Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization

We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.

The acoustic signature of fluid flow in complex porous media

Effective medium approximations for the frequency-dependent and complex-valued effective stiffness tensors of cracked/ porous rocks with multiple solid constituents are developed on the basis of the T-matrix approach (based on integral equation methods for quasi-static composites), the elastic - viscoelastic correspondence principle, and a unified treatment of the local and global flow mechanisms, which is consistent with the principle of fluid mass conservation. The main advantage of using the T-matrix approach, rather than the first-order approach of Eshelby or the second-order approach of Hudson, is that it produces physically plausible results even when the volume concentrations of inclusions or cavities are no longer small. The new formulae, which operates with an arbitrary homogeneous (anisotropic) reference medium and contains terms of all order in the volume concentrations of solid particles and communicating cavities, take explicitly account of inclusion shape and spatial distribution independently. We show analytically that an expansion of the T-matrix formulae to first order in the volume concentration of cavities (in agreement with the dilute estimate of Eshelby) has the correct dependence on the properties of the saturating fluid, in the sense that it is consistent with the Brown-Korringa relation, when the frequency is sufficiently low. We present numerical results for the (anisotropic) effective viscoelastic properties of a cracked permeable medium with finite storage porosity, indicating that the complete T-matrix formulae (including the higher-order terms) are generally consistent with the Brown-Korringa relation, at least if we assume the spatial distribution of cavities to be the same for all cavity pairs. We have found an efficient way to treat statistical correlations in the shapes and orientations of the communicating cavities, and also obtained a reasonable match between theoretical predictions (based on a dual porosity model for quartz-clay mixtures, involving relatively flat clay-related pores and more rounded quartz-related pores) and laboratory results for the ultrasonic velocity and attenuation spectra of a suite of typical reservoir rocks. (C) 2003 Elsevier B.V. All rights reserved.

Variation in dynamic elastic shear modulus of sandstone upon fluid saturation and substitution

Experimental acoustic measurements on sandstone rocks at both sonic and ultrasonic frequencies show that fluid saturation can cause a noticeable change in both the dynamic bulk and shear elastic moduli of sandstones. We observed that the change in dynamic shear modulus upon fluid saturation is highly dependent on the type of saturant, its viscosity, rock microstructure, and applied pressures. Frequency dispersion has some influence on dynamic elastic moduli too, but its effect is limited to the ultrasonic frequency ranges and above. We propose that viscous coupling, reduction in free surface energy, and, to a limited extent, frequency dispersion due to both local and global flow are the main mechanisms responsible for the change in dynamic shear elastic modulus upon fluid saturation and substitution, and we quantify influences.

Sonic to ultrasonic Q of sandstones and limestones: Laboratory measurements at in situ pressures

Laboratory measurements of the attenuation and velocity dispersion of compressional and shear waves at appropriate frequencies, pressures, and temperatures can aid interpretation of seismic and well-log surveys as well as indicate absorption mechanisms in rocks. Construction and calibration of resonant-bar equipment was used to measure velocities and attenuations of standing shear and extensional waves in copper-jacketed right cylinders of rocks (30 cm in length, 2.54 cm in diameter) in the sonic frequency range and at differential pressures up to 65 MPa. We also measured ultrasonic velocities and attenuations of compressional and shear waves in 50-mm-diameter samples of the rocks at identical pressures. Extensional-mode velocities determined from the resonant bar are systematically too low, yielding unreliable Poisson's ratios. Poisson's ratios determined from the ultrasonic data are frequency corrected and used to calculate the sonic-frequency compressional-wave velocities and attenuations from the shear- and extensional-mode data. We calculate the bulk-modulus loss. The accuracies of attenuation data (expressed as 1000/Q, where Q is the quality factor) are +/- 1 for compressional and shear waves at ultrasonic frequency, +/- 1 for shear waves, and +/- 3 for compressional waves at sonic frequency. Example sonic-frequency data show that the energy absorption in a limestone is small (Q(P) greater than 200 and stress independent) and is primarily due to poroelasticity, whereas that in the two sandstones is variable in magnitude (Q(P) ranges from less than 50 to greater than 300, at reservoir pressures) and arises from a combination of poroelasticity and viscoelasticity. A graph of compressional-wave attenuation versus compressional-wave velocity at reservoir pressures differentiates high-permeability (> 100 mD, 9.87 X 10(-14) m(2)) brine-saturated sandstones from low-permeability (< 100 mD, 9.87 X 10 (14) m(2)) sandstones and shales.

