Propagation of solitary waves and undular bores over variable topography

Description of the interaction of a shallow-water wave with variable topography is a classical and fundamental problem of fluid mechanics. The behaviour of linear waves and isolated solitary waves propagating over an uneven bottom is well understood. Much less is known about the propagation of nonlinear wavetrains over obstacles. For shallow-water waves, the nonlinear wavetrains are often generated in the form of undular bores, connecting two different basic flow states and having the structure of a slowly modulated periodic wave with a solitary wave at the leading edge. In this thesis, we examine the propagation of shallow-water undular bores over a nonuniform environment, and also subject to the effect of weak dissipation (turbulent bottom friction or volume viscosity). The study is performed in the framework of the variable-coefficient Korteweg-de Vries (vKdV) and variable-coefficient perturbed Korteweg-de Vries (vpKdV) equations. The behaviour of undular bores is compared with that of isolated solitary waves subject to the same external effects. We show that the interaction of the undular bore with variable topography can result in a number of adiabatic and non-adiabatic effects observed in different combinations depending on the specific bottom profile. The effects include: (i) the generation of a sequence of isolated solitons -- an expanding large-amplitude modulated solitary wavetrain propagating ahead of the bore; (ii) the generation of an extended weakly nonlinear wavetrain behind the bore; (iii) the formation of a transient multi-phase region inside the bore; (iv) a nonlocal variation of the leading solitary wave amplitude; (v) the change of the characteristics wavelength in the bore; and (vi) occurrence of a ``modulation phase shift" due to the interaction. The non-adiabatic effects (i) -- (iii) are new and to the best of our knowledge, have not been reported in previous studies. We use a combination of nonlinear modulation theory and numerical simulations to analyse these effects. In our work, we consider four prototypical variable topography profiles in our study: a slowly decreasing depth, a slowly increasing depth , a smooth bump and a smooth hole, which leads to qualitatively different undular bore deformation depending on the geometry of the slope. Also, we consider (numerically) a rapidly varying depth topography, a counterpart of the ``soliton fission" configuration. We show that all the effects mentioned above can also be observed when the undular bore propagates over a rapidly changing bottom . We then consider the modification of the variable topography effects on the undular bore by considering weak dissipation due to turbulent bottom friction or volume viscosity. The dissipation is modelled by appropriate right-hand side terms in the vKdV equation. The developed methods and results of our work can be extended to other problems involving the propagation of undular bores (dispersive shock waves in general) in variable media

Transformation of a shoaling undular bore

We consider the propagation of a shallow-water undular bore over a gentle monotonic bottom slope connecting two regions of constant depth, in the framework of the variable-coefficient Korteweg-de Vries equation. We show that, when the undular bore advances in the direction of decreasing depth, its interaction with the slowly varying topography results, apart from an adiabatic deformation of the bore itself, in the generation of a sequence of isolated solitons - an expanding large-amplitude modulated solitary wavetrain propagating ahead of the bore. Using nonlinear modulation theory we construct an asymptotic solution describing the formation and evolution of this solitary wavetrain. Our analytical solution is supported by direct numerical simulations. The presented analysis can be extended to other systems describing the propagation of undular bores (dispersive shock waves) in weakly non-uniform environments

Electricity consumption forecasting using Adaptive Neuro-Fuzzy Inference System (ANFIS)

Universiti Tun Hussein Onn Malaysia (UTHM) is a developing Malaysian Technical University. There is a great development of UTHM since its formation in 1993. Therefore, it is crucial to have accurate future electricity consumption forecasting for its future energy management and saving. Even though there are previous works of electricity consumption forecasting using Adaptive Neuro-Fuzzy Inference System (ANFIS), but most of their data are multivariate data. In this study, we have only univariate data of UTHM electricity consumption from January 2009 to December 2018 and wish to forecast 2019 consumption. The univariate data was converted to multivariate and ANFIS was chosen as it carries both advantages of Artificial Neural Network (ANN) and Fuzzy Inference System (FIS). ANFIS yields the MAPE between actual and predicted electricity consumption of 0.4002% which is relatively low if compared to previous works of UTHM electricity forecasting using time series model (11.14%), and first-order fuzzy time series (5.74%), and multiple linear regression (10.62%)

Forecasting electricity consumption using the second-order fuzzy time series

There is a great development of Universiti Tun Hussein Onn Malaysia (UTHM) infrastructure since its formation in 1993. The development will be accompanied by the increasing demand for electricity. Hence, there is a need to forecast UTHM electricity consumption accurately so that UTHM can plan for future energy demand and utility saving decisions. Previous studies on UTHM electricity consumption prediction have been carried out using time series models, multiple linear regression and first-order fuzzy time series (FTS). The first-order FTS yield the best accuracy among these three methods. Previous forecasting problem showed higher order FTS can yield better accuracy. Therefore, in this study, the second-order FTS with trapezoidal membership function was implemented on the UTHM monthly electricity consumption from January 2009 to December 2018 to forecast January to December 2019 monthly electricity consumption. The procedure of the FTS and trapezoidal membership function was described together with January data. The second-order FTS forecast UTHM electricity consumption better than the first-order FTS

