Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: This research study investigates the influence of specimen geometry and grading curve, on the performance of a typical South African unbound granular material. The experimental design incorporates three grading curves to evaluate the influence of grading. In addition, to evaluate the influence of specimen geometry, two specimen sizes were included into the experimental design. Laboratory testing consisted of monotonic tri-axial tests to evaluate the shear performance (Cohesion and Friction Angle) and more complex short duration dynamic tri-axial tests to evaluate the load spreading ability/stiffness (Resilient Modulus) of the selected materials. In order to achieve the objectives of this study, a large tri-axial apparatus was needed that could accommodate specimens as large as 300mm ϕ * 600mm high. This would allow a full grading of large aggregate (up to 50mm particle size) to be accurately evaluated. Further development and commissioning of such a large triaxial apparatus therefore formed part of this study. The representative parent material selected for testing consisted of a G2 graded crushed Hornfels stone. The material was dried and sieved into fractions where after it was carefully reconstituted to allow for accurate control of specimen grading during specimen preparation. The three grading curves consisted of two adjusted grading curves (referred to as S19 and G19C), adjusted from the full G2 grading, and the full G2 grading itself (referred to as the Full grading curve). Material property tests, Sieve Analysis, Bulk Relative Density (BRD) and Optimum Moisture Content (OMC) tests were performed to gain an understanding of the material characteristics. Moisture-Density relationship curves were developed to identify a common Moisture Content that, for all three grading curves, would yield a common Dry Density. A Moisture Content of 4.7% was identified that would yield a Dry Density of 2340 kg/m3 for all three grading curves. This density could be achieved for both sizes of specimen preparation apparatuses without damaging material particles. Specimens were compacted using the representative vibratory hammer compaction method, sealed and left for 24 hours to allow redistribution of moisture and initial development of Cohesion. The shear parameters (Cohesion and Friction Angle) were investigated through monotonic tri-axial testing. It was found that Cohesion and Friction Angle are influenced by both grading curve and specimen geometry. Cohesion was found to reduce as the coarseness of the material grading increased (i.e. finer S19 grading yielded higher Cohesion than its coarser G19C counterpart) and the Friction Angle was found to increase with increase coarseness (i.e. finer S19 grading yielded lower Friction Angles when compared to the G19C grading). The influence of specimen geometry was also investigated. It was observed than Cohesion decreased with an increase in specimen size. Friction Angle on the other hand was found to increase with increased specimen size. From dynamic tri-axial test results, it was observed that the Resilient Modulus is influenced by both specimen geometry and grading curve. The influence of specimen geometry however is complex and no constant trend throughout the grading curves tested could be identified. Grading curve however was found to increase the Resilient Modulus for coarser gradings (i.e. coarser G19C vs finer S19). Increased large particle-to-particle contact area yields higher friction within the material specimen, resulting in lower strains induced by higher stresses, i.e. higher Resilient Modulus. It was shown, for both monotonic and dynamic tri-axial tests, that the coarser G19C grading curve yields more representative results to that of the Full grading curve when compared to the finer S19 grading. This was observed for shear and resilient performance properties. Additionally, a simple design case study yields similar trends. In conclusion, material characterisation plays an important role in the design of unbound granular materials (UGM’s). Current laboratory characterisation techniques however used adjusted gradings to limit the effects stemming from the ratio between specimen diameter and maximum particle size. This research has shown that some of the current practices do not best represent the true in-situ grading. It has been shown that both grading curve and specimen geometry influence the performance of UGM’s which, in turn, influences the design of a pavement structure. Therefore, accurate modelling of the true in-situ grading, through testing apparatuses capable of accommodating in-situ gradings, is required. / AFRIKAANSE OPSOMMING: Hierdie navorsingsstudie evalueer die invloed van proefstukgeometrie en gradering, op die gedragseienskappe