Flow regime transition criteria for two-phase flow at reduced gravity conditions

Flow regime transition criteria are of practical importance for two-phase flow analyses at reduced gravity conditions. Here, flow regime transition criteria which take the friction pressure loss effect into account were studied in detail. Criteria at reduced gravity conditions were developed by extending an existing model with various experimental datasets taken at microgravity conditions showed satisfactory agreement. Sample computations of the model were performed at various gravity conditions, such as 0.196, 1.62, 3.71, and 9.81 m/s2 corresponding to micro-gravity and lunar, Martian and Earth surface gravity, respectively. It was found that the effect of gravity on bubbly-slug and slug-annular (churn) transitions in a two-phase flow system was more pronounced at low liquid flow conditions, whereas the gravity effect could be ignored at high mixture volumetric flux conditions. While for the annular flow transitions due to flow reversal and onset of dropset entrainment, higher superficial gas velocity was obtained at higher gravity level.

Morphology of osteocyte cells in normal and hyper-gravity

Osteocyte cells are the most abundant cells in human bone tissue. Due to their unique morphology and location, osteocyte cells are thought to act as regulators in the bone remodelling process, and are believed to play an important role in astronauts’ bone mass loss after long-term space missions. There is increasing evidence showing that an osteocyte’s functions are highly affected by its morphology. However, changes in an osteocyte’s morphology under an altered gravity environment are still not well documented. Several in vitro studies have been recently conducted to investigate the morphological response of osteocyte cells to the microgravity environment, where osteocyte cells were cultured on a two-dimensional flat surface for at least 24 hours before microgravity experiments. Morphology changes of osteocyte cells in microgravity were then studied by comparing the cell area to 1g control cells. However, osteocyte cells found in vivo are with a more 3D morphology, and both cell body and dendritic processes are found sensitive to mechanical loadings. A round shape osteocyte’s cells support a less stiff cytoskeleton and are more sensitive to mechanical stimulations compared with flat cellular morphology. Thus, the relative flat and spread shape of isolated osteocytes in 2D culture may greatly hamper their sensitivity to a mechanical stimulus, and the lack of knowledge on the osteocyte’s morphological characteristics in culture may lead to subjective and noncomprehensive conclusions of how altered gravity impacts on an osteocyte’s morphology. Through this work empirical models were developed to quantitatively predicate the changes of morphology in osteocyte cell lines (MLO-Y4) in culture, and the response of osteocyte cells, which are relatively round in shape, to hyper-gravity stimulation has also been investigated. The morphology changes of MLO-Y4 cells in culture were quantified by measuring cell area and three dimensionless shape features including aspect ratio, circularity and solidity by using widely accepted image analysis software (ImageJTM). MLO-Y4 cells were cultured at low density (5×103 per well) and the changes in morphology were recorded over 10 hours. Based on the data obtained from the imaging analysis, empirical models were developed using the non-linear regression method. The developed empirical models accurately predict the morphology of MLO-Y4 cells for different culture times and can, therefore, be used as a reference model for analysing MLO-Y4 cell morphology changes within various biological/mechanical studies, as necessary. The morphological response of MLO-Y4 cells with a relatively round morphology to hyper-gravity environment has been investigated using a centrifuge. After 2 hours culture, MLO-Y4 cells were exposed to 20g for 30mins. Changes in the morphology of MLO-Y4 cells are quantitatively analysed by measuring the average value of cell area and dimensionless shape factors such as aspect ratio, solidity and circularity. In this study, no significant morphology changes were detected in MLO-Y4 cells under a hyper-gravity environment (20g for 30 mins) compared with 1g control cells.