Simulation of Internal Undular Bores Propagating over a Slowly Varying Region

Internal undular bores have been observed in many parts of the world. Studies have shown that many marine structures face danger and risk of destruction caused by internal undular bores due to the amount of energy it carries. This paper looks at the transformation of internal undular bore in two-layer fluid flow under the influence of variable topography. Thus, the surface of the bottom is considered to be slowly varying. The appropriate mathematical model is the variable-coefficient extended Korteweg-de Vries equation. We are particularly interested in looking at the transformation of KdV-type and table-top undular bore over the variable topography region. The governing equation is solved numerically using the method of lines, where the spatial derivatives are first discretised using finite difference approximation so that the partial differential equation becomes a system of ordinary differential equations which is then solved by 4th order Runge-Kutta method. Our numerical results show that the evolution of internal undular bore over different types of varying depths regions leads to a number of adiabatic and non-adiabatic effects. When the depth decreases slowly, a solitary wavetrain is observed at the front of the transformed internal undular bore. On the other hand, when the depth increases slowly, we observe the generation of step-like wave and weakly nonlinear trailing wavetrain, the occurrence of multi-phase behaviour, the generation of transformed undular bore of negative polarity and diminishing transformed undular bore depending on the nature of the topography after the variable topography

Bioactive substance contents and antioxidant capacity of raw and blanched vegetables.

Five commonly consumed vegetables in Malaysia namely, four-angled bean (Psophocarpus tetragonolobus D.C.), French bean (Phaseolus vulgaris L.), long bean (Vigna sesquipedalis L.), snow pea (Pisum sativum var. macrocarpon L.) and snap pea (Pisum sativum) were blanched in boiling water for 10 min. The contents of total phenolics, ascorbic acid and β-carotene, and the antioxidant capacity as typified by β-carotene and free radical scavenging activity (DPPH) assays were determined for the raw and blanched vegetables. The study revealed that blanching caused a significant (p < 0.05) increase in β-carotene content [fresh (389–539 µg/100 g), blanched (510–818 µg/100 g)], except in snow pea. Conversely, there was a significant (p < 0.05) decrease in ascorbic acid content [fresh (1.2–7.8 mg/100 g), blanched (0.67–3.8 mg/100 g)]. After blanching, the total phenolic content and antioxidant activity either decreased or increased depending on the type of vegetables. The total phenolic content was positively correlated with the antioxidant activity of the studied vegetables to some extent, but not with ascorbic acid or β-carotene

Artificial Immune System based on Hybrid and External Memory for Mathematical Function Optimization

Artificial immune system (AIS) is one of the natureinspired algorithm for optimization problem. In AIS, clonal selection algorithm (CSA) is able to improve global searching ability. However, the CSA convergence and accuracy can be further improved because the hypermutation in CSA itself cannot always guarantee a better solution. Alternatively, Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) have been used efficiently in solving complex optimization problems, but they have a tendency to converge prematurely. Thus, a hybrid PSO-AIS and a new external memory CSA based scheme called EMCSA are proposed. In hybrid PSO-AIS, the good features of PSO and AIS are combined in order to reduce any limitation. Alternatively, EMCSA captures all the best antibodies into the memory in order to enhance global searching capability. In this preliminary study, the results show that the performance of hybrid PSO-AIS compares favourably with other algorithms while EMCSA produced moderate results in most of the simulations

Transformation of a shoaling undular bore

We consider the propagation of a shallow-water undular bore over a gentle monotonic bottom slope connecting two regions of constant depth, in the framework of the variablecoefficient Korteweg – de Vries equation. We show that, when the undular bore advances in the direction of decreasing depth, its interaction with the slowly varying topography results, apart from an adiabatic deformation of the bore itself, in the generation of a sequence of isolated solitons — an expanding large-amplitude modulated solitary wavetrain propagating ahead of the bore. Using nonlinear modulation theory we construct an asymptotic solution describing the formation and evolution of this solitary wavetrain. Our analytical solution is supported by direct numerical simulations. The presented analysis can be extended to other systems describing the propagation of undular bores (dispersive shock waves) in weakly non-uniform environments

Artificial Immune System Based Remainder Method for Multimodal Mathematical Function Optimization

Artificial immune system (AIS) is one of the nature-inspired algorithm for solving optimization problems. In AIS, clonal selection algorithm (CSA) is able to improve global searching ability compare to other meta-heuristic methods. However, the CSA rate of convergence and accuracy can be further improved as the hypermutation in CSA itself cannot always guarantee a better solution. Conversely, Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) have been used efficiently in solving complex optimization problems, but they have an inclination to converge prematurely. In this work, the CSA is modified using the best solutions for each exposure (iteration) namely Single Best Remainder (SBR) - CSA. Simulation results show that the proposed algorithm is able to enhance the performance of the conventional CSA in terms of accuracy and stability for single objective functions

Antibody Remainder Method Based Artificial Immune System for Mathematical Function Optimization

Artificial immune system (AIS) is one of the natureinspired algorithm for solving optimization problem. In AIS, clonal selection algorithm (CSA) is able to improve global searching ability. However, the CSA convergence and accuracy can be improved further because the hypermutation in CSA itself cannot always guarantee a better solution. Alternatively,Genetic Algorithms (GAs) and Particle Swarm Optimization(PSO) have been used efficiently in solving complex optimization problems, but they have a tendency to converge prematurely. In this study, the CSA is modified using the best solution for each exposure (iteration) namely Single Best Remainder (SBR) CSA. In this study, the results show that the performance of the proposed algorithm (SBR-CSA) compares favourably with other algorithms while Half Best Insertion (HBI) CSA produced moderate results in most of the simulations