An exact particle method for scalar conservation laws and its application to stiff reaction kinetics

An "exact" method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is as accurate as the applied ODE solver. Furthermore, the method is extended to stiff balance laws. A special correction approach yields a method that evolves detonation waves at correct velocities, without resolving their internal dynamics. The particle approach is compared to a classical finite volume method in terms of numerical accuracy, both for conservation laws and for an application in reaction kinetics.Comment: 14 page, 7 figures, presented in the Fifth International Workshop on Meshfree Methods for Partial Differential Equation

An optimized fractional grey model based on weighted least squares and its application

The fractional grey model is an effective tool for modeling small samples of data. Due to its essential characteristics of mathematical modeling, it has attracted considerable interest from scholars. A number of compelling methods have been proposed by many scholars in order to improve the accuracy and extend the scope of the application of the model. Examples include initial value optimization, order optimization, etc. The weighted least squares approach is used in this paper in order to enhance the model's accuracy. The first step in this study is to develop a novel fractional prediction model based on weighted least squares operators. Thereafter, the accumulative order of the proposed model is determined, and the stability of the optimization algorithm is assessed. Lastly, three actual cases are presented to verify the validity of the model, and the error variance of the model is further explored. Based on the results, the proposed model is more accurate than the comparison models, and it can be applied to real-world situations

Two striking head-Tail galaxies in the galaxy cluster IIZW108: Insights into transition to turbulence, magnetic fields, and particle re-Acceleration

We present deep Jansky Very Large Array observations at 1.4 and 2.7 GHz (full polarization), as well as optical OmegaWINGS/WINGS and X-ray observations of two extended radio galaxies in the IIZW108 galaxy cluster at z = 0.04889. They show a bent tail morphology in agreement with a radio lobed galaxy falling into the cluster potential. Both galaxies are found to possess properties comparable with narrow-Angle tail galaxies in the literature even though they are part of a low mass cluster. We find a spectral index steepening and an increase in fractional polarization through the galaxy jets and an ordered magnetic field component mostly aligned with the jet direction. This is likely caused by either shear due to the velocity difference of the intracluster medium and the jet fluid and/or magnetic draping of the intracluster medium across the galaxy jets. We find clear evidence that one source is showing two active galactic nuclei (AGN) outbursts from which we expect the AGN has never turned off completely. We show that pure standard electron cooling cannot explain the jet length. We demonstrate therefore that these galaxies can be used as a laboratory to study gentle re-Acceleration of relativistic electrons in galaxy jets via transition from laminar to turbulent motion