A fuzzy dynamic flood routing model for natural channels

A fuzzy dynamic flood routing model (FDFRM) for natural channels is presented, wherein the flood wave can be approximated to a monoclinal wave. This study is based on modification of an earlier published work by the same authors, where the nature of the wave was of gravity type. Momentum equation of the dynamic wave model is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. Hence, the FDFRM gets rid of the assumptions associated with the momentum equation. Also, it overcomes the necessity of calculating friction slope (S-f) in flood routing and hence the associated uncertainties are eliminated. The fuzzy rule based model is developed on an equation for wave velocity, which is obtained in terms of discontinuities in the gradient of flow parameters. The channel reach is divided into a number of approximately uniform sub-reaches. Training set required for development of the fuzzy rule based model for each sub-reach is obtained from discharge-area relationship at its mean section. For highly heterogeneous sub-reaches, optimized fuzzy rule based models are obtained by means of a neuro-fuzzy algorithm. For demonstration, the FDFRM is applied to flood routing problems in a fictitious channel with single uniform reach, in a fictitious channel with two uniform sub-reaches and also in a natural channel with a number of approximately uniform sub-reaches. It is observed that in cases of the fictitious channels, the FDFRM outputs match well with those of an implicit numerical model (INM), which solves the dynamic wave equations using an implicit numerical scheme. For the natural channel, the FDFRM Outputs are comparable to those of the HEC-RAS model.

Singularity-free cosmology: A simple model

The nonminimal coupling of a self-interacting complex scalar field with gravity is studied. For a Robertson-Walker open universe the stable solutions of the scalar-field equations are time dependent. As a result of this, a novel spontaneous symmetry breaking occurs which leads to a varying effective gravitational coupling coefficient. It is found that the coupling coefficient changes sign below a critical ‘‘radius’’ of the Universe implying the appearance of repulsive gravity. The occurrence of the repulsive interaction at an early epoch facilitates singularity avoidance. The model also provides a solution to the horizon problem.

Slow m=1 instabilities of softened gravity Keplerian discs

We present the simplest model that permits a largely analytical exploration of the m =1 counter-rotating instability in a `hot' nearly Keplerian disc of collisionless self-gravitating matter. The model consists of a two-component softened gravity disc, whose linear modes are analysed using the Wentzel-Kramers-Brillouin approximation. The modes are slow in the sense that their (complex) frequency is smaller than the Keplerian orbital frequency by a factor which is of order the ratio of the disc mass to the mass of the central object. Very simple analytical expressions are derived for the precession frequencies and growth rates of local modes; it is shown that a nearly Keplerian discm must be unrealistically hot to avoid an overstability. Global modes are constructed for the case of zero net rotation.

A possible model for fifth force

Recent reanalysis of the data of the Eötvös experiment suggested the existence of a new force. We show that a negative energy massive scalar field minimally coupled to gravity in a background Schwarzschild metric naturally leads to a potential which can explain the small anomalous effect in the Eötvös experiment.

Steady compressible flow of granular materials through a wedge-shaped hopper: The smooth wall, radial gravity problem

A continuum model based on the critical state theory of soil mechanics is used to generate stress and density profiles, and to compute discharge velocities for the plane flow of cohesionless materials. Two types of yield loci are employed, namely, a yield locus with a corner, and a smooth yield locus. The yield locus with a corner leads to computational difficulties. For the smooth yield locus, results are found to be relatively insensitive to the shape of the yield locus, the location of the upper traction-free surface and the density specified on this surface. This insensitivity arises from the existence of asymptotic stress and density fields, to which the solution tends to converge on moving down the hopper. Numerical and approximate analytical solutions are obtained for these fields and the latter is used to derive an expression for the discharge velocity. This relation predicts discharge velocities to within 13% of the exact (numerical) values. While the assumption of incompressibility has been frequently used in the literature, it is shown here that in some cases, this leads to discharge velocities which are significantly higher than those obtained by the incorporation of density variation.

Exact traveling- wave solution for model geophysical systems

Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.