Electrification of volcanic plumes

Volcanic lightning, perhaps the most spectacular consequence of the electrification of volcanic plumes, has been implicated in the origin of life on Earth, and may also exist in other planetary atmospheres. Recent years have seen volcanic lightning detection used as part of a portfolio of developing techniques to monitor volcanic eruptions. Remote sensing measurement techniques have been used to monitor volcanic lightning, but surface observations of the atmospheric electric Potential Gradient (PG) and the charge carried on volcanic ash also show that many volcanic plumes, whilst not sufficiently electrified to produce lightning, have detectable electrification exceeding that of their surrounding environment. Electrification has only been observed associated with ash-rich explosive plumes, but there is little evidence that the composition of the ash is critical to its occurrence. Different conceptual theories for charge generation and separation in volcanic plumes have been developed to explain the disparate observations obtained, but the ash fragmentation mechanism appears to be a key parameter. It is unclear which mechanisms or combinations of electrification mechanisms dominate in different circumstances. Electrostatic forces play an important role in modulating the dry fallout of ash from a volcanic plume. Beyond the local electrification of plumes, the higher stratospheric particle concentrations following a large explosive eruption may affect the global atmospheric electrical circuit. It is possible that this might present another, if minor, way by which large volcanic eruptions affect global climate. The direct hazard of volcanic lightning to communities is generally low compared to other aspects of volcanic activity.

Solar influences on climate

Understanding the influence of solar variability on the Earth’s climate requires knowledge of solar variability, solar-terrestrial interactions and the mechanisms determining the response of the Earth’s climate system. We provide a summary of our current understanding in each of these three areas. Observations and mechanisms for the Sun's variability are described, including solar irradiance variations on both decadal and centennial timescales and their relation to galactic cosmic rays. Corresponding observations of variations of the Earth’s climate on associated timescales are described, including variations in ozone, temperatures, winds, clouds, precipitation and regional modes of variability such as the monsoons and the North Atlantic Oscillation. A discussion of the available solar and climate proxies is provided. Mechanisms proposed to explain these climate observations are described, including the effects of variations in solar irradiance and of charged particles. Finally, the contribution of solar variations to recent observations of global climate change are discussed.

Origin and structure of Devensian depressions at Letton, Herefordshire

Groups of circular to oval enclosed depressions in soft sediments of Pleistocene age are relatively common in north-west Europe. These features are normally interpreted as being either glacial or periglacial in origin. Where these features are developed in glacial sediments, a glacial (and specifically ‘kettle hole’) genesis is considered most likely. Some groups of features, however, have been re-interpreted as being periglacial in origin and are thought to be the remains of cryogenic mounds (former pingos or palsas/lithalsas). The problem at many sites, of course, is correct identification and previously this was often resolved through extensive trenching of the sediments. The use of geophysics in the form of electrical resistivity tomography and ground probing radar, however, can aid investigation and interpretation and is less invasive. A group of enclosed depressions in the Letton area of Herefordshire within the Last Glacial Maximum ice limit (Late Devensian) have been investigated in this way. The morphology and internal structure of the features and their existence in glaciolacustrine sediments of Late Devensian age strongly suggests that these depressions are kettle holes resulting from ice block discharge into a shallow lakes or lakes, and hence a glacial origin is supported. The lack of any ramparts surrounding the depressions (at the surface or any evidence of these at depth) and the fact that they do not overlap (‘mutually interfere’) indicates that they are not the remains of cryogenic mounds.

