Analytic solutions for linear waves propagating in an ocean with variable bottom topography and their applications in renewable wave energy

Studies about ocean waves have been evolving over a period of time. Re¬cently, there has been renewed interest in problems of refraction, diffraction and radiation of ocean waves around structures. In this thesis, the analytic solutions for linear waves propagating in an ocean with variable bottom to¬pography and their applications in renewable wave energy are presented. In the first part, we present an analytic solution to the shallow water wave equa¬tion for long waves propagating over a circular hump. As a useful tool in coastal engineering, the solution may be used to study the refraction of long waves around a circular hump. It may also be used as a validation tool for any numerical model developed for coastal wave refraction. To validate the new analytic solution, we have compared our new analytical solution with a numerical solution obtained by using the finite difference method. The agreement between these two solutions is excellent. By using the analytic solution, the effect of the hump dimensions on wave refraction over the circular hump are examined. In the second part of this thesis, based on the mild-slope equation derived by Smith and Sprinks [1] and the extended refraction-diffraction equation developed by Massel [2], we have constructed a two-layer mild-slope equation for interfacial waves propagating on the interface of a two-layer ocean model. First, we follow Smith and Sprinks’s [1] approach to derive the mild-slope equation for the propagation of interfacial waves, with the higher-order terms proportional to the bottom slope and bottom curvature all being neglected. We then derived the extended version of the mild-slope equation with the higher-order terms included. While we were able to solve the first equation analytically, we presented a numerical solution for the second equation. As a part of the verification process, both solutions were compared with each other and also with the single-layer mild-slope equation when the density of the upper layer goes to zero. We then used the new solution to study the effect of the hump dimensions on the refraction of the interfacial waves over a circular hump. Finally, in the final section of this thesis, we have used what we have developed before to construct the two-layer mild-slope equation with free surface on top. By utilizing this equation, we then derived an analytic solu¬tion for long waves propagating over a circular hump with a hollow circular cylinder floating in the free surface. In order to validate our new analytic solution, we have compared our problem with Mac Camy and Fuchs [3] solu¬tion, because our solution has reduced to their solution when the lower water depth, h2, goes to zero. We have also compared our solution with the flat bottom case in order to further verified our solution. Finally, by using the new solution, both diffraction and refraction effects from the hollow cylinder and hump dimensions are examined and discussed

Dynamic modelling for assessing the impact of marine debris on the population of Sea Turtles

Marine debris has significant impacts on marine animals including the sea turtles, which are particularly vulnerable to the presence of waste in the marine environment. We propose a novel mathematical model with three compartments to examine this effect: the sea turtle population, the concentration level of pollution inside sea turtles’ bodies, and the concentration level of pollution in marine environment. We locate the equilibrium points (also known as equilibria) for the suggested model and perform an analytical check on their stability. We also use the bifurcation analysis to examine how changing a model parameter affects the stability of the model's equilibria. Our findings demonstrated the existence of two equilibria: the sea turtles' survival equilibrium and their extinction equilibrium. The eigenvalues of the Jacobian matrix applied to the proposed model have been used to demonstrate the conditions for stability of these equilibria. The resulting bifurcation diagram demonstrates that both equilibrium points undergo transcritical bifurcations when the values of response intensity of toxicity parameter is varied. The findings of this study can help local or national governments make decisions and educate the public about sea turtle conservation in order to sustain sea turtle populations in the future

Pengaruh Inflasi, Kurs, Bi 7 Day, Non Performing Financing (NPF) Dan Financing To Deposito Ratio (FDR) Terhadap Simpanan Deposito Mudharabah Bank Umum Syariah (BUS) Tahun 2016 - 2018

ABSTRACT This study aims to examine the effect of NPF, FDR, Exchange Rate, Inflation, and BI 7 Days on Mudharabah Deposit Deposits. The analytical method used is Ordinary Least Square (OLS). The data used are time series data published by the Financial Services Authority (OJK), Bank Indonesia (BI), and the Ministry of Domestic Trade (KEMENDAGRI) Based on the results of this study it can be concluded that partially NPF, FDR, and Inflation have a negative but significant effect against Mudharabah Deposits Deposits. Meanwhile, the exchange rate has a positive and significant effect on Mudharabah Deposit Deposits, simultaneously NPF, FDR, Exchange Rate, Inflation and BI 7 Day has a significant effect on Mudharabah Deposit Deposits. Keywords: Mudharabah Deposit, NPF, FDR, Exchange Rate, Inflation, BI 7 Day, OLS (Ordinary Least Square

