Discontinuous Profiles Research Articles

Molecular aspects of boundary lubrication

Recent molecular dynamics computer simulations of boundary lubrication, in which the lubricant and sliding solid surfaces are represented at an atomistic level, have given new insights into the mechanism of boundary lubrication. Combined with recent data from experiments on sliding surfaces, these simulations have forced us to modify our traditional view of lubrication in this regime. Stick-slip behaviour at low sliding velocities, discontinuous shear velocity profiles across the gap and lubricant states oscillating between solid-like and liquid-like extremes are some of the phenomena that occur in boundary lubrication. The Eyring model is discussed and directions for improvements proposed that would encompass stick-slip behaviour.

Pattern formation in fixed bed catalytic reactors—I

The possibility of spatial patterns in packed-bed catalytic reactors to improve reactor operation is addressed in this paper with respect to several fundamental issues. The analysis is accomplished with an early model of Liu and Amundson (1962, Ind. Engng Chem. Fundam. 1, 200) which assumes plug flow of the fluid phase and lumped transport resistance in the catalyst particles. Such patterns involve discontinuous concentration profiles in the catalyst phase. It is shown that patterns, which arise due to multiplicity behavior of individual catalyst particles, can be created by providing for an initial pattern in the reactor. Start-up strategies for such initial patterns are established using multiple feeds. Asymptotic stability of patterns in which neighboring particles lie in distinct stable branches is established. Computations demonstrating the achievement of spatial patterns from suitable initial conditions are made. It is shown that reactor operation is concerned with a class of patterns which can provide for an acceptable range of product quality. The significance of patterns lies in improving selective productivities of desired products in multi-reaction systems.

Penalty methods for the inverse problem in EIT

The conductivity profiles arising in medical applications of electrical impedance tomography (EIT) are often of `blocky' structure, i.e. they are relatively constant inside an organ and are rapidly varying at its boundary. Standard regularization methods for the inverse problem tend to blur these sharply defined edges. A penalty method is proposed which is especially designed for a better reconstruction of discontinuous conductivity profiles.

High accuracy profile measurement of a machined surface by the combined method

The combined method, which combines the generalized 2-point method with the inclination method, has been developed to measure profiles that include high-frequency components whose spatial wavelengths are shorter than the probe interval. It is suitable for measuring discontinuous profiles that include step-wise variations and abrupt changes. In this paper, we discuss the influences of the setting error of the probe interval, and the positioning error of sampling when we use the combined method to measure a step-wise profile. Results of theoretical analyses show that these errors cause the same kind of evaluation errors in the profile measured with the combined method, and large profile evaluation errors are caused by the edge part of a step-wise profile. The value of the profile evaluation error is concerned with the aperture size of the displacement probe and the height of the step-wise profile. The influence of the gain errors of the probe is also investigated. An automatic selection method that can select the standard area properly and quickly is developed to improve the accuracy of the combined method. A machined surface with a step-wise profile is measured by using two capacitance-type displacement probes. Experimental results that confirm the effectiveness of the combined method are also presented.

Interaction between Polyelectrolyte Brushes in Poor Solvents

This study examines the structure of planar polyelectrolyte brushes and the disjoining pressure between such brushes in a poor solvent. The self-consistent field theory is used in this work in contrast with the earlier studies that used a step-density model. We predict that upon the reduction in solvent quality the brush collapses continuously whereas the step-density model predicts a first-order collapse. In a sufficiently poor solvent the brush shows a discontinuous density profile: (i) between the grafting surface and the discontinuity the density is dominated by the solvent translational entropy and (ii) beyond the discontinuity the density is determined by the counterion translational entropy. The force−distance profiles are also always continuous unlike the prediction of the step-density model, which predicts discontinuous collapse under constant external pressure.

Applications and simulations of a discontinuous oral absorption pharmacokinetic model.

To illustrate the application of a discontinuous oral absorption model to cimetidine and ranitidine plasma concentration versus time data to demonstrate the use of the model for drugs which display discontinuous oral absorption profiles, and to illustrate the effect of various model parameters on plasma drug concentration versus time profiles and bioavailability. A discontinuous oral absorption model was used to fit ranitidine and cimetidine serum concentrations following oral and intravenous administration. The model was also used to simulate bioavailability and plasma concentrations versus time profiles for various parameter values. Serum concentrations following administration of ranitidine and cimetidine were well described by the model, and parameter estimates obtained were in agreement with literature values. Simulations demonstrate the effects of various absorption parameters and gastroin-testinal tract transit parameters on bioavailability and plasma concentration profiles. This discontinuous oral absorption pharmacokinetic model can be a useful tool in characterizing absorption phases, disposition, and bioavailability of drugs exhibiting two absorption peaks following oral administration.

Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves

A finely stratified cylinder model (FSCM) for calculation of the scattered fields of infinitely long, radially inhomogeneous, circular cylinders normally illuminated by electromagnetic plane waves is introduced for the first time, to our knowledge. Because of its capability of using a very large number of layers (more than 80,000), the model is useful for both continuous and discontinuous refractive-index profiles. Numerical results agree well with published solutions for radially inhomogeneous cylinders; for cylinders with a dimensionless size parameter larger than 60, results obtained with the FSCM agree with the geometric optics for both continuous and discontinuous refractive-index profiles.

Pleistocene palynology of the Petone and Seaview drillholes, Petone, Lower Hutt Valley, North Island, New Zealand

A mid to late Pleistocene coastal sedimentary sequence drilled to a depth of 311.2 m (299 m of which was composed of Quaternary sediments) at Petone, near Wellington, New Zealand, consists of fossiliferous sands, silts, clays, and occasional peaty and slightly carbonaceous horizons, and provides a discontinuous pollen profile extending from the Postglacial to as far back as about 350,000 years ago. The sequence includes four major cold periods and four major warm periods, although minor fluctuations are recognised within some of these periods. At Seaview, near Petone, another drillhole encountered similar sediments, with 175.3 m of sediment spanning the same period of time and representing a marked eastward thinning from the deeper part of the Lower Hutt/Port Nicholson basin penetrated by the Petone Drillhole. Large‐scale climatic shifts from warm to cool in the Petone area were represented by periods of substantial erosion and/or deposition of coarse gravel resulting in long breaks between pollen‐bearing sequences. Nine biozones can be recognised in the pollen profiles; these are related to the lithology, local and regional surface formations and local climatic stages, and tentatively correlated with oxygen isotope stages. Biozone P6 (late Pleistocene Oturi or Kaihinu Interglacial) contains taxa restricted today to the north of North Island, representing the period of maximum warmth recognised in the study, and may correlate with oxygen isotope stage 5. This comparison and the radiocarbon‐dated Postglacial (Biozone P9), form the two tie points required for an attempt to correlate the pollen sequence with the oxygen isotope scale. From the top of the sequence, the other biozones are correlated as follows: ‐ Biozone P8 with the peak of the Last Glaciation, Biozone P7 the earlier part of the Last Glaciation (Otira Glacial), Biozone P5 the Waimea Glacial, Biozone P4 the Terangi or Karoro Interglacial, Biozone P3 the Waimaunga Glacial, Biozone P2 the “Normandale” Interglacial and Biozone PI the Nemona Glacial and older stages. A discriminant function analysis of the complete sequence, starting with a comparison between the Postglacial and Last Glaciation spore and pollen assemblages, provides a graph indicating relative fluctuations in the vegetation, which bears a close similarity to the oxygen isotope scale for the same period of time. Abrupt changes in climate are indicated between, and occasionally within each glacial and interglacial. These changes are interpreted as representing periods of environmental instability of quite variable length, but possibly as short as 100 years.

Sm2Fe17Nx with discontinuous nitrogen profiles

Microprobe analysis and theoretical calculations based on Hooke's law are used to investigate Sm2Fe17Nx nitrides produced by N2 and NH3 interstitial modification. In the case of molecular nitrogen, stress and strain as well as Curie temperature, magnetization and anisotropy exhibit a smooth spatial variation, while nitrogen overloading due to the presence of ammonia leads to large excess strain and lattice incoherency. Discontinuous nitrogen profiles are associated with the occurrence of microcracks.