Physics of environmental flows interacting with obstacles

2017 Fall.Includes bibliographical references.The effects of natural and man-made obstacles on their surrounding environmental flows such as rivers, lakes, estuaries, oceans and the atmosphere has been the subject of numerous studies for many decades. The flow-obstacle interaction can lead to the generation of turbulence which determines local flow dynamics and even large-scale circulations. The characteristic chaotic and enhanced mixing properties of turbulence in conjunction with other environmental conditions such as the clustering of multiple obstacles and density variations raise a number of interesting problems pertaining to both fundamental fluid dynamics and practical engineering applications. Insights into these processes is of fundamental importance for many applications, such as determining the fate of deep water-masses formed in the abyssal ocean, optimizing the productivity and environmental impact of marine farms, predicting the amount of power that a group of turbines can generate, estimating carbon dioxide exchange between the forests and the atmosphere or modeling flood routing in vegetated rivers. The main aim of this dissertation is to use high-resolution numerical simulations to study environmental flows of different forcing mechanisms interacting with obstacles of different geometries. The objectives are multi-fold: (i) To gain insights into the three-dimensional hydrodynamics of constant-density flows interacting with a finite canopy; (ii) To develop an unambiguous geometrical framework for characterizing canopy planar geometry; (iii) To explore the fundamental differences in the flow dynamics between porous canopies and their solid counterpart; and (iv) To investigate the effect of ambient density stratification on flow-obstacle interactions. The first part of this dissertation focuses on the mean three-dimensional hydrodynamics in the vicinity of a suspended cylindrical canopy patch with a bulk diameter of D. The patch was made of Nc constituent solid circular cylinders with h in height and d in diameter, and was suspended in deep water (H/h ≫ 1 where H is the total flow depth). After the validation against published experimental data, large eddy simulations (LES) were conducted to study the effects of patch density (0.16 ≤ φ = Nc(d/D)2 ≤ 1, by varying Nc) and patch aspect ratio (0.25 ≤ AR = h/D ≤ 1, by varying h) on the near-field flow properties. It was observed qualitatively and quantitatively that an increase in either φ or AR decreases bleeding velocity along the streamwise direction but increases bleeding velocities along the lateral and vertical directions, respectively. A close examination at the flow inside the patch reveals that despite the similar dependence of vertical bleeding on φ and AR, the underlying physics are different. However, in contrast to the bleeding velocity, a flow-rate budget shows that the proportion of the vertical bleeding flow leaving the patch with respect to the total flow entering the patch (i.e. relative vertical bleeding) decreases with increasing AR. Finally, the interlinks between patch geometry, flow bleeding and flow diversion are identified: the patch influences the flow diversion not only directly by its real geometrical dimensions, but also indirectly by modifying flow bleeding which enlarges the size of the near-wake. While loss of flow penetrating the patch increases monotonically with increasing φ, its partition into flow diversion around and beneath the patch shows a non-monotonic dependence, highlighting the fundamental differences in the flow dynamics between porous patches and their solid counterpart. Next, the propagation of full-depth lock-exchange bottom gravity currents over a submerged array of circular cylinders is investigated using laboratory experiments and LES. Firstly, to investigate the front velocity of gravity currents across the whole range of array density φ, the array is densified from a flat-bed (φ = 0) towards a solid-slab (φ = 1) under a particular submergence ratio H/h, where H is the flow depth and h is the array height. The time-averaged front velocity in the slumping phase of the gravity current is found to first decrease and then increase with increasing φ. Next, a new geometrical framework consisting of a streamwise array density μx = d/sx and a spanwise array density μy = d/sy is proposed to account for organized but nonequidistant arrays (μx 6 ≠ μy), where sx and sy are the streamwise and spanwise cylinder spacings, respectively, and d is the cylinder diameter. It is argued that this two-dimensional parameter space can provide a more quantitative and unambiguous description of the current-array interaction compared with the array density given by φ = (π/4) μxμy. Both in-line and staggered arrays are investigated. Four dynamically different flow regimes are identified: (i) through-flow propagating in the array interior subject to individual cylinder wakes (μx: small for in-line array and arbitrary for staggered array; μy: small); (ii) over-flow propagating on the top of the array subject to vertical convective instability (μx: large; μy: large); (iii) plunging-flow climbing sparse close-to-impermeable rows of cylinders with minor streamwise intrusion (μx: small; μy: large); and (iv) skimming-flow channelized by an in-line array into several sub-currents with strong wake sheltering (μx: large; μy: small).Finally, the flow dynamics of intrusive gravity currents past a bottom-mounted obstacle in a continuously stratified ambient was numerically investigated, highlighting the effect of ambient stratification which is not considered in the previous sections. The propagation dynamics of a classic intrusive gravity current was first simulated in order to validate the numerical model with previous laboratory experiments. A bottom-mounted obstacle with a varying non-dimensional height of ˜D = D/H, where D is the obstacle height and H is the total flow depth, was then added to the problem in order to study the downstream flow pattern of the intrusive gravity current. For short obstacles, the intrusion re-established itself downstream without much distortion. However, for tall obstacles, the downstream flow was found to be a joint effect of horizontal advection, overshoot-spring back phenomenon, and associated Kelvin-Helmholtz instabilities. Analysis of the numerical results show that the relationship between the downstream propagation speed and the obstacle height can be subdivided into three regimes: a retarding regime (˜D ≈ 0 ∼ 0.3), an impounding regime (˜D ≈ 0.3 ∼ 0.6), and a choking regime (˜D ≈ 0.6 ∼ 1.0).Overall, at a fundamental level, this dissertation aims to contribute to an improved understanding of the physics associated with environmental flows interacting with obstacles. Moreover, the results from this research are expected to facilitate better parameterizations of this important class of flows

Generating artificial light curves: Revisited and updated

The production of artificial light curves with known statistical and variability properties is of great importance in astrophysics. Consolidating the confidence levels during cross-correlation studies, understanding the artefacts induced by sampling irregularities, establishing detection limits for future observatories are just some of the applications of simulated data sets. Currently, the widely used methodology of amplitude and phase randomisation is able to produce artificial light curves which have a given underlying power spectral density (PSD) but which are strictly Gaussian distributed. This restriction is a significant limitation, since the majority of the light curves e.g. active galactic nuclei, X-ray binaries, gamma-ray bursts show strong deviations from Gaussianity exhibiting `burst-like' events in their light curves yielding long-tailed probability distribution functions (PDFs). In this study we propose a simple method which is able to precisely reproduce light curves which match both the PSD and the PDF of either an observed light curve or a theoretical model. The PDF can be representative of either the parent distribution or the actual distribution of the observed data, depending on the study to be conducted for a given source. The final artificial light curves contain all of the statistical and variability properties of the observed source or theoretical model i.e. same PDF and PSD, respectively. Within the framework of Reproducible Research, the code, together with the illustrative example used in this manuscript, are both made publicly available in the form of an interactive Mathematica notebook.Comment: Accepted for publication in MNRAS. The paper is 23 pages long and contains 21 figures and 2 tables. The Mathematica notebook can be found in the web as part of this paper (Online Material) or at http://www.astro.soton.ac.uk/~de1e08/ArtificialLightCurves