van ‘n tipiese Suid Afrikaanse ongebinde granulêre aggregaat. Om die invloed van gradering te evalueer, is ‘n eksperimentele ontwerp ontwikkel wat drie materiaal graderings insluit. Verder, om die invloed van proefstukgeometrie te evalueer, is twee proefstukgroottes toegevoeg tot die eksperimentele ontwerp. Monotoniese drie-assige toetse is uitgevoer om die skuifsterkte (Kohesie en Wrywingshoek) van die materiaal te ondersoek. Addisioneel is die styfheid (Veerkragmodulus) van die materiaal ondersoek deur dinamiese drieassige toetse. Om die doelwitte van hierdie studie te bereik was ‘n groot skaalse die-assige toets apparaat benodig wat groot, 300mm ϕ * 600mm hoogte, proefstukke kan akkommodeer. So ‘n apparaat laat toe dat die volle gradering van aggregaat (tot en met 50mm korrels) akkuraat geëvalueer kan word. Daarom vorm die ontwikkeling en opstelling van so ‘n apparaat deel van hierdie studie. Die tipiese Hornfels gebreekte klip, met ‘n G2 gradering, wat ondersoek is, was gedroog en in verskeie fraksies gesif om die akkuraatheid van proefstuk voorbereiding te beheer. Die drie graderings bestaan uit twee aangepaste graderings (S19 en G19C gradering skale), aangepas vanaf die volle G2 gradering, en die vol G2 gradering homself (verwys na as die “Full” gradering skaal). Materiaal gedragstoetse, Sif Analises, Nat Gekompakteerde Relatiewe Digtheid (BRD) en Optimum Vog Inhoud (OVI) toetse, was uitgevoer om die materiaal eienskappe te ondersoek. Om ‘n gemeenskaplike Vog Inhoud en Droë Digtheid, wat vir al drie graderings geld, te vind, is Vog-Digtheid verhoudingskurwes ontwikkel. Vanaf die kurwes is identifiseer dat ‘n Vog Inhoud van 4.7% ‘n Droë Digtheid van 2340 kg/m3 vir al drie graderings sal lewer. Vibrasie kompaksie is toegepas om albei skale van proefstukke te kompakteer waarna die proefstukke vir 24 uur geseel is om vogverspreiding en ontwikkeling van Kohesie toe te laat. Monotoniese drie-assige toetse is uitgevoer om die skuifsterkte parameters (Kohesie en Wrywingshoek) te ondersoek. Die resultate het gewys dat beide gradering en proefstukgeometrie die Kohesie en Wrywinshoek beinvloed. gradering lewer hoër Kohesie waardes i.v.m. die growwer G19C gradering). Die Wrywingshoek is gevind om te verhoog soos die grofheid van die gradering verhoog (m.a.w. die fyner S19 gradering het laer Wrywingshoeke gelewer i.v.m. die growwer G19C gradering). Resultate het verder gewys dat groter proefstukke laer Kohesie en hoër Wrywingshoeke lewer. Daar kan wel gedebateer word dat variasie in materiaal die verandering van die skuifsterkte parameters gee, maar die proefstukvariasie is beperk om sodoende die invloed daarvan onopmerkbaar te maak.. Verder is die verlaging in Kohesie en verhoging in Wrywingshoek, a.g.v. ‘n vergroting in proefstuk grootte, vir albei aangepaste graderings geobserveer. Dit is ‘n moontlike aanduiding dat die verandering nie materiaal afhanklik is nie maar eerder beinvloed word deur die grens toestande tydens kompaksie. Dinamiese drie-assige toets resultate het gewys dat die Veerkragmodulus beinvloed word deur beide proefstuk geometrie en gradering. Daar is gevind dat die invloed van proefstukgeometrie kompleks is, en geen konstante verhouding, wat vir alle toets graderings geld, kon identifiseer word nie. Vir die invloed van gradering is daar gewys dat die Veerkragmodulus hoër is vir die growwer gradering (m.a.w. G19C gradering lewer hoër styfheid as S19 gradering). ‘n Verhoging in korrel-tot-korrel kontak area lewer hoër interne wrywing in die proefstuk wat bydrae tot laer vervorming by hoër spannings, m.a.w. hoër Veerkragmodulus. Baie interessant, vir beide monotoniese en dinamiese drie-assige toetse is gevind dat die growwer G19C gradering, i.v.m. die fyner S19 gradering, die ware G2 (Full) gradering beter verteenwoordig. Hierdie observasie is geldig vir beide die skuifsterkte parameters en weerstands eienskappe. Aggregaat karakterisering is ‘n belangrike deel in die ontwerp van ‘n ongebinde granulêre materiaal laag. Huidige karakterisering metodes gebruik aangepaste graderings sodat resultate nie beinvloed word deur die verhouding tussen proefstuk diameter en maksimum klipgrootte nie. Hierdie ondersoek het gevind dat van die huidige aanpassings nie die ware gradering verteenwoordig nie. Die resultate wys dat beide gradering en proefstuk geometrie die gedrag van die ongebinde granulêre materiaal beinvloed, so ook die ontwerp van ‘n padstruktuur. Daar is dus ‘n behoefte om die ware gradering te ondersoek wat slegs moontlik is met groot skaalse toets apparaat, wat groot klip korrels kan toets. Verder, indien daar ‘n verstandhouding tussen huidige (klein skaalse) toets apparaat en groot skaalse apparaat ontwikkel kan word, kan resultate aangepas word, vanaf die klein skaalse resultate, om die ware materiaal gedrag meer te verteenwoordig.