Inverse scattering method for one-dimensional inhomogeneous lossy medium by using a microwave networking technique

The formulation of reflection coefficients from an inhomogeneous lossy medium illuminated by TE and TM waves is approximately derived, in closed form, by using a microwave network method. From the formulation, a novel inverse scattering scheme to reconstruct simultaneously the permittivity and conductivity profiles, is proposed. This scheme is suitable for both continuous and discontinuous profiles, under both the weak scattering and strong scattering conditions. It has also been shown that when the conductivity of the medium equals zero, the reconstructed result of this scheme will reduce to the one formulated by Ladouceur and Jordan (1985). Numerical and closed-form reconstruction examples show the validity of the scheme.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Variable gastric emptying and discontinuities in drug absorption profiles: Dependence of rates and extent of cimetidine absorption on motility phase and pH

The influence of various fasting-state gastrointestinal parameters on variability in absorption of cimetidine was studied using simulation and cimetidine administration as a duodenal infusion and as an oral tablet in fistulated mongrel dogs. In the simulation studies, the frequency of double-peak occurrence in plasma profiles was estimated employing average gastric emptying rates as well as interdigestive-migrating-motor-complex (IMMC) phase lengths that were systematically altered. Emptying rates and phase lengths were modeled as periodic step functions. Simulations indicated that double peaks occur when gastric emptying of the drug begins in early phase I or late phase II/III, which represent the periods of very low, medium, and high gastrointestinal motility, respectively. The incidence is increased for longer phase-I duration and higher elimination rate constants. For a compound with a 2 h elimination or disposition half-life, two concentration maxima (double peaks) were found in 12% of the simulated concentration-time profiles. The double peak frequency in simulated curves was considerably higher for t1/2 < 30 min. When cimetidine was administered to dogs as a duodenal infusion in the active and quiescent motility phases, discontinuous profiles were observed, although the variability of the various parameters was reduced when compared. Pharmacokinetic models were set up that were characterized by multi-segmental input (one- to 3-lag-time models were used) for the profiles resulting from oral and duodenal administration. The lag time for the first process characterized the onset of absorption. A significant difference between phases was detected for infusions at pH 8, where the initial lag time was longer in the quiescent phase. The mean input time (MIT) was calculated as the integral input parameter. There was a tendency for the MIT to be higher for pH 6 infusions than for pH 4 and pH 8. Bioavailability analysis indicated that cimetidine was more rapidly and completely absorbed at pH 8 than at pH 6. Bioavailability was also slightly higher at pH 4 than at pH 6. We concluded that gastric emptying increased the variability of the cimetidine concentration-against-time profiles and that it plays a role with respect to double-peak occurrence, although it is only one of several causative factors.

A novel inverse scattering solution for a one-dimensional inhomogeneous medium using a microwave networking technique

For weak scatterers, simple relations have been discovered between physical properties and the Fourier transforms of their scattering fields, but they are invalid under strong-scattering conditions. In this paper, a microwave networking technique is used to investigate the one-dimensional inverse scattering problem, from which a novel inverse scattering solution for the permittivity profile is derived by considering the equivalent microwave network of the permittivity profile discontinuity at the interface of free space with the medium. This novel solution is essentially different from previous relations and is valid for both weak-scattering and strong-scattering conditions. Closed-form and numerical reconstruction examples show that the novel solution is accurate in comparison with exact theory and is applicable to both continuous and discontinuous permittivity profiles.

Zakharov-Shabat inverse problem with meromorphic reflection coefficient

We analyze the Zakharov-Shabat-type inverse problem when the reflection coefficient contains poles in the eigenvalue plane, as an extension of the earlier work by Atkinson in the case of the Schrodinger problem. It is demonstrated that due to the mutual influence of such a pole and the usual bound-state pole, a discontinuous solitary wave profile is generated. Furthermore, we also examine the form of the nonlinear field only due to the pole of the reflection coefficient. A different approach is necessary to convert the GLM equation into a purely differential one for its solution.

Critical Large Deviations for Gaussian Fields in the Phase Transition Regime, I

We investigate large deviations for the empirical distribution functional of a Gaussian random field on $\mathbb{R}^{\mathbb{Z}^d}, d \geq 3$, in the phase transition regime. We first prove that the specific entropy governs an $N^d$ volume order large deviation principle outside the Gibbsian class. Within the Gibbsian class we derive an $N^{d-2}$ capacity order large deviation principle with exact rate function, and we apply this result to the asymptotics of microcanonical ensembles. We also give a spins' profile description of the field and show that smooth profiles obey $N^{d-2}$ order large deviations, whereas discontinuous profiles obey $N^{d-1}$ surface order large deviations.

