation in three-layer aluminum laminates to values obtained using the model. Good agreement with the experimental results is achieved for several types of adhesives and for different ratios of adhesive-to-layer thicknesses. The influence of Young's modulus of the adhesive on the efficiency of load transfer in three-layer laminates is investigated.

Efficient multilayer shallow-water simulation system based on GPUs

The computational simulation of shallow stratified fluids is a very active research topic because these types of systems are very common in a variety of natural environments. The simulation of such systems can be modeled using multilayer shallow-water equations but do impose important computational requirements, especially when applied to large domains.General Purpose Computing on Graphics Processing Units (GPGPU) has become a vivid research field due to the arrival of massively parallel hardware platforms (based on graphics cards) and adequate programming frameworks which have allowed important speed-up factors with respect to not only sequential but also parallel CPU based simulation systems.In this work we present simulation of shallow stratified fluids with an arbitrary number of layers using GPUs. The designed system does fully adapt to the many-core architecture of modern GPUs and several experiments have been carried out to illustrate its scalability and behavior on different GPU models. We propose a new multilayer computational scheme for an underlying 2D mathematical model. This scheme is capable of handling an arbitrary number of layers. The system adds no overhead when used for two-layer scenarios, compared to an existing 2D system specifically designed for just two layers.Our proposal is aimed at creating a GPU-based computational scheme suitable for the simulation of multilayer large-scale real-world scenarios.

Analytical Study of Delamination in Multilayered Two-Dimensional Functionally Graded Non-Linear Elastic Beams

AbstractThe present paper is focused on the delamination fracture in a multilayered two-dimensional functionally graded beam configuration which exhibits non-linear behavior of the material. The beam is loaded by two longitudinal forces applied at the beam free ends. The beam contains a delamination crack which is located symmetrically with respect to the beam mid-span. The delamination is studied analytically in terms of the strain energy release rate. TheJ-integral approach is applied for verification of the analysis of the strain energy release rate. The solution derived is valid for a beam made of an arbitrary number of layers. It is assumed that each layer has individual thickness and material properties. Also, the material is two-dimensional functionally graded in the cross-section of each layer. The solution obtained can be applied for a delamination crack located arbitrary along the height of the beam cross-section. It is shown that the solution is very convenient for investigating the influences of material gradients and crack location on the delamination fracture behavior. The results obtained can be used for optimization of multilayered two-dimensional functionally graded structural members and components with respect to their delamination fracture performance.