Discontinuous Profiles Research Articles

Analysis of the Frequency Response of a Fluid Amplifier Using Unsteady Flow Characteristics

This paper is mainly concerned with the theoretical and experimental study of the frequency response of an analog fluid amplifier. The channels are considered as distributed parameter systems and the frequency effects on the charcteristics of nozzles, vents, and jet interaction are taken into account. The paper considers the dynamic behavior of the flow in vortex vents and the interaction of two jets : a discontinuous profile is used to approximately describe the average velocity distribution in the jet in order that a recursive solution for the eigenvalues resulting from a small perturbation be obtained. The amplifier was tested by means of an electropneumatic signal generator at frequencies up to 3000 Hz. A comparison with experiments performed in the potential core region shows that the linear theory correctly predicts the passband of the jet which is constant provided a local Strouhal number is used.

Use of Metzler’s NONLIN Program for Fitting Discontinuous Absorption Profiles

□ An alternative to the use of integral hybrid flow/compartmental model (HFCM) equations in fitting cases I and II discontinuous absorption profiles is presented. It is proposed that HFCM-integral equations be replaced by a system of differential equations in which sequential sets of equations describe the absorption profile from time zero to infinity. The required sets of differential equations for these two cases are presented as they apply to a two-compartment drug, potentially undergoing multiple absorption steps. It was shown that the use of the NONLIN program in the differential equation mode provides good fits for some unusually shaped absorption profiles of buformin, sulfisoxazole, and griseofulvin. The values of the parameter estimates and the sum of squared deviations, ƩSD, obtained with NONLIN were almost identical to those obtained with the FITSI2 program utilizing HFCM equations. While HFCM-integral equations required less computer time, they introduced the potential for negative absorption times. This problem is avoided by use of the differential equations method.

Cratering due to surface defects in the Gaussian model

Surface defects on freshly applied liquid films like the phenomenon of cratering are characterized by almost discontinuous interfacial profiles. Our purpose is to model the effect of surface inhomogeneities and impurities that influence the equilibrium configuration of the surface film. We therefore employ the Gaussian model which is known to provide a simple equilibrium statistical thermodynamics description of the liquid–vapor interface. By modifying previous work by Weeks, we allow for additional external forces acting on the interface and discuss the resulting shape of the surface profile. Even local application of external forces leads to deviation from the plane surface decaying on a macroscopic length scale. This does not accurately model the cratering phenomenon. In systems, which can be described by our Gaussian model, surface tension forces will always lead to a smooth interfacial profile.

Upper mantle modelling using long-period SH body-wave trains

The resolution of fine shear-velocity structure in the upper mantle is difficult because of the low signal-to-noise conditions in most recordings of short-period S waves, and the poor resolving power of long-period S data. The resolution obtainable from the latter could be improved if a greater proportion of the SH body-wave train at distances less than about 40°, presumably comprised of arrivals from a variety of multiple paths through the upper mantle, could be separated into its component signals. Attempts at deconvolving these wave trains by standard techniques, however, usually result in “noisy” spike sequences which are extremely difficult to interpret. The authors have devised an empirical method of decomposing an SH body-wave train into its component arrivals, based on sequential removal of the response wavelets from the train. Although the method is approximate in that it assumes the absence of phase distortion, it provides clear spike sequences which can be used to derive a starting model for the application of refinement techniques. Application of the method to SH wave trains recorded at NORSAR from Mediterranean earthquakes has enabled the construction of an SH-velocity model for the upper mantle beneath eastern Europe in which the discontinuity profile is strikingly similar to those of recent detailed P-velocity models for the upper mantle beneath central Australia.

The formation of metasomatic reaction veins in dolomitic marble roof pendants in the Bergell Intrusion (Province Sondrio, northern Italy)