The crux of elliptic curve cryptography, a popular mechanism for securing data, is an asymmetric problem. The elliptic curve discrete logarithm problem, as it is called, is hoped to be generally hard in one direction but not the other, and it is this asymmetry that makes it secure. This paper describes the mathematics (and some of the computer science) necessary to understand and compute an attack on the elliptic curve discrete logarithm problem that works in a special case. The algorithm, proposed by Nigel Smart, renders the elliptic curve discrete logarithm problem easy in both directions for elliptic curves of so-called "trace one." The implication is that these curves can never be used securely for cryptographic purposes. In addition, it calls for further investigation into whether or not the problem is hard in general.

The efficiency of one fluid displacing another in a permeable medium depends on the pore-scale dynamics at the main wetting front. Experiments have shown that the frontal dynamics can result in two different flow regimes: a sharp and a diffuse front. In the sharp front regime, the displacing fluid occupies nearly all the pores and throats behind the main wetting front and the saturation changes abruptly. In contrast, in the diffuse front regime, pores are filled gradually at the main wetting front, and the saturation change is gradual in space. The different fronts can greatly alter the relative permeability curves, the trapping mechanisms, and the displacement efficiency. Directly measuring the sharpness of the front is difficult. Instead, here we correlate the front sharpness to saturation overshoot, which occurs for moderate to high flux vertical displacements of low density fluid by a higher density fluid in 1-D homogeneous permeable media. We hypothesize the sharpness of wetting front can be explained by competition between two different pore - filling mechanisms (called snap-off and piston-like) with the competition controlled by the velocity of the front and thus the injected flux. We conduct series of infiltration experiments to determine the saturation profile as a function of flux for seven different fluids. We find that for each fluid there is a flux (called overshoot flux) below which saturation overshoot ceases and the front is diffuse. We find that the overshoot flux depends inversely on the invading fluid’s viscosity, and shows little or no dependence on the invading fluid’s surface tension, vapor pressure, and its miscibility with water / text

Gamma-ray bursts (GRBs) are the mysterious, short and intense flashes of gamma-rays in the space, and are believed to originate from the rare, explosively devastating, stellar events that happens at cosmological distances. Enormous progress has been made from four decades of GRB research endeavor but the ultimate understanding of their origins has yet to arrive. Recently revealed features in their early afterglows broadened the opportunity space for exploration. We have carried out extensive studies on various physical processes in GRBs. We showed that the distribution of electrons' energy spectral index in GRBs and other relativistic sources is inconsistent with the prediction from the first-order Fermi theory of the shock particle acceleration. We investigated the photon scattering processes within the relativistic outflow that produces the GRB and calculated the resultant emission flux from it. We showed the scattering of the GRB prompt photons by the circum-burst dust, although an attractive possibility, can not explain the puzzling plateau component in the GRB afterglow light curve. We made meaningful constraint on the GRB prompt emission radius, R [greater-than or equal to] 10¹⁴, by studying the synchrotron self absorption for a small sample of bursts with good data. We showed that a late jet, which is thought to be producing the late X-ray flares in GRB afterglows, will produce detectable emissions from its interactions with other components in the explosive event of GRB, and identification of these emissions could verify the existence of the late jet and further prove the massive star origin of long-duration GRBs. / text

<p>Previous studies of agricultural conditions in the Mekong Delta (MD) have identified soil compaction as an obstacle to sustainable production. A conceptual model for soil formation was presented to demonstrate the link between soil hydrology and plant response. Detailed studies of soil moisture dynamics in agricultural fields were conducted using a dynamic process-orientated model. Pressure head and water flow were simulated for three selected sites during a year for which empirical data were available. Daily meteorological data were used as dynamic input and measured pressure head was used to estimate parameter values that satisfied various acceptance criteria. The Generalised Likelihood Uncertainty Estimation (GLUE) approach was applied for calibration procedures with 10,000 runs, each run using random values within the chosen range of parameter values. To evaluate model performance and uncertainty estimation, re-sampling was carried out using coefficient of determination (R2) and mean error (ME) as the criteria. Correlations between parameters and R2 (and ME) and among parameters were also considered to analyse the relationship of the selected parameter set in response to increases/decreases in the acceptable simulations. The method was successful for two of the three sites, with many accepted simulations. For these sites, the uncertainty was reduced and it was possible to quantify the importance of the different parameters.</p><p> </p>

