Slab Of Finite Thickness Research Articles

Calibration and measurement of dielectric properties of finite thickness composite sheets with open-ended coaxial sensors

The application of open-ended coaxial sensors for dielectric measurement of finite thickness composite sheets is studied. Expressions for calculation of the complex aperture admittance for two geometries are presented. These expressions are used to calculate the dielectric constant of infinite half-space as well as finite thickness slabs. A more efficient method of such calculations, using a personal computer, for low to medium loss dielectrics is demonstrated. The question of when a dielectric layer may be considered as infinitely thick is also addressed, and examples are presented. A different calibration technique (compared to the conventional ones) is described and successfully implemented. This calibration technique utilizes a dielectric sheet with known dielectric properties and thickness. Measurements for different airgaps between the open-ended coaxial line and the dielectric sheet are used to perform and enhance the calibration. The results of this calibration technique and several subsequent measurements are presented and discussed. >

An exact solution of the diffusion equation with shrinking

An exact solution for diffusion from a shrinking slab of finite thickness, assuming a constant mutual diffusion coefficient, has been obtained. This has been accomplished by first casting the appropriate differential equation into the form of an equation describing diffusion in a semi-infinite slab with a fixed domain of integration but with a quadratic concentration dependence of the diffusivity and then making use of Fujita's analytical solution for that equation. The present results are of potential interest in the fields of drying, dyeing, ion exchange and solid—liquid extraction.

Pulse stabilization in a strongly heterogeneous layered medium

A strongly heterogeneous stratified elastic medium occupies a slab of finite thickness. The medium parameters vary randomly with correlation length of O(ϵ 2). A pulse with O(ϵ) wavelength enters the slab at one end. It travels coherently through the slab with a slowness near to that predicted by effective medium theory. Relative to a certain realization- dependent co-moving frame of reference the pulse stabilizes to its mean as ϵ tends to zero. It broadens as it travels as in the O'Doherty-Anstey theory, but here the variations in medium properties are not assumed to be small as in that theory, and the pulse travels with a travel time differing significantly from the characteristic first arrival time.

Planar defects in photonic crystals

We establish the existence of an absolute frequency gap of the electromagnetic field in photonic crystals with tetragonal symmetry, and examine the dependence of the gap on the geometry of the structure. We calculate the transmittance through a slab of finite thickness of the material, and show that planar defects in the slab produce interface states of the electromagnetic field, at frequencies within the photonic gap, manifested by sharp resonances in the transmittance of these systems.

Solution of the general phonon Boltzmann equation: boundary and mass defect scattering

The phonon Boltzmann equation is considered in its general form in the presence of mass defect interactions and boundary scattering. A variational method is applied to calculate the phonon thermal conductivity for a non-metallic slab of finite thickness and fixed temperatures at its two faces. In comparison with previous work the present study has the advantage that the different phonon polarizations are taken into account. Moreover, it has been shown that the operator involved in the study is positive definite which, in turn, implies that the variational method yields an upper bound on the phonon thermal conductivity.

Resolution limits for optical transillumination of abnormalities deeply embedded in tissues

Random walk theory is used to calculate the line spread function (LSF) of photons as they cross the midplane of a slab of finite thickness. The relationship between the LSF and the photon transit time in transillumination time-resolved experiments is investigated. It is found that the LSF is approximately Gaussian distributed, with a standard deviation, sigma, which can be used as a criterion of the spatial resolution of the imaging system. Results are substantiated by comparison with actual data in the literature. Any given resolution can be improved by reducing the excess transit time delta t, but heterogeneity of the scattering medium and low levels of detected light enormously complicate the achievement of subcentimeter spatial resolution. The latter point is discussed by using optical parameters of breast tissues for visible and near-infrared radiation (NIR) light.

Density profiles of charged test particles diffusing in a slab of finite thickness

Density profiles of charged test particles diffusing in a slab of finite thickness

Experimental study of the dimensionality in Bi2Sr2CaCu2O8+x: Temperature and magnetic field dependence.

