Inhomogenities

However, before extrapolating the arguments from the gross patterns through the reactor for homogeneous reactions to solid-catalyzed reactions, it must be recognized that in catalytic reactions the fluid in the interior of catalyst pellets may diSer from the main body of fluid. The local inhomogeneities caused by lowered reactant concentration within the catalyst pellets result in a product distribution different from that which would otherwise be observed. 

Although still used the Langmuir equation is only of limited value since in practice surfaces are energetic inhomogeneous and interactions between adsorbed species often occur. 

Homogeneity of data. Homogeneous data will be uniform in structure and composition, usually possible to describe with a fixed number of parameters. Homogeneous data is encountered in simple NDT inspection, e.g. quality control in production. Inhomogeneous data will contain various combinations of indications from construction elements, defects and noise sources. An example of inhomogenous data are ultrasonic B-scan images as described in [Hopgood, 1993] or as encountered in the ultrasonic rail-inspection system described later in this paper. 

Expert systems. In situations where the statistical classifiers cannot be used, because of the complexity or inhomogeneity of the data, rule-based expert systems can sometimes be a solution. The complex images can be more readily described by rules than represented as simple feature vectors. Rules can be devised which cope with inhomogeneous data by, for example, triggering some specialised data-processing algorithms. 

A novel optimization approach based on the Newton-Kantorovich iterative scheme applied to the Riccati equation describing the reflection from the inhomogeneous half-space was proposed recently [7]. The method works well with complicated highly contrasted dielectric profiles and retains stability with respect to the noise in the input data. However, this algorithm like others needs the measurement data to be given in a broad frequency band. In this work, the method is improved to be valid for the input data obtained in an essentially restricted frequency band, i.e. when both low and high frequency data are not available. This... 

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.J. Cui and C.H. Liang, Reconstruction of the permittivity profile of an inhomogeneous medium using an equivalent network method, 1993, IEEE Trans. Antennas Propagat., 41, pp. 1719-1726. 

T.M. Habashy, W.C. Chew, and E.Y. Chow, Simultaneous reconstruction of permittivity and conductivity profiles in a radially inhomogeneous slab, Radio Sci., 1986,21,... 

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

Numerical Modeling of Elastic Wave Propagation in Inhomogeneous Anisotropic Media. 

Recently, EFIT has been extended to simulate elastic waves in homogeneous anisotropic media [3, 4] and inhomogeneous anisotropic media [5, 6]. Since Waite et al. [7,... 

Note some particularities of new USCT method. At first, data collection and search of areas with anomalous (inhomogeneous)SD of acoustic parameters (velocities of spreading of US waves) is joined. As a sought image, on which anomalies is revealed, it is offered total image B (r), which practically is the low frequency copy of restored fimction g(f). As PMF SD of... 

Let us consider a domain U e R, representing the three-dimensional flaw imbedded in a homogeneous conductive media, with electric conductivity uo and permeability The flawed region D is assumed to be inhomogeneous, and characterized by the relative real conductivity ... 

W.C. Chew. Waves and fields in inhomogeneous media. Library of Congress Cataloging-in-Publication Data, ISBN 0-442-23816-9, 1990. 

Flomogeneity Likewise, IQIs according to EN 462-1 or EN 462-2 can be used to monitor homogeneity. Typical inhomogeneities are caused by burns in the input window of the image converter. 

For applications on indications it is assumed that the visibility level VL of rectangular objects (indications) is the same as for circles with the same area. The lenght 1 and width w of indications are correlated in very different manners, mainly dependant on the geometrie of the inhomogenity (crack). From some observations, the following correlation between w and 1 was introduced w (mm) = 0.05 + 0.03 1 (e g. 1=1.5 mm, w a 0.1 mm). For the same areas, the length 1 of the indication can be introduced in Fig. 1 as a second scale. 

A homogeneous metastable phase is always stable with respect to the fonnation of infinitesimal droplets, provided the surface tension a is positive. Between this extreme and the other thennodynamic equilibrium state, which is inhomogeneous and consists of two coexisting phases, a critical size droplet state exists, which is in unstable equilibrium. In the classical theory, one makes the capillarity approxunation the critical droplet is assumed homogeneous up to the boundary separating it from the metastable background and is assumed to be the same as the new phase in the bulk. Then the work of fonnation W R) of such a droplet of arbitrary radius R is the sum of the... 

Gerlioh D 1992 Inhomogeneous RF fields a versatile tool for the study of prooesses with slow ions State-Selected and State-to-State Ion-Molecule Reaction Dynamics Part 1. Experiment ed C Ng and M Baer (New York Wiley)... 

For homogeneous particles, it represents the number of distances within the particle. For inhomogeneous particles, it has to take into account the different electron density of the volume elements. Thus it represents the number of pairs of difference in electrons separated by the distance r. A qualitative description of shape and internal structure of the... 

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

Diffusion may be defined as the movement of a species due to a concentration gradient, which seeks to maximize entropy by overcoming inhomogeneities within a system. The rate of diffusion of a species, the flux, at a given point in solution is dependent upon the concentration gradient at that particular point and was first described by Pick in 1855, who considered the simple case of linear difflision to a planar surface ... 

Tokmakoff A and Fayer M D 1995 Homogeneous vibrational dynamics and inhomogeneous broadening in glass-forming liquids infrared photon echo experiments from room temperature to 10 KJ. Chem. Phys. 103 2810-26... 

Flohenberg P and Kohn W 1964 Inhomogeneous electron gas Phys. RevB 136 864-72... 

This fomi is called a Ginzburg-Landau expansion. The first temi f(m) corresponds to the free energy of a homogeneous (bulk-like) system and detemiines the phase behaviour. For t> 0 the fiinction/exliibits two minima at = 37. This value corresponds to the composition difference of the two coexisting phases. The second contribution specifies the cost of an inhomogeneous order parameter profile. / sets the typical length scale. 

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