Weak Heterogeneity Research Articles

Induction of bleomycin resistance in a human oral squamous carcinoma cell line and characterisation of bleomycin-resistant and -sensitive clones

We examined the change of sensitivity to antitumour agents by repeated treatment with bleomycin (BLM) using two oral squamous carcinoma cell lines, SCCTF and SCCKN. SCCTF exhibited minimal sensitivity to BLM and strong heterogeneity in BLM sensitivity, whereas SCCKN was highly sensitive to BLM and showed weak heterogeneity. When SCCTF was treated continuously with low-dose BLM (0.1 microgram/ml) but not intermittently with high-dose BLM (1 microgram/ml), the BLM sensitivity was rapidly decreased to acquire drug resistance. On the other hand, SCCKN was completely killed by the same treatments. To investigate the mechanism of induction of resistance in SCCTF, BLM-sensitive and -resistant clones, TF-S and TF-R, were isolated and analysed. Consequently, TF-R showed decreased cellular accumulation and retention of BLM, increased BLM hydrolase activity and elevated DNA repair activity concomitant with increased poly(ADP-ribose) polymerase activity as compared with TF-S. Therefore, it was suggested that antitumour drug-resistant clones were selectively grown from heterogeneous tumour cell population.

Effects of random quenched impurities on wetting of solids: a Monte Carlo study

This paper presents the results of a Monte Carlo simulation study of the effects of randomly distributed quenched impurities on prewetting and wetting transitions in adsorbed layers. We concentrate on simple model systems with only two types of adsorption sites and investigate how the concentration of impurities affects wettability of a surface. It is demonstrated that the impurities may change the character of the prewetting transition and considerably change the wetting temperature. In particular, it is shown that even very weak heterogeneity destroys the first-order character of the prewetting transition and may induce or exclude wetting of a solid substrate.

The effect of a weak heterogeneity of a porous medium on natural convection : C. Braester & P. Vadasz, Journal of Fluid Mechanics, 254, 1993, pp 345–362

The effect of a weak heterogeneity of a porous medium on natural convection : C. Braester & P. Vadasz, Journal of Fluid Mechanics, 254, 1993, pp 345–362

Influence of substrate heterogeneities on the spreading of a drop.

The dynamics of spreading of monolayers of completely wetting liquids on substrates with various degrees of heterogeneity is studied here experimentally and numerically at a microscopic level. The radius of spreading of the first layer of the drop always presents two different diffusive regimes as a function of time if the temperature is higher than the two-dimensional (2D) critical temperature of the liquid. The associated spreading rate increases when the substrate becomes heterogeneous at the molecular scale. If the temperature is lower than the 2D critical temperature of the liquid, the second diffusive regime occurs only on heterogeneous substrates. The spreading rate again increases with the substrate heterogeneity, at least for weak heterogeneities. The agreement between the experimental results and the simulation, using the Kawasaki double spin exchange dynamics [K. Kawasaki, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, London, 1972), Vol. 2] is very satisfactory.

The effect of a weak heterogeneity of a porous medium on natural convection

The results of an investigation on the effect of a weak heterogeneity of a porous medium on natural convection are presented. A medium heterogeneity is represented by spatial variations of the permeability and of the effective thermal conductivity. As a general rule the existence of horizontal thermal gradients in heterogeneous porous media provides a sufficient condition for the occurrence of natural convection. The implications of this condition are investigated for horizontal layers or rectangular domains subject to isothermal top and bottom boundary conditions. Results lead to a restriction on the classes of thermal conductivity functions which allow a motionless solution. Analytical solutions for rectangular weak heterogeneous porous domains heated from below, consistent with a basic motionless solution, are obtained by applying the weak nonlinear theory. The amplitude of the convection is obtained from an ordinary non-homogeneous differential equation, with a forcing term representative of the medium heterogeneity with respect to the effective thermal conductivity. A smooth transition through the critical Rayleigh number is obtained, thus removing a bifurcation which usually appears in homogeneous domains with perfect boundaries, at the critical value of the Rayleigh number. Within a certain range of slightly supercritical Rayleigh numbers, a symmetric thermal conductivity function is shown to reinforce a symmetrical flow while antisymmetric functions favour an antisymmetric flow. Except for the higher-order solutions, the weak heterogeneity with respect to permeability plays a relatively passive role and does not affect the solutions at the leading order. In contrast, the weak heterogeneity with respect to the effective thermal conductivity does have a significant effect on the resulting flow pattern.