At its eastern margin the Berge11 intrusion contains large numbers of well exposed dolomitic marble roof pendants and inclusions. Symmetrically zoned reaction veins occurring in these dolomites are related to a regional fracture system which was possibly formed during the cooling and uplift of the intrusion. The vein thicknesses range from a few millimeters to a maximum of 0.6 m. Mineral assemblages found in individual zones of the veins include: calcite + olivine, calcite -I-diopside, calcite + amphibole, calcite + antigorite, calcite + talc. Biotite may be present in all zones. The zone sequences found in different veins show a large variation. The most abundant vein type consists of a single but internally banded amphibole + calcite zone. The internal zonation is caused by discontinuous changes in the amphibole composition. Ironand aluminium-rich amphiboles are found close to the vein center, whereas pure tremolite occurs at the metasomatic front. These discontinuous composition profiles across amphibolite + calcite zones lead to the conclusion that the transport process for many of the veins was infiltration metasomatism. Comparing modal abundances of vein minerals with model vein rocks it is suggested that MgO was conserved during vein formation, and the veins were formed essentially by Si0:-metasornatism. The composition of the vein minerals suggest however that iron and aluminium were transported as well. From phase relations among the different zone assemblages, it may be concluded that vein formation occurred over a pressure-temperature interval (cooling-uplift interval) but that the formation of an Individual vein was an isothermal isobaric process occurring in the presence of gradients in a s ioaq and small gradients in X002 in the vein forming fluid. Geometric relations suggest that the veins may have grown by both deposition of material along an opening central fracture and reaction of a Si0 2-rich aqueous fluid with the adjacent dolomite.

The hard-sphere and square-well models for the surface properties of liquid metals

Abstract The statistical mechanical deduction of Fowler for surface tension from the assumption of a discontinuous step function profile of the surface density is used in conjunction with Evan's pseudo-atom theory to calculate surface properties such as surface entropy and tension for hard-sphere and square-well types of interactions in liquid metals. The resulting values of surface tension are in reasonable agreement.

Some aspects of discreteness-of-charge and ion-size effects for ions adsorbed at charged metal/aqueous electrolyte interfaces

It is argued that the self-image potential of an ion adsorbed on a charged metal from an aqueous electrolyte is described in terms of multiple imaging and not single imaging in the metal as proposed by Bockris. The image potential of an isolated ion situated on the i.H.p. in the inner region with a continuously and smoothly varying dielectric profile is calculated. This is compared with the corresponding potential for an inner region model with a discontinuous dielectric profile. It is shown that when the position of the i.H.p. relative to the o.H.p. is changed, the two potentials will in general cross each other such that the discontinuous model has the more negative self-image potential when the i.H.p. approaches the o.H.p. The scaled-particle expression for the entropic contribution due to ion-size effects in the adsorption isotherm of an ion in the inner region is compared with the corresponding Flory-Huggins formula. It is demonstrated that the two theories can give very different results. In particular, when the adsorbed ions are considerably larger than the solvent molecules, it is possible that scaled-particle theory leads to a ‘negative’ ion-size entropy term, which decreases with increase in density of adsorbed ion.

Early diagenesis of fatty acids in lacustrine sediments—III. Changes in fatty acid composition in the sediments from a brackish water lake

A 3-m sediment core taken from Lake Suigetsu, in which a shift from fresh to brackish water occurred about three hundred years ago, has been examined for variation with depth of organic carbon and fatty acids. From the difference in total amounts of sulphur between sediments under fresh and brackish water environments, the surface sediments above approximately 35 cm depth were deduced to be accumulated under a brackish water environment. The total contents of organic carbon and fatty acids, and percentage composition of fatty acids gave discontinuous profiles above and below the 35–40 cm sediment layer. At a depth of 12.5 cm, the distribution in chain length of the fatty acids changed from a unimodal (the predominance of C 12-C 18 over C 20-C 34) to a bimodal pattern, which was mirrored by the composition diversity index (CDI). Although the fatty acids in the surface sediments (0–40 cm) from Lake Suigetsu seemed to suffer milder degradation through microbial activity than those in a core (0–150 cm) from Lake Suwa, a freshwater eutrophic lake, both lacustrine sediments showed similar trends in the alteration of fatty acid composition with depth.

The Fr�chet derivative for the one-dimensional electromagnetic induction problem

Summary. From consideration of the higher order terms, it is shown that the magneto-telluric response is Frechet differentiable with respect to conductivity; this result remains valid for discontinuous profiles, which is not so in the case of the corresponding free-oscdlation problem for the elastic earth. The remainder term in the Frechet formula is shown to be O|δσ|2 and a numerical estimate is made of the bounding constant for a restricted class of conductivity models.

