Layer Of Arbitrary Thickness Research Articles

On a technique for deriving explicit transfer matrices of orthotropic layers

This paper presents a technique by which the transfer matrix in explicit form of an orthotropic layer can be easily obtained. This transfer matrix is applicable for both the wave propagation problem and the reflection/transmission problem. The obtained transfer matrix is then employed to derive the explicit secular equation of Rayleigh waves propagating in an orthotropic half-space coated by an orthotropic layer of arbitrary thickness.

Propagation regimes of interfacial solitary waves in a three-layer fluid

Abstract. Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation) bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps) are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equations (KdV-type equations with combined nonlinearity) for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown that both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.

An optical monitoring method for depositing dielectric layers of arbitrary thickness using reciprocal of transmittance.

An approach extracting information of both optical monitoring signal and phase thickness of deposited layer on a trace diagram is proposed. Realtime fitting and calculation are performed to get both practical thickness and refractive index of deposited layer with the assist of quartz crystal monitoring for keeping steady rate of deposition. Monitoring error of thickness using this approach is analyzed. It was used to obtain the refractive indices and thickness of Ge layer and SiO layer in in situ measurement mode, and the results were compared with those of ex-situ spectral measurement using infrared spectrometer. The effectiveness of the proposed monitoring method was verified by fabricating narrow bandpass filter consisting of quarter-wave and non-quarter-wave layers.

Lithium ion rechargeable battery, galvanostatics: Computer simulation and calculation of characteristics of the anode active layer of arbitrary thickness with low lithium diffusivity

The work of a lithium ion rechargeable battery operating under galvanostatic discharge conditions is simulated. Attention is focused on the complete mathematical description of processes in electrode active layers. The central problem in the theory of lithium ion batteries is the possibility of analyzing the following two processes that proceed simultaneously in space and time: depletion and enrichment of the active substance (intercalator) grains with lithium atoms and the ohmic-limitation-induced redistribution of the electrode potential in time throughout the active layer thickness. A new approach to the central problem is considered. It is based on comparing the characteristic times of two main processes occurring in electrodes. Here, the lithium atom diffusivity in intercalator grains plays the decisive role. Two regions of diffusivity values, i.e., high and low, can be singled out. Algorithms are developed for solving the complete system of equations for the most complicated case, namely, active layers of arbitrary thickness with low diffusivity of lithium atoms. The following electrode working parameters (for anode) are calculated: optimal active layer thickness, discharge time, anode specific capacitance, and final potential at the active layer/interelectrode space interface.

Contact problem for two-layer elastic coating of solid cylinder

The paper proposes analytical method of solving the contact problem for a two-layer elastic coating of solid cylinder applicable for circular layers of arbitrary thickness, simultaneously in case of compressible and incompressible materials. The law of contact pressure change is expressed in a form of an infinite series, containing an infinite number of unknown constants that are defined by the decomposition of known function of the built orthogonal functions.

A Two-Band Tight-Binding Model of Spin-Polarized Transport in Magnetic Tunnel Junctions

The main features determining spin-dependent transport in magnetic tunnel junctions are well appreciated now mainly due to ab initio calculations. Nevertheless, it seems useful to have a comparatively simple model which reproduces the salient characteristics of spin-dependent transport in magnetic multilayers. We present two-band tight-binding model of magnetic tunnel junction with the layers of arbitrary thickness and non-collinear magnetization configuration. The model accounts for different symmetry of the tunneling electrons and their mixing on the interfaces. As an illustration for double-barrier structure we calculate I-V curves and spin-transfer torque. The calculations demonstrate the resonant character of the I-V dependences. Also, the significant difference in the magnitude of the torque acting on the various planes of the same magnetic layer is found.

Competition between the barrier and injection mechanisms of nonlinearity of the current-voltage characteristic in Mott-barrier detector diodes

We obtain an analytical solution to the problem of transverse injection current in an undoped semiconductor i layer of arbitrary thickness with account of self-consistent boundary conditions. Charge transfer in the semiconductor bulk is described in the drift-diffusion approximation. Current transfer through the boundaries of an undoped layer is described in terms of the thermoelectron emission theory. Thus, the generalized thermoemission-diffusion approach applies for semiconductors with both low and high mobilities of charge carriers. On the basis of the obtained solution, we analyze the characteristics of the current nonlinearity of the Mott-barrier diodes. The generalized approach is used for describing current transfer in low-barrier diodes based on Mott contacts with near-surface δ-doping. Characteristics of detection of low-barrier diodes are analyzed. Limiting values of the volt-watt and threshold sensitivities of the detectors based on these diodes in the subterahertz frequency range (up to 1 THz) are determined.