Radiative transfer and multiple scattering of diffuse ultrasound in polycrystalline media

A model for the multiply scattered incoherent field in a continuous polycrystalline elastic medium is presented. Unlike a previous development based upon energy and flux conservation considerations [J. A. Turner and R. L. Weaver, J. Acoust. Soc. Am. 93, 2312 (A) (1993)] for a medium containing discrete random scatterers, the present model has been developed from the wave equation and first principles. Appropriate ensemble averaging of the wave equation leads to Dyson and Bethe–Salpeter equations that govern the mean Green’s function and the covariance of the Green’s function, respectively. These equations are expanded for weak heterogeneity and equations of radiative transfer are obtained. The result is valid for attenuations that are small compared to wave number: α/k≪1. Polarization effects are included, as before, through five elastodynamic Stokes parameters, one longitudinal and four shear. The theory is applied to a statistically homogeneous cubic polycrystalline half‐space immersed in a fluid and illuminated by a plane wave. Results on the angular and temporal dependence of backscattered intensity are presented and compared with the predictions of a single‐scattering theory. It is anticipated that this approach may be applicable to microstructural characterization through the study of the time, space, ultrasonic frequency, and angular dependence of multiply scattered ultrasound in elastic media. [Work supported by NSF.]

Liquid core structure and PKP station anomalies derived from PKP(BC) propagation times

PKP(BC) travel time residuals in the distance range 148.5–155.5° have been extracted from the catalogues of the International Seismological Centre and inverted to retrieve possible heterogeneities or anisotropy at the base of the liquid core, and PKP(BC) station anomalies. A binning has first been applied to the data to minimize the biases that result from the uneven sampling of the Earth by the PKP(BC) rays and from the heterogeneities in the source regions. For the liquid core structure, the data reveal weak heterogeneities, with travel time delays slightly higher near the South Pole and lower beneath southeast Asia, but most of these variations stay below the error bar level. The search for anisotropy at the base of the liquid core also leads to inconclusive results, with a weak tendency for lower velocities in the direction of the Earth's rotation axis. Station anomalies appear to be by far the major contribution to the PKP(BC) residuals. Their values are compared with the P station corrections, and with the values predicted by lower-mantle tomographic models. They show that the lower mantle makes an important contribution to the PKP residuals at medium wavelengths; these delays are generally underpredicted by tomographic models.

Effects of capillary heterogeneity on vapor—liquid counterflow in porous media

Based on a continuum description, the effect of capillary heterogeneity, induced by variation in permeability, on the steady state, countercurrent, vapor—liquid flow in porous media is analyzed. It is shown that the heterogeneity acts as a body force, that may enhance or diminish gravity effects on heat pipes. Selection rules that determine the steady states reached in homogeneous, gravity-driven heat pipes are also formulated. It is shown that the ‘infinite’ two-phase zone may terminate by a substantial change in the permeability somewhere in the medium. The two possible sequences, liquid—liquid dominated—dry, or liquid—vapor dominated—dry find applications in geothermal systems. Finally, it is shown that although weak heterogeneity affects only gravity controlled flows, stronger variations in permeability can give rise to significant capillary effects.