We present an experimental study of the dimensional crossover present in the extremely anisotropic superconductor ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathit{x}}$ by means of measurements of the onset field for the dissipation ${\mathit{H}}^{\mathrm{*}}$ as a function of the temperature and of the orientation \ensuremath{\vartheta} between the field direction and the a,b plane. The crossover is experimentally shown to depend on the strength of the applied magnetic field in a narrow temperature range below ${\mathit{T}}_{\mathit{c}}$. The entire set of experimental data is described by a coupled-layers model, in which a decoupling can be induced by a sufficiently high magnetic field. The anisotropy ratio is found to depend strongly on the temperature and the model of coupled slabs of finite thickness quantitatively describes the data.

Build-up Factors for High Energy Gamma Rays Normally Incident on Slabs of Lead, Iron, Concrete and Water

Build-up factors and albedos for high energy gamma rays incident normally on slabs of finite thickness have been calculated by a Monte Carlo photon transport code incorporating a detailed bremsstrahlung model based on thick target bremsstrahlung yields and the continuous slowing down approximation for electrons. Build up factors and albedos are presented for photon source energies from 10 to 100 MeV and for slab thicknesses from 1 to 10 mean free paths. Total albedos are also reported for thick slabs.

Waves in a magnetically structured slab configuration

The problem of wave-propagation in a magnetically structured compressible slab configuration is investigated, allowing for different magnetic field strengths inside and outside the slab and also a general orientation of the field vectors relative to each other and to the propagation vector. Several magnetic field geometries such as equal parallel, and equal orthogonal fields are considered. Properties of body and surface waves both for symmetric and asymmetric modes of perturbation propagating along and normal to the slab field are investigated idealising the slab to be incompressible, or considering the limiting case of wide and slender compressible slab. Numerical results are also obtained for a compressible slab of finite thickness for a specific choice of sound and Alfven speeds involved.

BCS theory of two-dimensional Landau-level superconductivity.

A strictly two-dimensional uniform plane with a perpendicular magnetic field is used in order to study the BCS phase diagram for ${\mathit{H}}_{\mathit{c}2}$, both for weak and intermediate coupling, with a uniformly vanishing order parameter. The phase diagram has a conventional form for weak coupling, but there are oscillations in ${\mathit{H}}_{\mathit{c}2}$(T) for stronger coupling. The slope of ${\mathit{H}}_{\mathit{c}2}$ near T=${\mathit{T}}_{\mathit{c}}$ is singular for ordered planes with g=0 but is finite if g is different from zero, or if disorder is added. Increasing the width of finite-thickness slabs rapidly gives way to fewer Landau levels and therefore to the extreme quantum limit as one moves closer to the three-dimensional crystal, confirming previous results. We show that in two dimensions, in contrast to three dimensions, finite values of ${\mathit{H}}_{\mathit{c}2}$ in the weak-field limit at T=0 are achievable for weak coupling.

Inverse scattering problem with two flux methods

The inverse two flux (SS, SP and CC) approximations are presented for determining single scattering albedo and asymmetry factor from the hemispherical transmittance and reflectance data for an anisotropically scattering slab of finite thickness subjected to isotropic incident radiation at one of its boundary surfaces. Analytical expressions of the reflectance and transmittance are derived with the two flux methods and applied to determine the parameters with the use of an IMSL subroutine for solving the nonlinear constrained least mean square equation formulated. The results of inversed parameters are compared to those obtained by the P1 method. The accuracy of the predictions of both two-flux and P1 methods are also discussed.

Coherent enhancement of light-pulse backscattering by random slab

An exact analytic solution is found for the problem of enhancement of backscattering of a short pulse signal from a slab of finite thickness with isotropic scattering centers.

Translational correlations in the vortex array at the surface of a type-II superconductor.

We discuss the statistical mechanics of magnetic flux lines in a finite-thickness slab of type-II superconductor. The long wavelength properties of a flux-line liquid in a slab geometry are described by a hydrodynamic free energy that incorporates the boundary conditions on the flux lines at the sample's surface as a surface contribution to the free energy. Bulk and surface weak disorder are modeled via Gaussian impurity potentials. This free energy is used to evaluate the two-dimensional structure factor of the flux-line tips at the sample surface. We find that surface interaction always dominates in determining the decay of translational correlations in the asymptotic long-wavelength limit. On the other hand, such large length scales have not been probed by the decoration experiments. Our results indicate that the translational correlations extracted from the analysis of the Bitter patterns are indeed representative of behavior of flux lines in the bulk.

