Bacterial degradation of fossil fuel waste in aqueous and solid media

The generation of environmental pollutants worldwide is mainly due to over reliance on fossil fuels as a source of energy. As a result of the negative impacts of these pollutants on the health of humans, animals, plants and microorganisms, global attention has been directed towards ways of containing this problem. Biodegradation of fossil fuel is one of the most effective methods used to remediate contaminated systems. However with regard to coal waste, much of what is known is based on the ability of fungal species to biosolubilize this material under enrichment conditions in a laboratory setting. For effective biodegradation as a remediation technique, there is an immediate need to source, isolate, enrich and incorporate other microorganisms such as bacteria into bioremediation technologies. The goal of this dissertation was to isolate bacteria from fossil fuel contaminated environments and to demonstrate competence for petroleum hydrocarbon degradation which was achieved using a combination of analytical methods such as spectrophotometry, FT-IR, SEM and GC-MS. Screening for biodegradation of coal and petroleum hydrocarbon waste resulted in the isolation of 75 bacterial strains of which 15 showed good potential for use in developing remedial biotechnologies. Spectrophotometric analysis of bacteria both in coal and petroleum hydrocarbons (all in aqueous media) revealed a high proliferation of bacteria in these media suggesting that these microbes can effectively utilize the various substrates as a source of carbon. The isolated bacteria effectively degraded and converted waste coal to humic and fulvic acids; products required to enrich coal mine dumps to support re-vegetation. Scanning electron microscopy showed the attachment of bacteria to waste coal surfaces and the disintegration of coal structures while FT-IR analysis of extracted humic-like substances from biodegraded waste coal revealed these to have the same functional groups as commercial humic acid. Specific consortia which were established using the isolated bacterial strains, showed greater potential to biodegrade coal than did individual isolates. This was evident in experiments carried out on coal and hydrocarbons where the efficient colonization and utilization of these substrates by each bacterial consortium was observed due to the effect of added nutrients such as algae. The biodegradation of liquid petroleum hydrocarbons (diesel and BTEX) was also achieved using the 15 bacterial isolates. GC-MS analysis of extracted residual PHC from aqueous and solid media revealed rapid breakdown of these contaminants by bacteria. Different bacterial consortia established from the individual isolates were shown to be more efficient than single isolates indicating that formulated consortia are the biocatalysts of choice for fossil fuel biodegradation. This study represents one of the most detailed screenings for bacteria from fossil fuel contaminated sites and the isolation of strains with potential to biodegrade coal and petroleum hydrocarbon wastes. Several consortia have been developed and these show potential for further development as biocatalysts for use in bioremediation technology development. An evaluation of efficiency of each established bacterial consortium for biodegradation in a commercial and/or industrial setting at pilot scale is now needed

Zhou Method for the Solutions of System of Proportional Delay Differential Equations

In this paper, we consider a viable semi-analytical approach for the approximate-analytical solutions of certain system of functional differential equations (SFDEs) engendered by proportional delays. The proposed semi-analytical technique is built on the basis of the classical Differential Transform Method (DTM). The effectiveness and robustness of the proposed technique is illustratively demonstrated and the results are compared with their exact forms. We note also that using this method, the SFDEs with proportional delays need not be converted to SFDEs with constant delays before obtaining their solutions, and no symbolic calculation or initial guesstimates are required

Strain-Based Mechanical Failure Analysis of Buried Steel Pipeline Subjected to Landslide Displacement Using Finite Element Method

Landslide displacement is one of the major threats to the structural integrity of buried oil and natural gas pipelines that are often located far from major markets with terrains prone to permanent ground deformations. These pipelines can experience large longitudinal strains and circumferential deformation resulting from the differential ground movements thereby potentially impacting pipeline safety by adversely affecting structural capacity and leak tight integrity. In order to proffer theoretical basis for the design, safety evaluation and maintenance of pipelines, the failure analysis and mechanical behavior of buried API X65 steel pipeline perpendicularly crossing landslide area was investigated with the Finite Element Method (FEM), considering soil – pipeline interaction using the strain-based approach in this thesis. The soil – pipe interaction system was rigorously modeled through finite elements using the ANSYS Parametric Design Language (APDL) Mechanical Finite Element (FE) software, which accounts for large strains, displacement, non-linear material behavior and special conditions of contact and friction on the soil – pipe interface. Various diameter – thickness ratios (D/t-96 and D/t-72) pipeline models was used. This thesis focuses on the influence of various soil and pipeline parameters on the structural response of the pipeline, with particular emphasis on identifying pipeline failure (excessive longitudinal strains). The influence of soil strength and stiffness, and internal pressure on the structural response was also examined. Furthermore, a comparison of the conventional stress-based design approach versus strain-based approach was made. The results show that there are two high strain areas on the buried pipeline sections where the bending deformations are bigger. The maximum strains on the pipeline were mostly tensile at the maximum soil displacement of 0.5 m in the deformation process. The compressive strains resulted in local buckling of the pipeline. Buried pipeline in the landslide bed with hard soil (non-cohesive) is more prone to failure. The biggest deformations appear on the pipeline sections that are on either side of the interface between the sliding soil and the stable surrounding soil at around 20 m and 16 m, respectively. The maximum displacement of the pipeline is smaller than the landslide displacement due to soil-pipe interaction. Bending deformations and tensile strain of the pipeline increase with landslide displacement increase. An increase in the soil’s elastic modulus, cohesion (changing the soil from cohesive to non-cohesive) and diameter thickness (D/t) ratio of the pipeline resulted in increased bending deformation and tensile strain of the pipeline. Comparing stress-based to strain-based analysis of the pipeline showed that the stress-based approach is more conservative and attained the yield limit over two times earlier in the deformation process when compared to the strain-based approach which maximizes the plastic and ductile properties of steel pipes under landslide displacement. The strain limit of ε_(x,max) ≤ 2% is in the strain-based approach in accordance with the strain-based design codes of DNV-OS-F101 (2000), CZA-Z662-07 and ASCE (2005). The results are presented in diagrams, tables, and plot curves form