Seismic body waves in a 3-D, slightly aspherical Earth - I: testing the Born approximation

SUMMARY The first stage of a method for calculating long-period body wave seismograms in a laterally heterogeneous Earth is presented. First, the elastodynamic equation of motion in spherical coordinates, which is valid for weak lateral heterogeneity, is established using a generalized spherical harmonic expansion of the displacement and traction fields and the elastic parameters. It is shown that the equations for the displacement-traction components can be simplified by using high-wavenumber asymptotic approximations to the first-order coefficients, which are appropriate for 5s - 20s body waves in the mid- to upper mantle. The Born approximation is then used to develop a computationally efficient method for calculating me first-order scattered field in terms of the high-frequency asymptotic solution for a laterally homogeneous Earth. This efficiency is increased further by decomposing the wavefield into its P, SV, and SH components. Finally, the numerical integration of the displacement-traction components is performed for a few selected frequencies and a restricted band of angular degrees, in order to test the validity of the Born approximation. Comparison of these results with those calculated using the Born approximation indicates that the latter is well suited to models of weak lateral heterogeneity in the Earth, for which the elastic parameters can be expressed as a sum of low-order spherical harmonics. It is demonstrated that, for this particular class of models, the Born approximation yields a good representation of the scattered field for frequencies within the long-period body wave band of 0.05–0.2 Hz.

Modelling of the hydroxyl group population using an energetic analysis of the temperature-programmed desorption of pyridine from silica gel

The temperature-programmed desorption (TPD) of pyridine from silica gel has been analysed with the variable heating, constant coverage procedure proposed by Richards and Rees (R. E. Richards and L. V. C. Rees, Zeolites, 1986, 6, 17). This results in curves of activation energies of desorption as a function of coverage. A weak heterogeneity of the silica gel surface is observed in contrast with other pyridine sorption studies. Two adsorption sites, the free and bridged hydroxyl groups, contribute to the surface heterogeneity. The relative amounts of the two sites on the surface are deduced from the calculated activation energy vs. coverage profiles. An attempt is made to extrapolate the absolute concentrations of free and bridged hydroxyls from the relative site coverages.

Physical properties of deep crustal reflectors in southern California from multioffset amplitude analysis

Analysis of reflection waveforms before stack can constrain the physical properties of reflectors in the deep crust. To simplify this analysis, recorded amplitudes are assumed to be reflections from weak elastic heterogeneities. With these assumptions, trends in reflection amplitudes with offset may indicate whether the signs of a reflector’s density and rigidity contrast agree with or oppose the sign of its Lamé’s parameter contrast. The slope of the trend indicates the degree of Poisson’s ratio contrast. No attempt is made to invert for the individual modulus or density contrasts. By examining only gross amplitude‐versus‐offset (AVO) trends, deep reflections constrain some crustal properties. Two seismic reflection surveys in the Mojave Desert recorded deep reflections that show amplitude changes with offset. Both the 1985 Calcrust Ward Valley survey in the eastern Mojave and the 87 km COCORP Mojave line 3 in the western Mojave incorporate long offsets of 10 km or more. Prestack traces are equalized using a quantile technique assuming a constant noise level at large time, then corrected for spherical divergence. Gross AVO trends that are summarized for each survey in amplitude trend stacks suggest that the strongest reflectors in the middle and deep crust represent Poisson’s ratio contrasts of at least 10 percent. In the eastern Mojave, a transition to a basal‐crustal zone, at ∼23 km depth, may include an increase in Poisson’s ratio with depth. Poisson’s ratio may also increase at the Moho.

Meniscus shape and contact angle of a slightly deformed axisymmetric drop

Although the meniscus of a pure liquid drop placed on a perfectly smooth and homogeneous solid surface is a spherical cap (when gravity is negligible and the contact angle finite), the general solution of Laplace's capillary equation represents a complex mathematical task. The author obtains a formulation for the limited class of problems in which an essentially axisymmetric sessile drop of low intrinsic contact angle is perturbed by weak heterogeneities, either chemical or physical, on the solid surface. The contact line is disturbed from its circular form by local (positive) heterogeneities and an effect of 'digitation' results. Modification of the meniscus, although becoming attenuated, extends to the drop centre.