A model for static foam drainage

A model for static foam drainage, based on the pentagonal dodecahedral shape of bubbles, that takes into account the surface mobility of both films and Plateau border walls has been developed. The model divides the Plateau borders into nearly horizontal and nearly vertical categories and assigns different roles to them. The films are assumed to drain into all the adjacent Plateau borders equally. The horizontal Plateau borders are assumed to receive liquid from films and drain into vertical Plateau borders, which in turn form the main component for gravity drainage. The model yields the liquid holdup values for films, horizontal Plateau borders and vertical Plateau borders as functions of height and time. The model has been tested on static foams whose cumulative drainage was measured as a function of time. The experimental data on the effect of foam height, initial holdup, surface viscosity, etc. can be explained by the model quantitatively.

Rheometry of granular materials in cylindrical Couette cells: Anomalous stress caused by gravity and shear

The cylindrical Couette device is commonly employed to study the rheology of fluids, but seldom used for dense granular materials. Plasticity theories used for granular flows predict a stress field that is independent of the shear rate, but otherwise similar to that in fluids. In this paper we report detailed measurements of the stress as a function of depth, and show that the stress profile differs fundamentally from that of fluids, from the predictions of plasticity theories, and from intuitive expectation. In the static state, a part of the weight of the material is transferred to the walls by a downward vertical shear stress, bringing about the well-known Janssen saturation of the stress in vertical columns. When the material is sheared, the vertical shear stress changes sign, and the magnitudes of all components of the stress rise rapidly with depth. These qualitative features are preserved over a range of the Couette gap and shear rate, for smooth and rough walls and two model granular materials. To explain the anomalous rheological response, we consider some hypotheses that seem plausibleapriori, but showthat none survive after careful analysis of the experimental observations. We argue that the anomalous stress is due to an anisotropic fabric caused by the combined actions of gravity, shear, and frictional walls, for which we present indirect evidence from our experiments. A general theoretical framework for anisotropic plasticity is then presented. The detailed mechanics of how an anisotropic fabric is brought about by the above-mentioned factors is not clear, and promises to be a challenging problem for future investigations. (C) 2013 AIP Publishing LLC.

Differential evolution based 3-D guidance law for a realistic interceptor model

This paper presents a novel, soft computing based solution to a complex optimal control or dynamic optimization problem that requires the solution to be available in real-time. The complexities in this problem of optimal guidance of interceptors launched with high initial heading errors include the more involved physics of a three dimensional missile-target engagement, and those posed by the assumption of a realistic dynamic model such as time-varying missile speed, thrust, drag and mass, besides gravity, and upper bound on the lateral acceleration. The classic, pure proportional navigation law is augmented with a polynomial function of the heading error, and the values of the coefficients of the polynomial are determined using differential evolution (DE). The performance of the proposed DE enhanced guidance law is compared against the existing conventional laws in the literature, on the criteria of time and energy optimality, peak lateral acceleration demanded, terminal speed and robustness to unanticipated target maneuvers, to illustrate the superiority of the proposed law. (C) 2013 Elsevier B. V. All rights reserved.

Nonlinear gravity-wave interactions in stratified turbulence

To investigate the dynamics of gravity waves in stratified Boussinesq flows, a model is derived that consists of all three-gravity-wave-mode interactions (the GGG model), excluding interactions involving the vortical mode. The GGG model is a natural extension of weak turbulence theory that accounts for exact three-gravity-wave resonances. The model is examined numerically by means of random, large-scale, high-frequency forcing. An immediate observation is a robust growth of the so-called vertically sheared horizontal flow (VSHF). In addition, there is a forward transfer of energy and equilibration of the nonzero-frequency (sometimes called ``fast'') gravity-wave modes. These results show that gravity-wave-mode interactions by themselves are capable of systematic interscale energy transfer in a stratified fluid. Comparing numerical simulations of the GGG model and the full Boussinesq system, for the range of Froude numbers (Fr) considered (0.05 a parts per thousand currency sign Fr a parts per thousand currency sign 1), in both systems the VSHF is hardest to resolve. When adequately resolved, VSHF growth is more vigorous in the GGG model. Furthermore, a VSHF is observed to form in milder stratification scenarios in the GGG model than the full Boussinesq system. Finally, fully three-dimensional nonzero-frequency gravity-wave modes equilibrate in both systems and their scaling with vertical wavenumber follows similar power-laws. The slopes of the power-laws obtained depend on Fr and approach -2 (from above) at Fr = 0.05, which is the strongest stratification that can be properly resolved with our computational resources.

