Inhomogeneous layer

Consider the reflection of a normally incident time-harmonic electromagnetic wave from an inhomogeneous layered medium of unknown refractive index n(x). The complex reflection coefficient r(k,x) satisfies the Riccati nonlinear differential equation [2] ... 

T. Uno and S. Adachi, Inverse scattering method for one-dimensional inhomogeneous layered media, 1987, IEEE Trans. Antennas Propagat., 35, pp. 1456-1466. 

Follow an outside-in strategy. Consider a semi-infinite body with permittivity eout, coated with an inhomogeneous layer of constant thickness D and permittivity e(z), facing a medium em of variable thickness Z. Subscripts for a, b, L, and R will be added later (Fig. L3.14). 

The effective thickness of the liquid film rigidly attached to the oscillating surface is equal to I - and is less than the thickness of the inhomogeneous layer, I. The increase of the permeability leads to the enhancement of the velocity gradient in the layer, which results in a decrease of the shift due to mass loading, and an increase of the width caused by the energy dissipation. When the layer thickness is the shortest length of the problem, K 5, L < and < S, the frequency shift is also proportional to the density of the liquid and does not depend on viscosity ... 

The method of diffuse transmittance (DT) is based on measurement of the radiation component 7dt (Fig. 1.22) that passes diffusely through an inhomogeneous layer. This method was first applied to the IR spectroscopic analysis of thin films on samples in powder form by Tolstoy in 1985 [116, 117], who obtained DT spectra of water adsorbed onto silica gel. When used in conjunction with a FTIR spectrometer, the method is called diffiise-transmittance infrared Fourier transform spectroscopy (DTIFTS). DTIFTS is the most recently developed IR spectroscopic methods for studying powder surfaces and has already found application in high-performance liquid chromatography (HPLC) and thin-layer chromatography (TLC) [118, 119]. Of increasing popularity are DTIFTS measurements of powders that use an IR microscope to collect radiation [112, 119] (Section 4.3). 

The experimentally obtained isotherms rose after the onset of the collapse (Fig. 4), and the simulation reproduced this behaviour. The increasing surface pressure of the layer during the collapse is a consequence of the different potential energy of the particles owing to the inhomogeneous layer structure. 

Keywords Scanning-angle reflectometry Reflectance of inhomogeneous layers Layer of silica nanoparticles Stober silica... 

Surface tension originates in intermolecular forces of cohesion. These forces are short-range but nonlocal. The equilibrium density should minimize the free energy. Near the interphase boundary, the density varies in space, and the interfacial energy can be computed as an excess energy of this inhomogeneous layer. 

A method to solve the problem is to determine in the Fourier space the connection between the logarithm of refractive index values and the amplitude reflection and transmission coefficients, represented as complex wavelength-dependent functions. The global minimum of thus obtained dependence is then determined. The solution is an inhomogeneous layer, further transformed into a two-material system and subsequently subjected to a new procedure of fine optimization. 

The method of quadratic programming starts from a quality function equal to the integral of the ratio R(X)/[1 - R( t)] over wavelength from the beginning to the end of the optimization interval. The solution here is also an inhomogeneous layer transformed subsequently into a two-material one and finely optimized [158]. 

The dimensioning of plastics components for defined operating times and corresponding service life has to fulfill strict requirements. Components made from unreinforced plastics exhibit viscoelasticity, physical and geometric non-linearity. In reinforced plastics, viscosity is less critical, but inhomogeneity, layer sequence and anisotropy become relevant. The exact determination of these characteristics is always a very complicated mathematical task. 

Ellipsometric formulas for an inhomogeneous layer with arbitrary refractive index profile" (with J.C. Charmet), J. Opt. Soc. Am.. 12, 1777-1784 (1983). 

Tsipis and co-workers (1436) reported that reaction of a cobalt-loaded zeolite with NaS2CNEt2 results in the crystallization of [Co(S2CNEt2)3] on the surface of the zeolite, forming an inhomogeneous layer patterned on the zeolite. 

Equations (2.3.9) and (2.3.10) define the outgoing upward and downward radiation fields emitted from a composite inhomogeneous layer. Repeated applications of the procedure admit solutions for an atmosphere composed of any finite number of layers with individually different thermal and scattering properties. It is also... 

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