On the temporal stability of the coda of ambient noise correlations

We analyze the sensitivity of cross correlations to the anisotropy of the incident field in the context of seismic ambient noise monitoring of small velocity changes. Numerical simulations of elastic waves are performed in a 2D scattering plate with a focus on the comparative character of the direct and coda waves in the cross-correlation. We show that coda waves reconstructed from cross-correlations are far more robust than direct waves in the presence of azimuthal anisotropy of the incident field. We observe similar behavior with real data recorded on Erebus volcano, where a database of impulsive icequakes is used to simulate an anisotropic source field. We propose a simplified approach to evaluate the sensitivity of scattered waves to the anisotropy of the incoming noise field. We rely on previous results obtained for direct waves and on intrinsic properties of scattered waves to predict the errors produced by strong source anisotropy with numerical experiments. These results also yield realistic values for monitoring the accuracy to be expected with real data at crustal scales. Our analysis shows that high-precision noise-based monitoring could be performed with coda waves in the correlation functions, even in the presence of variations in the azimuthal distribution of the ambient noise field

Prediction of petro-physical properties for carbonates

This thesis is concerned with the inversion of lattice pore-network model parameters of carbonate rocks using only the capillary pressure, and then the use of the inverted parameters to predict the water-flooding relative permeabilities of the carbonate rocks. Background: There has been a tendency to claim that pore-network modelling using three-dimensional micro-computed tomography or 3D mathematically created images can predict imbibition relative permeabilities for wettabilities other than strongly water/oil-wetting. This is based on the flexibility for matching data, which is a weakness of pore-network modelling. The method proposed in this thesis is important because a large percentage of the porosity in carbonates is microporosity. Conclusions: We applied stochastic inversion of lattice pore-network model parameters using Hamiltonian Dynamics (Hamiltonian Monte Carlo) to three carbonate rock samples and we predicted water-flooding relative permeabilities with good accuracy by using as constraint only routinely obtained data, such as mercury intrusion capillary pressure (MICP) and oil/water capillary pressure. We found that there is a strong correlation between the amount of microporosity and the volume exponent parameter. This suggests that when microporosity is ignored, the volume exponent will tend to be systematically strongly underestimated. HMC found large variability in wettability that causes mid-sized pores to be invaded at the same level of pressure as larger pores. The coexistence of these events reduces the tendency for preferential flow through large pores, resulting in more uniform flow at the pore scale compared with the case in which flow is restricted only to large pores. Mid-sized pores have an important effect on the connectivity because they could have higher contact angles than larger pores. Therefore, they do not spontaneously imbibe and shield larger pores, improving water-flooding displacement. The wettability of micropores could better explain the gentle curvature of the imbibition water relative permeability compared with the generally assumed mixed-wet large wettability model. The importance of the maximum and minimum observed capillary pressure is directly connected to accounting for the full pore-size distribution. Thus, the common assumption that microporosity can be ignored is unsatisfactory. The ranges of advancing contact angles obtained from the HMC inversion were wider than the ranges of apparent advancing contact angles obtained with analytical determinations in previous studies, and in one case our results were contradictory to the analytical determination. It follows that variability in advancing and receding contact angles is not reflected in the apparent contact angle data outside porous media. Apparent contact angle data outside porous media cannot completely characterise the wettability in porenetwork models because the data does not capture the contact angle variability in porous media. The existence of wetting films depends on the maximum capillary pressure during drainage, and thus wettability alteration during ageing. Our results suggest that matching both connate water at the maximum drainage capillary pressure before ageing and matching residual oil at the minimum imbibition capillary pressure leads to better estimation of the advancing and receding variability in the contact angles

VOID STRUCTURE, COLLOID AND TRACER TRANSPORT PROPERTIES OF STRATIFIED POROUS MEDIA

The characterisation of the properties of porous materials is of great importance in the effective management of natural and manmade systems. A sophisticated network model, 'Pore-Cor', of some of these properties has been previously developed. The present study has significantly extended the scope of the model's predictive capabilities. Flow and transport behaviour was examined in laboratory sand columns of various depths. These experiments examined unsaturated flow of water and conservative solute tracer transport through homogeneous sand samples. Flow through these was not homogeneous or repeatable. Experimental observations found that this may have been due to subtle random variations in packing, and the network model was shown to be able to simulate these. Solute transport of bromide was studied, applied both uniformly and from a point source. Both scenarios were modelled using a convection-dispersion equation, and it was demonstrated that the lateral component of such transport was highly significant. It was shown how convection-dispersion equation predictions of uniformly applied tracer transport might be improved by the application of the network model and a method for improving predicted lateral solute transport was outlined. It has been shown that levels of correlation in the distribution of differently sized voids within porous material may be responsible for large variations in permeability. This can make accurate modelling of permeability very difficult. A technique was developed for assessing the degree and nature of such correlations. The new method was tested on a variety of artificial and real samples and demonstrated to provide a quantitative assessment of such correlations. A method by which this could be used to improve network model simulations of materials possessing such correlation was described