Combining data sets of satellite-retrieved products for basin-scale water balance study: 2. Evaluation on the Mississippi Basin and closure correction model

In this study, we applied the integration methodology developed in the companion paper by Aires (2014) by using real satellite observations over the Mississippi Basin. The methodology provides basin-scale estimates of the four water budget components (precipitation P, evapotranspiration E, water storage change Delta S, and runoff R) in a two-step process: the Simple Weighting (SW) integration and a Postprocessing Filtering (PF) that imposes the water budget closure. A comparison with in situ observations of P and E demonstrated that PF improved the estimation of both components. A Closure Correction Model (CCM) has been derived from the integrated product (SW+PF) that allows to correct each observation data set independently, unlike the SW+PF method which requires simultaneous estimates of the four components. The CCM allows to standardize the various data sets for each component and highly decrease the budget residual (P - E - Delta S - R). As a direct application, the CCM was combined with the water budget equation to reconstruct missing values in any component. Results of a Monte Carlo experiment with synthetic gaps demonstrated the good performances of the method, except for the runoff data that has a variability of the same order of magnitude as the budget residual. Similarly, we proposed a reconstruction of Delta S between 1990 and 2002 where no Gravity Recovery and Climate Experiment data are available. Unlike most of the studies dealing with the water budget closure at the basin scale, only satellite observations and in situ runoff measurements are used. Consequently, the integrated data sets are model independent and can be used for model calibration or validation.

The cold mode: a phenomenological model for the evolution of density perturbations in the intracluster medium

Cool cluster cores are in global thermal equilibrium but are locally thermally unstable. We study a non-linear phenomenological model for the evolution of density perturbations in the intracluster medium (ICM) due to local thermal instability and gravity. We have analysed and extended a model for the evolution of an overdense blob in the ICM. We find two regimes in which the overdense blobs can cool to thermally stable low temperatures. One for large t(cool)/t(ff) (t(cool) is the cooling time and t(ff) is the free-fall time), where a large initial overdensity is required for thermal runaway to occur; this is the regime which was previously analysed in detail. We discover a second regime for t(cool)/t(ff) less than or similar to 1 (in agreement with Cartesian simulations of local thermal instability in an external gravitational field), where runaway cooling happens for arbitrarily small amplitudes. Numerical simulations have shown that cold gas condenses out more easily in a spherical geometry. We extend the analysis to include geometrical compression in weakly stratified atmospheres such as the ICM. With a single parameter, analogous to the mixing length, we are able to reproduce the results from numerical simulations; namely, small density perturbations lead to the condensation of extended cold filaments only if t(cool)/t(ff) less than or similar to 10.

Modified Einstein's gravity as a possible missing link between sub- and super-Chandrasekhar type Ia supernovae

We explore the effect of modification to Einstein's gravity in white dwarfs for the first time in the literature, to the best of our knowledge. This leads to significantly sub- and super-Chandrasekhar limiting masses of white dwarfs, determined by a single model parameter. On the other hand, type Ia supernovae (SNeIa), a key to unravel the evolutionary history of the universe, are believed to be triggered in white dwarfs having mass close to the Chandrasekhar limit. However, observations of several peculiar, under- and over-luminous SNeIa argue for exploding masses widely different from this limit. We argue that explosions of the modified gravity induced sub- and super-Chandrasekhar limiting mass white dwarfs result in under- and over-luminous SNeIa respectively, thus unifying these two apparently disjoint sub-classes and, hence, serving as a missing link. Our discovery raises two fundamental questions. Is the Chandrasekhar limit unique? Is Einstein's gravity the ultimate theory for understanding astronomical phenomena? Both the answers appear to be no!