Analytical Solution for Controlled Drug Release with Time-Dependent Diffusion Parameter

Drugs seem to diffuse in different manners in a delivery device due to the increment of the device pore size during swelling. However, the diffusion parameter, D, is often assumed constant. In this work, a new developed controlled drug release model with a time-dependent diffusion parameter is compared to one- and two-phase models. The new model was obtained as an improvement of the previous constant and piece-wise constants models. The models are developed by solving an advection–diffusion equation using the Landau transformation method and the separation of variables method. To test these models, we fit experimental data by the developed models using the least squares fitting technique. The curve-fitting result shows that the least squares error of the two-phase and the time-dependent models are 10 times smaller than the single-phase model. The CPU time for the time-dependent model is the lowest, showing that a time-dependent model is the best option among all three tested models considering both factors of the determined least squares error and the time consumption

Adaptation Of Residual Power Series Approach For Solving Time-Fractional Nonlinear Kline-Gordon Equations With Conformable Derivative

In this paper, the time-fractional nonlinear Kline-Gordon equations are considered and solved using the adaptive of residual power series method. The fractional derivative is considered in a conformable sense. Analytical solutions are obtained based on conformable Taylor series expansion by substituting the truncated conformable series solutions to residual error functions. This adaptation can be implemented as a novel alternative technique to handle many nonlinear issues occurring in physics and engineering. Effectiveness, validity, and feasibility of the proposed method are demonstrated by testing some numerical applications. Tabular and graphic results indicate that the method is superior, accurate and appropriate for solving these fractional partial differential models with compatible derivatives

Analysis of Drag Coefficients around Objects Created Using Log-Aesthetic Curves

A fair curve with exceptional properties, called the log-aesthetic curves (LAC) has been extensively studied for aesthetic design implementations. However, its implementation in terms of functional design, particularly hydrodynamic design, remains mostly unexplored. This study examines the effect of the shape parameter α of LAC on the drag generated in an incompressible fluid flow, simulated using a semi-implicit backward difference formula coupled with P2−P1 Taylor–Hood finite elements. An algorithm was developed to create LAC hydrofoils that were used in this study. We analyzed the drag coefficients of 47 LAC hydrofoils of three sizes with various shapes in fluid flows with Reynolds numbers of 30, 40, and 100, respectively. We found that streamlined LAC shapes with negative α values, of which curvature with respect to turning angle are almost linear, produce the lowest drag in the incompressible flow simulations. It also found that the thickness of LAC objects can be varied to obtain similar drag coefficients for different Reynolds numbers. Via cluster analysis, it is found that the distribution of drag coefficients does not rely solely on the Reynolds number, but also on the thickness of the hydrofoil

Analysis of Drag Coefficients around Objects Created Using Log-Aesthetic Curves

A fair curve with exceptional properties, called the log-aesthetic curves (LAC) has been extensively studied for aesthetic design implementations. However, its implementation in terms of functional design, particularly hydrodynamic design, remains mostly unexplored. This study examines the effect of the shape parameter α of LAC on the drag generated in an incompressible fluid flow, simulated using a semi-implicit backward difference formula coupled with P2−P1 Taylor–Hood finite elements. An algorithm was developed to create LAC hydrofoils that were used in this study. We analyzed the drag coefficients of 47 LAC hydrofoils of three sizes with various shapes in fluid flows with Reynolds numbers of 30, 40, and 100, respectively. We found that streamlined LAC shapes with negative α values, of which curvature with respect to turning angle are almost linear, produce the lowest drag in the incompressible flow simulations. It also found that the thickness of LAC objects can be varied to obtain similar drag coefficients for different Reynolds numbers. Via cluster analysis, it is found that the distribution of drag coefficients does not rely solely on the Reynolds number, but also on the thickness of the hydrofoil