The attenuation of surface waves due to scattering

Summary Surface wave attenuation is usually attributed to inelastic properties of the Earth, but a considerable part of the surface wave attenuation may be due to scattering by lateral heterogeneities. For body waves, the theory describing attenuation due to scattering is well known. In this paper, a similar theory is presented, which describes the attenuation of surface waves due to scattering. The Born approximation is used to derive the scattered wavefield, therefore only weak heterogeneities can be described. Some numerical experiments are performed for periods between 25 and 100 s. For realistic scatterers the conversions from the fundamental mode to the higher modes cannot be neglected. The Q−1 values computed for scattering media are of the same order of magnitude as measured Q−1 data. A whole range of attenuation curves as a function of frequency can be obtained by varying the parameters of the scattering experiment. This leads to believe that Q−1 data inversions to Q−1 depth models should be regarded with some suspicion, because the contribution of scattering to the attenuation cannot be neglected.

Vector-scattering of elastic waves by directional structural space gradients

A nonstochastic and noniterative theory of vector scattering in inhomogeneous media is presented. The elastodynamic vector wave-equation for 3D inhomogeneous media is solved for a weak heterogeneity at the high-frequency region. It is shown that there exists a forward scattered field which decays slowly along the source-receiver path. Its rate of attenuation depends on the azimuth of the path relative to the direction of the inhomogeneity, but is independent of frequency. The Green's tensor for the above regime is derived in closed form and leads to the quantification of fields of dipolar sources in weak inhomogeneous media. The inhomogeneity at the source creates a source-induced scattering (in addition to path-scattering) having a radiation-pattern that bears the signature of the source. The availability of the analytic Green's tensor, in conjunction with the Huygens-Kirchhoff-Helmholtz formalism, opens new ways to calculate the scattered fields due to various structural inhomogeneities applicable to exploration and earthquake seismology. The theoretical results of this study point to the conclusion that the scalar wave approximation may not always be valid for the propagation of seismic waves in the earth's lithosphere.

First Born and Rytov approximations: Modeling and inversion conditions in a canonical example

First Born and, more recently, first Rytov approximations are widely used for solving complex forward and inverse seismic scattering problems. The exact pressure-field response from a one-dimensional velocity slab included in an infinite constant velocity medium is expressed analytically. This solution is used for testing these two approximations in modeling and in inversion. Conditions of applicability and parameter estimates lead to the following results: The first Rytov approximation is best suited for modeling and inverting the transmitted, or forward scattered, part of the wave field, whereas the first Born approximation is best suited for modeling and inverting the primary reflected, or backscattered, part of the wave field. If the long wavelength condition holds, linearization of the field with respect to slowness squared is preferable over linearization with respect to slowness, allowing for a very large velocity contrast between the slab and the reference medium. However, if the weak heterogeneity condition holds (i.e., small velocity contrast), the linearization choice is reversed. Numerical examples show and display these differences quantitatively.