Wave breakdown in stratified shear flows

The wave-mechanical condition (Landahl 1972) for breakdown of an unsteady laminar flow into strong small-scale secondary instabilities is applied to some simple stratified inviscid shear flows. The cases considered have one or two discrete density interfaces and simple discontinuous or continuous velocity profiles. A primary wavelike disturbance to such a flow produces a perturbation velocity that is discontinuous at a density interface. The resulting instantaneous system, defined as the sum of the mean flow and the primary oscillation, develops a local secondary shear-flow instability that has a group velocity equal to the arithmetic mean of the instantaneous velocities on the two sides of the interface. According to the breakdown criterion, the disturbed flow will become critical whenever this velocity reaches a value equal to the phase velocity of the primary wave. The calculations show that for a single density interface breakdown may occur for low to moderate wave amplitudes in a fairly narrow range of Richardson numbers on the stable side of the stability boundary. On the other hand, in the unstable regime maximum wave slopes of order unity may be reached before breakdown occurs; this conclusion is in qualitative agreement with experiments. When the system includes two density interfaces, it is found that there exists a range of high Richardson numbers far into the stable regime for which breakdown may take place even for very small and zero wave interface deflexions.

Oxidation-reduction potential measurements on chloroperoxidase and its complexes.

The oxidation-reduction potential of chloroperoxidase, an enzyme which catalyzes peroxidative chlorination, bromination, and iodination reactions, has been investigated. In addition to catalyzing biological halogenation reactions, chloroperoxidase is unusual in that the carbon monoxide complex of ferrous chloroperoxidase shows the typical long wavelength Soret absorption associated with P-450 hemoproteins. The pH dependence of the chloroperoxidase oxidation-reduction potential shows a discontinuity around pH 4.7. Similarly, measurements of the affinity of ferrous chloroperoxidase for carbon monoxide monitored both by spectroscopic and potentiometric titration exhibit a discontinuity in the pH 4.7 region. Oxidation-reduction potential measurements on chloroperoxidase in a CO atmosphere also show a discontinuous pH profile. These results suggest that ferrous chloroperoxidase undergoes reversible modification at low pH and that these changes are reflected in the oxidation-reduction potential. The oxidation-reduction potential of chloroperoxidase at pH 6.9 is - 140 mV, close to that measured for cytochrome P-450cam in the presence of substrate. The oxidation-reduction potential of chloroperoxidase at pH 2.7, the pH optimum for enzymatic chlorination, is +150 mV. The oxidation-reduction potentials of the halide complexes of chloroperoxidase (chloride, bromide, and iodide) are essentially identical with the potential measurements on the native enzyme. These observations suggest that, although halide anions bind to the enzyme, they probably do not bind as an axial ligand to the heme ferric iron.

Investigation of the development of laminar flow at the entrance of a two-dimensional channel, using a laser-doppler velocimeter

The results of an experimental investigation of the velocity structure of Poiseuille flow at the entrance section of a two-dimensional horizontal channel with a discontinuous velocity profile at the entrance, at Re=300 and 500, are given. The experimental facility and the technique for measuring the velocity field in this channel using a laser-Doppler velocimeter (LDV) are discussed. Velocity profiles are obtained which are concave on the channel axis, and this agrees with the results of the numerical computations of [1].

Hydromagnetic stability of parallel flow of an ideal heterogeneous fluid

The magnetohydrodynamic and Boussinesq approximations are used on a fully ionized ideal fluid with a longitudinal magnetic field. The flow is in a direction normal to the gravity vector and all variations in velocity, density and magnetic field. The stability characteristics, mainly for normal-mode perturbations, are investigated. Two simple problems with discontinuous profiles are solved analytically. For a double shear layer, an appropriate range of magnetic field values destabilizes the flow. A long wave theory is presented and applied to several problems, some of which are destabilized by an appropriate magnetic field. Finally, the solution for continuous profiles is presented and shown to decay algebraically in time for any stable stratification.

The stability of a thermally radiating stratified shear layer

A linear stability analysis is applied to a stratified, thermally radiating, un-bounded shear layer. Temperature disturbances are assumed to be optically thin. Both viscous and inviscid neutral stability boundaries are determined numerically for hyperbolic-tangent mean velocity and potential-temperature profiles. For these profiles, long-wavelength disturbances are completely destabilized (the critical Richardson number Ric → ∞ as the wavenumber k → 0) in the inviscid limit. A similar situation is found for the case of discontinuous step-function profiles. However, in contrast to the non-radiating problem, the functional form of the neutral stability boundary is not the same for both the continuous and discontinuous profiles in the limit k → 0. Application of the viscous results to the atmospheres of the earth and Venus yield critical Richardson numbers in excess of ¼.