Thermal noise in half-infinite mirrors with nonuniform loss: A slab of excess loss in a half-infinite mirror

We calculate the thermal noise in half-infinite mirrors containing a layer of arbitrary thickness and depth made of excessively lossy material but with the same elastic material properties as the substrate. For the special case of a thin lossy layer on the surface of the mirror, the excess noise scales as the ratio of the coating loss to the substrate loss and as the ratio of the coating thickness to the laser beam spot size. Assuming a silica substrate with a loss function of 3x10-8 the coating loss must be less than 3x10-5 for a 6 cm spot size and a 7 micrometers thick coating to avoid increasing the spectral density of displacement noise by more than 10%. A similar number is obtained for sapphire test masses.

Stability of a Circular Sandwich Ring under an Axially Symmetric Temperature Field Inhomogeneous across the Thickness

The linearized problems on the stability of a circular sandwich ring of symmetric structure under an axially symmetric temperature field inhomogeneous across the core thickness are stated and analytical solutions to them are given. The first problem deals with the mixed flexural buckling form (BF) of the ring as a whole, realized as a result of buckling in one of the load-carrying layers due to formation of precritical pressure stresses in the layer. The second problem considers purely shear BFs when one load-carrying layer is rotated relative to the other. The deformation processes for the load-carrying layers are described by the Kirchhoff-Love model, and for the core of arbitrary thickness - by two models, namely by the equations of the plane problem of elasticity theory and by the model of a transversely soft layer of arbitrary thickness (the same equations simplified by the assumption of zero circumferential normal stresses). Within the frames of the first model adopted for the core, the shear BF is theoretically possible but practically unrealizable, since the mixed flexural BF arises earlier than the shear BF.

Simulation of the vector wave field of a low-frequency sound source in the ocean: Some important features

An approach to the simulation of low frequency vector wave fields in stratified media (mainly in the ocean) is considered. The approach is characterized by an improved stability with respect to dividing the medium into many layers of arbitrary thickness. The model for the sound field of a point source is based on an integral representation of two-dimensional, cylindrically symmetric vector wave fields in inhomogeneous media, so that the contributions of all types of waves are included automatically. The model medium is subdivided into N horizontally homogeneous layers for which 4(N−1) equations are formulated to satisfy the boundary conditions between adjacent layers. The method of the generalized Schmidt matrix is used to obtain the coefficients of the equations; these coefficients are substituted into the expressions (of the Fourier-Bessel integral type) for the local parameters of the field. The latter are calculated according to the numerical procedure, and the results are used to model the distributions of the acoustic pressure and the horizontal and vertical components of the particle velocity in liquid and elastic media. The instability of the calculation procedure may result in a disagreement between the model and the exact solution. However, the disagreement is shown to occur mainly in models containing excessively thick layers. A way for improving the stability of the numerical model is suggested. The simulation results are compared with the exact analytical solution for the simplest example and with the results obtained according to the commonly used generalized matrix procedure (the benchmark problem). The examples of the practical application of the model for investigating more complex seismoacoustic wave fields in the ocean are presented.

Electromagnetic wave propagation in a plane dielectric layer under critical conditions

An exact solution to the problem of a plane wave propagation in a plane-stratified dielectric layer of arbitrary thickness is studied. An approach based on self-consistent finite differences is suggested, replacing the layer by a stack of homogeneous sublayers of variable thickness matched to the local behavior of the permittivity profile. For the region around zero permittivity, it is predicted that small perturbations of the physical parameters of the problem cause qualitative and quantitative changes in the solution. The conditions for the excitation of a surface wave are formulated. Computed data for the wave are presented.

Scattering of electromagnetic waves from planar chiral structures

A rigorous solution is found for the problem of reflection of E- and H-polarized plane electromagnetic waves from a metal plane covered by a chiral layer of arbitrary thickness. The dependence of the electromagnetic wave reflection on the chirality parameter and the layer thickness is studied. The reflection of the depolarized component is examined. The results, obtained using two different forms of the constitutive relations for a chiral medium, are compared.

Investigation of the electromagnetic fields at a jump in the dielectric constant

The passage of a plane wave through an inhomogeneous flat insulator layer of arbitrary thickness without absorption is considered. A method is given for solving the problem in terms of elementary functions, which reduces the number of independent parameters of the layer. A similarity principle for layers having equivalent reflectivities is described. It is shown that the electric field intensity can increase to infinity near the critical point where ɛ=0.

Rayleigh-Taylor Instability of A Thin Magnetic Fluid Layer in A Tangential Magnetic Field

A viscous magnetic fluid layer in a uniform horizontal magnetic field is considered. The upper boundary of the layer is a horizontal rigid wall and the lower boundary a the free surface. It is assumed that at the initial instant the free surface represents a randomly weakly deformed horizontal plane. A dispersion relation for the waves in a layer of arbitrary thickness is obtained within the framework of the linearized system of ferrohydrodynamic equations describing the evolution of spatial perturbations. The effect of a tangential magnetic field on the breakdown of a thin layer is investigated theoretically and experimentally.