Due to the fast development in 3D technology during recent decades, many approaches in 3D representation technologies have been proposed worldwide. In order to get an accurate information to render a 3D representation, more data need to be recorded compared to normal video sequence. In this case, how to find an efficient way to transmit the 3D representation data becomes an important part in the whole 3D representation technology. Recent years, many coding schemes based on the principle of encoding the depth have been proposed. Compared to the traditional multiview coding schemes, those new proposed schemes can achieve higher compression efficiency. Due to the development of depth capturing technology, the accuracy and quality of the reconstructed depth image also get improved. In this thesis we propose an efficient depth data compression scheme for 3D images. Our proposed depth data compression scheme is platelet based coding using Lagrangian optimization, quadtree decomposition and quadratic curve fitting. We study and improve the original platelet based coding scheme and achieve a compression improvement of 1-2 dB compared to the original platelet based scheme. The experimental results illustrate the improvement provided by our scheme. The quality of the reconstructed results of our proposed curve fitting based platelet coding scheme are better than that of the original scheme.

It was recently discovered by Joux [30] and Sakai, Ohgishi and Kasahara [47] that bilinear maps could be used to construct cryptographic schemes. Since then, bilinear maps have been used in applications as varied as identity-based encryption, short signatures and one-round tripartite key agreement. This thesis explains the notion of bilinear maps and surveys the applications of bilinear maps in the three main fields of cryptography: encryption, signature and key agreement. We also show how these maps can be constructed using the Weil and Tate pairings in elliptic curves.

The main problems of numerical analysis involve performing analytical operations, such as integration, differentiation, finding zeroes, interpolation, and so forth, of a function when all the data available are some samples of the function. Therefore, the purpose of this paper is to investigate the following problem: given a set of data points (x[sub i], y[sub i]) which are samples of some function, determine an approximating function. Further, extend the problem to that of determining an approximating function for a surface given some samples (x[sub i], y[sub j], z[sub ij]) of the surface.

Large-amplitude vibration of thin plates and shells has been critical design issues for many engineering structures. The increasingly more stringent safety requirements and the discovery of new materials with amazingly superior properties have further focused the attention of research on this area. This thesis deals with the vibration problem of rectangular, circular and angle-ply composite plates. This vibration can be triggered by an initial vibration amplitude, or an initial velocity, or both. Four types of boundary conditions including simply supported and clamped combined with in-plane movable/immovable are considered. To solve the differential equation generated from the vibration problem, Lindstedt's perturbation technique and Runge-Kutta method are applied. In previous works, this problem was solved by Lindstedt's Perturbation Technique. This technique can lead to a quick approximate solution. Yet based on mathematical assumptions, the solution will no longer be accurate for large amplitude vibration, especially when a significant amount of imperfection is considered. Thus Runge-Kutta method is introduced to solve this problem numerically. The comparison between both methods has shown the validity of the Lindstedt's Perturbation Technique is generally within half plate thickness. For a structure with a sufficiently large geometric imperfection, the vibration can be represented as a well-known backbone curve transforming from soften-spring to harden-spring. By parameter variation, the effects of imperfection, damping ratio, boundary conditions, wave numbers, young's modulus and a dozen more related properties are studied. Other interesting research results such as the dynamic failure caused by out-of-bound vibration and the change of vibration mode due to damping are also revealed.

The performance of the Hugershoff curve on fitting the growth trends of tree-ring series was tested using ring-width series with different starting years. The fitted values tend to be biased by tree-ring series close to pith, a phenomenon that was referred to as the ‘‘start-fitting problem’’. We determined three parameters with specific biological age-related meanings for the Hugershoff growth curve, i.e. the maximum growth, the maximum slope and the maximum changing ratio of slopes. A set of modified Hugershoff curves with different starting years was proposed to mitigate the start-fitting problem. Behavior of the modified Hugershoff curves on tree-ring series standardizations was tested and discussed. The ‘‘end-fitting problem’’ suggests that deviations in one interval could bias the fitted values of other time periods by using the Hugershoff curve.