Multiple Time Series Regression with Integrated Processes

This paper develops a general asymptotic theory of regression for processes which are integrated of order one. The theory includes vector autoregressions and multivariate regressions amongst integrated processes that are driven by innovation sequences which allow for a wide class of weak dependence and heterogeneity. The models studied cover cointegrated systems such as those advanced recently by Granger and Engle and quite general linear simultaneous equations systems with contemporaneous regressor error correlation and serially correlated errors. Problems of statistical testing in vector autoregressions and multivariate regressions with integrated processes are also studied. It is shown that the asympotic theory for conventional tests involves major departures from classical theory and raises new and important issues of the presence of nuisance parameters in the limiting distribution theory. Unlike many of the time series encountered in the natural sciences, economic time series frequently exhibit characteristics that are widely believed to be intrinsically nonstationary. For example, real macroeconomic variables such as output and consumption typically display a strong secular or growth component as well as cyclical behaviour; and many financial series like common stock prices behave in general as if they had no fixed mean. Recognizing these typical characteristics of economic time series, econometricians have devoted attention to the problem of describing and modelling nonstationarity. In the 1960's important contributions in the area were made by Granger, Hatanaka and their associates in Granger and Hatanaka (1964), Granger and Morgenstern (1963), Brillinger and Hatanaka (1968) and Hatanaka and Suzuki (1967). Later, following the influential work of Box and Jenkins (1976), attention shifted to the role of integrated processes in modelling economic time series. While undoubtedly restricting the class of nonstationary models, integrated processes of the ARIMA type have been found to produce highly satisfactory representations of many observed time series in economics. Quite recently, Nelson and Plosser (1982) have published a detailed empirical study of historical economic time series for the U.S.A. These authors provide some convincing evidence that macroeconomic time series normally thought to be stationary about a time trend are better described as integrated processes with drift. Amongst the latest research in this field have been the studies of cointegration by Granger and Weiss (1983) and Granger and Engle (1985). Two time series are said to be cointegrated if some linear combination of the series has a lower order of integration than the individual series. These authors argue that the notion of (steady state) equilibrium in economics implies the existence of such relationships. Thus, a classical economist's view of the interaction of money growth and price movements would require these series

Contact angle on heterogeneous surfaces: Weak heterogeneities

We investigate the equilibrium merging of a liquid-vapor interface and of a solid surface with a weak and random heterogeneity in the mechanical approximation. To keep a well-posed problem one must introduce an external length as the capillary length in a gravity field or the diameter of a liquid drop. The contact angle hysteresis is much smaller than the surface heterogeneity when this one is small and at random.

Progressing and oscillatory waves for hybrid synthesis of source-excited propagation in layered media

Summary. Progressing and oscillatory waves provide alternative descriptions of propagation in layered media. The former characterizes the wave motion in terms of direct and multiple wavefronts or rays, and the latter in terms of resonances or modes. Each description is convenient and physically incisive when it requires few elements but inconvenient and physically less transparent when it requires many elements. In the latter event, it is desirable to express many inconvenient elements collectively as fewer convenient ones. For a variety of propagation environments, this can be done by expressing rays collectively in terms of modes, or modes collectively in terms of rays. When performed selectively, there emerges a hybrid representation combining ray fields and modal fields in uniquely defined proportions. Rigorous for longitudinally invariant layers, the ray-mode equivalence can be extended approximately also to layered media with weak longitudinal heterogeneity. The theory, based on Poisson summation and on alternative treatments of wave spectra, is presented here and is illustrated for applications in electromagnetics, underwater acoustics and SH elastic motion.

A model for contact angle hysteresis

We discuss the behavior of a liquid partially wetting a solid surface, when the contact angle at equilibrium θ0 is small, but finite. The solid is assumed to be either flat, but chemically heterogeneous (this in turn modulating the interfacial tensions), or rough. For weak heterogeneities, we expect no hysteresis, but the contact line becomes wiggly. For stronger heterogeneities, we first discuss the behavior of the contact line in the presence of a single, localized defect, and show that there may exist two stable positions for the line, obtained by a simple graphic construction. Hysteresis shows up when the strength of the defect is above a certain threshold. Extending this to a dilute system of defects, we obtain formulas for the ‘‘advancing’’ and ‘‘receding’’ contact angles θa, θr, in terms of the distribution of defect strength and defect sharpness. These formulas might be tested by controlled contamination of a solid surface.

A derivation of the radiation transfer theory for random media

The wave propagation in a medium with randomly varying material parameters is considered. Starting from a quite general form of the Bethe-Salpeter equation for the two-point moment of the field, a spectral balance equation is derived. In a first step, a Wigner transformation is carried out which converts the two-point moment into a function depending on position, time, wave vector and frequency. Then, for wavelengths which are long compared to the correlation length of the medium, this function is split up into a relevant part and a background. Eliminating the background leads to the usual radiation transfer theory and provides us a general and concise expression for the effective scattering in terms of the effective operators involved in the Bethe-Salpeter equation. In the case of weak heterogeneity, the result reduces to those previously obtained.