Polynomial characterization of inhomogeneous media and their reconstruction using an open-ended waveguide

B. Sanadiki and M. Moustafavi (1991) described how an inhomogeneous continuously varying dielectric profile can be inverted using a stepwise successive refinement procedure when an open-ended waveguide is used as the source. Here, an alternative approach based on polynomial characterization of the dielectric medium is discussed. It is shown that this method is more efficient and avoids the convergence difficulties of the previous method for most cases except for discontinuous or stratified profiles.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Split-operator calculations of reflected electric field profiles

A previously introduced split-operator reflection technique is adapted to near- and far-field calculations by inverting the operator ordering with respect to that presented in earlier publications. The method is used to examine reflection from an interface between two refractive index media with discontinuous index profiles. The method is further extended to arbitrarily polarized electric fields.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Use of Magnetic‐Susceptibility Measurements in Assessing Soil Uniformity in Chronosequence Studies

AbstractRecent observations show that soils with vertical morphological differentiation often exhibit a distinct ferrimagnetic profile with the magnetic susceptibility (MS) of eluvial horizons enhanced with respect to that of illuvial, Cr, or R horizons. In addition, pedogenic ferrimagnetic material is mostly superparamagnetic (SP) and single domain (SD) (&lt;30 nm), whereas inherited titanomagnetites are predominantly multidomain (MD) grains. We suggest that the continuous pedogenic development of a soil profile in homogeneous parent material results in enhancement of MS and in a gradual shift from MD to SD and SP magnetic states, and that deviations from this pattern arise from discontinuities in the soil or from climatic or topographic changes. This hypothesis was tested on 18 northern California pedons, formed in four marine and river terrace systems and in volcanic parent material. The ages of the terraces range from 600 yr to 1.6 million yr and the MS of the parent materials range from 10 to &gt; 1000 × 10−8 m3 kg−1. Established chronosequence members were used to determine that enhancement of MS and shifts in magnetic domain state are correlated with age. Exceptionally large or small magnetic susceptibilities throughout the soil profile, lack of magnetic enhancement, and discontinuous magnetic profiles in other soils could each be related to morphologically or chemically determined discontinuities. Thus, magnetic susceptibility, an easily measured soil attribute, can be used to evaluate the suitability of pedons for chronosequence studies.

Resonant structures within incompressible ideal MHD

The resonant characteristics of an incompressible ideal MHD fluid are highly structured. To help expose this structure, an equivalent electrical analogue of the MHD system is developed. The model, in the form of a transmission line, makes it possible to identify a number of new and important concepts, one of which is the effective impedance. This in turn enables entire regions of MHD fluid to be replaced with equivalent impedances. When fully exploited, the model also provides a more consistent interpretation of the spectrum of ideal MHD. The discrete Alfvén modes are found to be highly degenerate, while the transition to a discontinuous profile is accompanied by a redistribution of an uncountably infinite number of ‘poles’ from the continuous spectrum and onto the Alfvén modes. In addition, the electrical analogue shows that within a continuously structured fluid the characteristic behaviour is not necessarily dominated by the ‘surface mode’ alone. This view is also supported by the results of a numerical simulation of the linear MHD equations. Depending on the initial conditions, the collective behaviour can have any frequency within the range spanned by the transition zone. The energy itself is monitored using a new pair of energy and flux expressions derived from a variational (Lagrangian) description of the MHD system. Again the electrical model is used to provide a physical interpretation of the individual terms within these expressions. In particular, it allows a partition of the total energy into separate kinetic- and potential-energy terms.

Improvement of finite difference methods for step-index optical waveguides

New 3-point finite difference formulae with equally spaced grid points are given for the analysis of scalar or semivectorial fields in waveguides with discontinuous refractive index profiles. The new formulae lead to more accurate calculations for the modes than the previously known methods, irrespective of the location of the discontinuities with respect to the grid points and without averaging the permittivity over meshes.

Kinetic energy of Rayleigh–Taylor and Richtmyer–Meshkov instabilities

General expressions for the kinetic energy associated with Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities in incompressible fluids are derived. The results are valid for small perturbations in continuous as well as discontinuous density profiles. It was found that KERT /KERM=ge2γτ /(ΔvΓ)2=(geγτ/Δvγ)2, where τ=time, g=acceleration, Δv=velocity jump, and γ is the exponential growth rate of the RT amplitude. The linear growth rate of the RM amplitude is ΔvΓ2=Δvγ2/g, and is found by solving an eigenvalue equation for a given density profile subject to appropriate boundary conditions. In general, KERT asymptotes to a constant value at large k (k=2π/λ, λ=wavelength), while KERM continues to grow with k. Several analytic examples are illustrated and the k dependence of the kinetic energies is displayed.