ON APPROXIMATE AND CLOSED-FORM SOLUTION METHOD FOR INITIAL-VALUE WAVE-LIKE MODELS

This work presents a proposed Modified Differential Transform Method (MDTM) for obtaining both closed-form and approximate solutions of initial-value wave-like models with variable, and constant coefficients. Our results when compared with the exact solutions of the associated solved problems, show that the method is simple, effective and reliable. The results are very much in line with their exact forms. The method involves less computational work without neglecting accuracy. We recommend this simple proposed technique for solving both linear and nonlinear partial differential equations (PDEs) in other aspects of pure and applied sciences

On Duality Principle in Exponentially Lévy Market

This paper describes the effect of duality principle in option pricing driven by exponentially Lévy market model. This model is basically incomplete - that is; perfect replications or hedging strategies do not exist for all relevant contingent claims and we use the duality principle to show the coincidence of the associated underlying asset price process with its corresponding dual process. The condition for the ‘unboundedness’ of the underlying asset price process and that of its dual is also established. The results are not only important in Financial Engineering but also from mathematical point of view

Perturbation Iteration Transform Method for the Solution of Newell-Whitehead-Segel Model Equations

In this study, a computational method referred to as Perturbation Iteration Transform Method (PITM), which is a combination of the conventional Laplace Transform Method (LTM) and the Perturbation Iteration Algorithm (PIA) is applied for the solution of Newell-Whitehead- Segel Equations (NWSEs). Three unique examples are considered and the results obtained are compared with their exact solutions graphically. Also, the results agree with those obtained via other semi-analytical methods viz: New Iterative Method and Adomian Decomposition Method. This present method proves to be very efficient and reliable. Mathematica 10 is used for all the computations in this stud

ANALYTICAL STUDY AND GENERALISATION OF SELECTED STOCK OPTION VALUATION MODELS

In this work, the classical Black-Scholes model for stock option valuation on the basis of some stochastic dynamics was considered. As a result, a stock option val- uation model with a non-�xed constant drift coe�cient was derived. The classical Black-Scholes model was generalised via the application of the Constant Elasticity of Variance Model (CEVM) with regard to two cases: case one was without a dividend yield parameter while case two was with a dividend yield parameter. In both cases, the volatility of the stock price was shown to be a non-constant power function of the underlying stock price and the elasticity parameter unlike the constant volatility assumption of the classical Black-Scholes model. The It^o's theorem was applied to the associated Stochastic Di�erential Equations (SDEs) for conversion to Partial Dif- ferential Equations (PDEs), while two approximate-analytical methods: the Modi�ed Di�erential Transformation Method (MDTM) and the He's Polynomials Technique (HPT) were applied to the Black-Scholes model for stock option valuation; in both cases the integer and time-fractional orders were considered, and the results obtained proved the latter as an extension of the former. In addition, a nonlinear option pric- ing model was obtained when the constant volatility assumption of the classical linear Black-Scholes option pricing model was relaxed through the inclusion of transaction cost (Bakstein and Howison model). Thereafter, this nonlinear option pricing model was extended to a time-fractional ordered form, and its approximate-analytical solu- tions were obtained via the proposed solution technique. For e�ciency and reliability of the method, two cases with �ve examples were considered: Case 1 with two ex- amples for time-integer order, and Case 2 with three examples for time-fractional order, and the results obtained show that the time-fractional order form generalises the time-integer order form. Thus, the Black-Scholes and the Bakstein and Howison models for stock option valuation were generalised and extended to time-fractional order, and analytical solutions of these generalised models were provided

The Solution of Initial-value Wave-like Models via Perturbation Iteration Transform Method

This work is based on the application of the new Perturbation Iteration Transform Method (PITM), which is a combined form of the Perturbation Iteration Algorithm (PIA) and the Laplace Transform (LT) method on some wave-like models with constant and variable coefficients. The method provides the solution in closed form, is efficient and it involves less computational work

Solving Linear Schrödinger Equation through Perturbation Iteration Transform Method

This paper applies Perturbation Iteration Transform Method: a combined form of the Perturbation Iteration Algorithm and the Laplace Transform Method to linear Schrödinger equations for approximate-analytical solutions. The results converge rapidly to the exact solution

The h-Integrability and the Weak Laws of Large Numbers for Arrays

In this paper, the concept of weak laws of large numbers for arrays (WLLNFA) is studied, and a new notion of uniform integrability referred to as h-integrability is introduced as a condition for WLLNFA in obtaining the main results