Séparation isotopique d'azote 15—I Influence du débit, de la hauteur de collone et de la température pour le système NO [sbnd]HNO 3

Abstract The authors have systematically studied the influence of hydrodynamic parameters, feed flow, packing, height of column on the enrichment in nitrogen 15 of the nitric acid for the system HNO 3 NO, NO 2. An empirical law permitting the determination of the number of theoretical plates as a function of the flow and of the height of packing is proposed for operation with total reduction reflux gases. The systematic study of the influence of the temperature indicates the existence of an optimum isotherm (45°C). The utilization of a discontinuous temperature profile leads to an enrichment that is lower than that at isothermic operation.

Diffusion interactions in glasses arising from discontinuities in anion concentration

A multicomponent diffusion formalism based on the Nernst-Planck equation is presented which is capable of generating from tracer diffusion data the discontinuous cation diffusion profiles which arise in diffusion couples when a stationary anion concentration profile contains a step discontinuity. Such couples can be constructed with ion exchange resins, zeolites, and glasses. This formalism introduces the electroneutrality condition through the zero flux (ΣZ1J1=0) condition alone, thus avoiding the mathematical difficulties associated with the application of the discontinuous neutrality condition (ΣZiCi=0) to a set of differential equations. The agreement between the predictions and the experiments for a series of silica glass couples is found to be good. It is argued that the well-known contradiction between the electroneutrality constraint on the real charge and the nonuniform field predicted within the Nernst-Planck formalism can be removed if the proposition is accepted that a distribution of dipoles, and therefore of dipole charge, is associated with each diffusion profile of such magnitude that solutions of the Poisson equation become exactly consistent with the diffusion-generated electric field.

The existence of a discontinuity in the profile of a slow shock magnetohydrodynamic wave

An analysis is made of the structure of the profile of a slow shock magnetohydrodynamic wave of arbitrary intensity in a nonviscous medium. It is shown that the condition for the formation of a discontinuous profile coincides with the condition for the creation of an isothermal discontinuity in conventional gas dynamics.

Viscous Stability Theory for Thermally Stratified Flow: Discontinuous Jets and Shear Layers

The method used by Drazin to investigate the stability of unbounded, viscous, homogeneous, parallel shear flow to small wavenumber disturbances is extended to study the effect of thermal stratification on the stability of unbounded jets and shear layers. By this method the stability characteristics of continuous profiles are inferred from the stability characteristics of discontinuous profiles. The characteristic value problem for discontinuous jet and shear layers is posed by the requirement that the solutions of the governing differential equation satisfy the matching conditions and boundedness conditions for layers that extend to infinity. The analysis leads to a characteristic determinant which is required to vanish for the characteristic values of the parameters: the Reynolds number, the wavenumber, and the wave speed. The stabilizing effect of the thermal stratification as parameterized by the Richardson number was found to be most stabilizing for small wavenumber (large-scale) disturbances.

Effects of Plasma Flow on Electrostatic Disturbances in a Q Machine

The evolution of a large discontinuity in density in a single-ended Q machine has been found to be adequately described by a free-streaming model of the ions modified by a density gradient electric field due to a finite electron temperature. As the electron temperature is increased through microwave heating at cyclotron resonance, the profile of the discontinuity is found to broaden spatially as predicted by the theoretical model. The plasma ion drift velocity along the magnetic field can be measured from the motion of the discontinuity and is found to be in close agreement with the drift velocity measured from the propagation of small-amplitude ion-acoustic waves. An estimate of the ion thermal velocity parallel to the magnetic field can also be obtained from the broadening of th discontinuity profile. The ion drift velocity exhibits systematic variation with changes in oven and ionizer temperatures which is attributable to the electron-ion balance in the region surrounding the hot ionizer.

Spreading Loss of Sound in an Inhomogeneous Medium

Geometric spreading of sound in a medium with any given continuous velocity profile is investigated theoretically. The sound velocity is assumed to be dependent on one space coordinate only. The analysis is based on Snell's law. Time and initial angle of the ray are the two independent variables. A set of differential equations describing spreading loss is developed. These equations are solved analytically for the case of constant-velocity gradient yielding well-known results. A short discussion of both analog- and digital-computer solutions for the general case is given. Discontinuous velocity profiles and the interchange of sound source and receiver are also considered.