A novel Bayesian approach to drug design with simple and complex enzymes: Use with lens aldehyde dehydrogenase and the glyoxalase pathway

Purpose: Acquiring details of kinetic parameters of enzymes is crucial to biochemical understanding, drug development, and clinical diagnosis in ocular diseases. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. Methods: We have developed Bayesian utility functions to minimise kinetic parameter variance involving differentiation of model expressions and matrix inversion. These have been applied to the simple kinetics of the enzymes in the glyoxalase pathway (of importance in posttranslational modification of proteins in cataract), and the complex kinetics of lens aldehyde dehydrogenase (also of relevance to cataract). Results: Our successful application of Bayesian statistics has allowed us to identify a set of rules for designing optimum kinetic experiments iteratively. Most importantly, the distribution of points in the range is critical; it is not simply a matter of even or multiple increases. At least 60 % must be below the KM (or plural if more than one dissociation constant) and 40% above. This choice halves the variance found using a simple even spread across the range.With both the glyoxalase system and lens aldehyde dehydrogenase we have significantly improved the variance of kinetic parameter estimation while reducing the number and costs of experiments. Conclusions: We have developed an optimal and iterative method for selecting features of design such as substrate range, number of measurements and choice of intermediate points. Our novel approach minimises parameter error and costs, and maximises experimental efficiency. It is applicable to many areas of ocular drug design, including receptor-ligand binding and immunoglobulin binding, and should be an important tool in ocular drug discovery.

A role for Notch signaling in human corneal epithelial cell differentiation and proliferation

PURPOSE. To identify the role of Notch signaling in the human corneal epithelium. METHODS. Localization of Notch1, Notch2, Delta1, and Jagged1 in the human corneal epithelium was observed with the use of indirect immunofluorescence microscopy. Gene and protein expression of Notch receptors and ligands in human corneal epithelial cells was determined by RT-PCR and Western blot analysis, respectively. The effects of Notch inhibition (by {gamma}-secretase inhibition) and activation (by recombinant Jagged1) on epithelial cell proliferation (Ki67) and differentiation (CK3) were analyzed after Western blotting and immunocytochemistry. RESULTS. Immunofluorescent labeling localized Notch1 and Notch2 to suprabasal epithelial cell layers, whereas Delta1 and Jagged1 were observed throughout the corneal epithelium. Notch1, Notch2, Delta1, and Jagged1 genes and proteins were expressed in human corneal epithelial cells. {gamma}-Secretase inhibition resulted in decreased Notch1 and Notch2 expression, with an accompanying decrease in Ki67 and increased CK3 expression. The activation of Notch by Jagged1 resulted in the upregulation of active forms of Notch1 and 2 proteins (P < 0.05), with a concurrent increase in Ki67 (P < 0.05) and a decrease in CK3 (P < 0.05) expression. Interestingly, {gamma}-secretase inhibition in a three-dimensional, stratified corneal epithelium equivalent had no effect on Ki67 or CK3 expression. In contrast, Jagged1 activation resulted in decreased CK3 expression (P < 0.05), though neither Notch activation nor inhibition affected cell proliferation in the 3D tissue equivalent. CONCLUSIONS. Notch family members and ligands are expressed in the human corneal epithelium and appear to play pivotal roles in corneal epithelial cell differentiation.

Can misalignments in typical infants be used as a model for infantile esotropia?

PURPOSE. To investigate the nature of early ocular misalignments in human infants to determine whether they can provide insight into the etiology of esotropia and, in particular, to examine the correlates of misalignments. METHODS. A remote haploscopic photorefraction system was used to measure accommodation and vergence in 146 infants between 0 and 12 months of age. Infants underwent photorefraction immediately after watching a target moving between two of five viewing distances (25, 33, 50, 100, and 200 cm). In some instances, infants were tested in two conditions: both eyes open and one eye occluded. The resultant data were screened for instances of large misalignments. Data were assessed to determine whether accommodative, retinal disparity, or other cues were associated with the occurrence of misalignments. RESULTS. The results showed that there was no correlation between accommodative behavior and misalignments. Infants were more likely to show misalignments when retinal disparity cues were removed through occlusion. They were also more likely to show misalignments immediately after the target moved from a near to a far position in comparison to far-to-near target movement. DISCUSSION. The data suggest that the prevalence of misalignments in infants of 2 to 3 months of age is decreased by the addition of retinal disparity cues to the stimulus. In addition, target movement away from the infant increases the prevalence of misalignments. These data are compatible with the notion that misalignment are caused by poor sensitivity to targets moving away from the infant and support the theory that some forms of strabismus could be related to failure in a system that is sensitive to the direction of motion.