Sliding Tractions on a Deformable Porous Layer

The problem of sliding surface tractions on a porous biphasic layer with viscous interstitial fluid is solved, which can serve as the basis for solving problems of elastohydrodynamic lubrication of deformable porous layers bonded to a rigid substrate. A general small strain solution is derived for a layer of arbitrary thickness, using Fourier transform methods. The applied tractions, consisting of two normal components and two shear components, have arbitrary distributions and are assumed to slide at a constant speed along the layer surface. It is found that the solution to this problem is dependent on five nondimensional parameters; one of these, Rh, is the ratio of the sliding speed to the characteristic speed of fluid flow within the porous layer; another, τf, controls the transition between Darcy-like and Navier-Stokes flow. Results are presented for various values of these parameters, particularly in relation to the flux of fluid relative to the solid phase along the tangential and normal directions to the layer surface. Discussion of these results and their potential effect on the analysis of elastohydrodynamic lubrication of deformable porous bearings is provided.

Power spectra of bulk and surface plasmons in a semi-infinite superlattice of electron gas layers

A Green's function formalism is employed to calculate the power spectra of bulk and surface plasmons in a semi-infinite superlattice composed of two-dimensional electron gas layers separated by dielectric layers. The theory takes account of effects due to a capping layer of arbitrary thickness and also charge depletion near the superlattice surface. Applications are made to semiconductor superlattices.

New Method of Time Domain Analysis of the Performance of Multilayered Ultrasonic Transducers

A method is presented for the analysis of the transmitting and receiving characteristics of ultrasonic probes between a piezoelec- tric vibrator and human tissue as the load. The probes have multiple intermediate layers of arbitrary thickness. This method uses recursion formulas to analyze force waves that propagate while undergoing re- peated reflection and transmission at the boundaries between probe media having different acoustic impedances and plots the transmitted and received waveforms on a time axis to determine the performance characteristics of the probe. Upon applying this method to the analysis of the characteristics of probes with from one to four quarter-wave- length matching layers, the width of the transmitted and received pulses tends to shorten as the number of matching layers increases. In the case of probes with a single matching layer, analysis which factored in the bonding layer thickness showed that the matching layer thickness which maximizes sensitivity deviates from a quarter-wavelength, and that the amount of this deviation agrees fairly well with experimental results.

Reflection Coefficient for Plane Waves in a Fluid Incident on a Layered Elastic Half-Space

The reflection coefficient is derived for an isotropic, homogeneous elastic layer of arbitrary thickness that is perfectly bonded to such an elastic half-space of a different material for the case when plane waves are incident from an inviscid fluid onto the layered solid. The derived function is studied analytically by considering several limiting cases of geometry and materials to recover previously known results. Approximate reflection coefficents are then derived using various plate models for the layer to obtain simpler expressions that are useful for small values of σd, where σ is the wave number and d is the layer thickness. Numerical results based on all the models for the propagation of interface waves localized near the fluid-solid boundary are obtained and compared. These results are also compared with some previously published experimental measurements.

Energy losses of fast electrons in multi-layer systems

Starting from Maxwell's equations a formula for the energy loss probability of fast electrons in systems of a given number of thin layers is derived for normal incidence. Retardation effects are neglected. For three layers of arbitrary thickness the equations are fully solved. As examples, a two-metallic-layer system with energy-dependent dielectric functions is discussed. Furthermore, the tarnish of metals e.g. Al−Al2O3, Be−BeO, Ag−Ag2S is considered as three-layer systems. The energy loss spectrum of the system Al2O3−Al−Al2O3 is calculated in agreement with the experiment. It turns out that the bulk longitudinal optical mode of the covering layer is excited in the infra-red. In the case of the oxidation of a dielectric film the transversal mode of the oxide is expected to prevail in the energy loss spectrum.

Notes on hydrodynamic modes in a He II layer of arbitrary thickness

Hydrodynamic modes of a given frequency which can exist in a layer of superfluid helium adiabatically enclosed between two plane parallel boundaries are investigated. Starting from the linearized Landau-Khalatnikov equations the exact dispersion relations and fields of all possible modes are calculated numerically and compared with previous results obtained by various approximations. E.g., it is shown that the existence of the strongly attenuated thermoviscous wave in the bulk fluid implies the existence of many modifications of it in a layer, and that the layer modifications of the viscous wave exist in a classical fluid, too, but behave differently in the thin layer region. For the resistance parameter needed in the often used approximation of averaging the two-fluid-equations over the layer the correct thickness dependence is given for the region of thick layers. The necessity of a fourth boundary condition is discussed.