Casimir effect in absorbing media.

The Casimir force between two dielectric slabs of finite thickness is calculated for the case of dissipative media. The medium is modeled as a continuous field of quantum harmonic oscillators interacting with the heat bath. The electromagnetic field inside and outside the cavity formed by the plates is found for the ground state of the coupled system, and its pressure is calculated. Two terms in the expression for the Casimir force are distinguished. One is the electromagnetic vacuum pressure, which is the only contribution in the case of lossless media. The other arises from the Langevin forces that appear together with the damping as the result of the interaction of atoms with the heat bath. It is shown that both contributions are necessary in order to arrive at a finite result.

Mutual coupling between parallel columns of periodic slots in a ground plane surrounded by dielectric slabs

Arrays of slots with arbitrary orientation in an infinite conducting plane that are infinitely periodic in one dimension and finitely periodic in another dimension are considered. The plane is bounded on each side of dielectric slabs of finite thickness and infinite extent. Single columns of slots are represented by equivalent magnetic scattering currents, which are solved for by the moment method. The mutual coupling (admittance) between slot columns in the presence of the stratified media is found by the array scanning method, which expresses the admittance as the average of the scan admittance of an artificially constructed doubly infinite array of slots over all real scan angles. The technique avoids the use of Sommerfeld integrals, but still gives rise to singularities at scan angles corresponding to the resonant excitation of surface waves. An analytical approximation removes these surface wave singularities, making numerical implementation of the method practical. >

Planar solidification in a finite slab: Effects of density change

Planar solidification in a slab of finite thickness, cooled from below, is addressed. The solid density is supposed to be greater than the liquid density. The fluid flows toward the moving phase-change front, accompanied by heat transfer in the emerging solid, in the liquid and cavity, resulting due to the contraction of the volume of the material, are analyzed. The Rubinstein transformation, which immobilizes the interface, is modified in order to take the density change into account. It enables one to reduce the problem to that without the density change. Several approximate analytic solutions for transient solidification, some of which are new even for equal solid and liquid densities, are presented.

Plasma losses by charged particles in thin films: Effects of spatial dispersion, phonons, and magnetic field.

The energy loss of a charged particle to a solid-state plasma film or slab of finite thickness is treated here, both for motion parallel to the slab faces as well as for penetration across the slab. In this, we extend the early work of Ritchie to include nonlocal dispersive plasma features, in addition to the dynamic response features associated with the excitation of slab collective modes. We employ the diagonal approximation for the slab random-phase-approximation inverse dielectric response function, and the plasma electrons are subject to the specular-reflection boundary condition at the slab faces. For parallel motion within the slab, we find modifications to the result of N\'u\~nez, Echenique, and Ritchie due to the finite width of the slab. For particle penetration across the slab, we incorporate the dynamic plasma response features associated with phonon polarization and a magnetic field to determine the role of bulk and surface magnetopolaritons in energy loss. Our detailed field-free calculations clearly demonstrate energy-loss contributions associated with the excitation of symmetric and antisymmetric slab surface polaritons as well as bulk polaritons, with computations carried out in full for GaAs.

Coherent wave backscattering by random medium. Exact solution of the albedo problem

We study the effect of coherent wave backscattering by a system of point-like scatterers. An exact solution of the albedo problem is found both for a semi-finite medium and for a random slab. It is shown that in the cases considered the diffusion approximation breaks down rapidly when oblique incidence and finite slab thickness are taken into account. It is determined that the intensity of the coherent peak tails falls off as 1 θ , where θ is the angle between backscattering and observation directions.

FIRST-PRINCIPLES CALCULATIONS OF THE ELECTRONIC STRUCTURE OF GRAIN BOUNDARIES

FIRST-PRINCIPLES CALCULATIONS OF THE ELECTRONIC STRUCTURE OF GRAIN BOUNDARIES