A Parameter Estimation Technique for a Groundwater Flow Model
Joseph Acquah,
Francis Benyah,
Jerry Samuel Yao-Kuma
Issue:
Volume 5, Issue 4, December 2020
Pages:
202-213
Received:
31 August 2020
Accepted:
12 October 2020
Published:
16 December 2020
Abstract: In this paper, the problem of ill-posedness of solution in identifying multiple groundwater flow parameters from hydraulic head data and other ancillary data was assessed. The solution approach to the parameter identification problem is sought by applying the Least Squares, the Adjoint, the Conjugate Gradient Method and a proposed Parameter Transformation Method. Numerical test for a 1D and 2D flow models governed by PDEs were used to assess the accuracy and stability of the proposed method. The proposed method gave an appreciable solution estimates with minimal error-norm compared with the o ptimisation techniques explored in the study as a measure to the PTM The results revealed that when the adapted methods and the PTM were simulated numerically on a 1D and 2D test problems, the PTM gave a more stable solution estimates with a residual norm-error value of 2.23500 for the 1D test problem compared with that of the Adjoint method which prove to be the comparing solution with a norm-error value of 2.66500. For the 2D test case, the results also revealed that the PTM was stable with a residual norm-error value of 10.98310 compared with that of the Conjugate Gradient method with value of 86.562. Thus in conclusion, the study revealed that the PTM is capable of yielding realistic solution estimates compared with the studied optimisation methods.
Abstract: In this paper, the problem of ill-posedness of solution in identifying multiple groundwater flow parameters from hydraulic head data and other ancillary data was assessed. The solution approach to the parameter identification problem is sought by applying the Least Squares, the Adjoint, the Conjugate Gradient Method and a proposed Parameter Transfo...
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Modeling the Rate of Vitamin C Loss in Five Different Fruits During Storage
Timothy Marhiere Akpomie,
Musa Safiyanu Tanko,
Umar Faruk Hassan
Issue:
Volume 5, Issue 4, December 2020
Pages:
214-220
Received:
8 November 2020
Accepted:
18 November 2020
Published:
25 December 2020
Abstract: Vitamin C, also known as ascorbic acid, in five different fruit samples of orange, mango, watermelon, pawpaw and pineapple were determined with the view of developing suitable mathematical models for subsequent estimation of the vitamin in the fruits after several days of storage at temperatures of 4 and 29 (±1°C) respectively prior to consumption. The iodometric titration was used to evaluate the vitamin C content of the fruit samples alongside their pH values. Measurements were done on the 1st, 4th, 8th, 12th and 15th day of storage. The results obtained were then fed into a Minitab 18 Statistical Computer programme for model development. The developed model was quadratic in nature and was of the form y=c±at±bt2. For the orange sample, the model at 29°C was Vit. C=15.48 – 0.2814 t - 0.0042 t2, while at 4°C, the model was Vit. C=15.34 – 0.135 t – 0.0099 t2. Other models were; mango: Vit. C=8.113- 0.3962 t + 0.0077 t2 & Vit. C=8.050 – 0.229 t – 0.0011t2, watermelon: Vit. C=5.793 – 0.573 t + 0.0203 t2 & Vit. C=5.338 – 0.175 t + 0.003 t2, pawpaw: Vit. C=8.534 – 0.227 t - 0.0069 t2 & Vit. C=8.804 –0.291 t – 0.0009 t2 and pineapple: Vit. C=6.459 – 0.673 t + 0.0282 t2 & Vit. C=5.937 – 0.069 t – 0.0044 t2. All models were found to be highly correlated (r2=86.90 – 100.00%) at 95% confidence level. Simulation using the respective models at 29 and 4°C respectively indicated that the initial concentrations of orange (15.45±1.04), mango (7.82±1.76), watermelon (6.05±0.94), pawpaw (5.48±0.94) and pineapple (8.35±1.09 mg/100 cm3) would respectively take (36, 33), (30, 31), (23, 60), (22, 30) and (21, 30) days to be lost completely. Results also indicated that refrigeration slowed down or conferred some stability on the vitamin C content except in the orange juice. The percentage losses of vitamin C in the analytes were found to be: water melon (71.00), pawpaw (60.00), pineapple (58.00), mango (52.00) and orange (35.00) respectively. The respective models could be used to simulate the concentration of vitamin C at any particular time (days). This would save time and cost of experimentation and would therefore give an estimate of the concentration of the vitamin present in such fruits when refrigerated or stored in the open air given the post-harvest number of days.
Abstract: Vitamin C, also known as ascorbic acid, in five different fruit samples of orange, mango, watermelon, pawpaw and pineapple were determined with the view of developing suitable mathematical models for subsequent estimation of the vitamin in the fruits after several days of storage at temperatures of 4 and 29 (±1°C) respectively prior to consumption....
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Modelling Transmission of Buruli Ulcer in the Central Region of Ghana
Nyarko Christiana Cynthia,
Nyarko Peter Kwesi,
Ampofi Isaac,
Asante Emmanuel
Issue:
Volume 5, Issue 4, December 2020
Pages:
221-230
Received:
11 June 2020
Accepted:
10 September 2020
Published:
31 December 2020
Abstract: The pathogen of Buruli Ulcer (BU) is known to be Mycobacterium Ulcerans whose mode of transmission is entirely not known, although the disease is recognised to be associated with contaminated water. The hypothesised transmission involves humans being bitten by the water bugs (vector) that prey on mollusks, snails and young fishes. The hypothesised transmission also involves humans feeding on an infected fish or frog. This study seeks to contribute to the dynamics and analyses of the transmission mechanism of Buruli Ulcer in communities along Offin River in the Central Region of Ghana. The model equilibria were determined and conditions for the equilibria were also established. The basic reproduction number, was derived using the Next Generation approach and its estimated value was 1.20771. The result reveals that, is greater than 1, indicating a horizontal spread of the infection across the population. The transmission dynamics of Buruli Ulcer model of the Susceptible, Infected and Recovered (SIR) type also show that the disease will continue to spread at the study areas as long as the reservoir for Mycobacterium Ulcerans continue to sustain enough infected water bugs and infected fish or infected frog to contain the disease. The study further concludes that, the rate of spread of Buruli Ulcer in the affected communities continue to be high due to its mode of transmission. This study suggest that adequate control measures including mass education and prompt treatment to curb the spread should be emphasized.
Abstract: The pathogen of Buruli Ulcer (BU) is known to be Mycobacterium Ulcerans whose mode of transmission is entirely not known, although the disease is recognised to be associated with contaminated water. The hypothesised transmission involves humans being bitten by the water bugs (vector) that prey on mollusks, snails and young fishes. The hypothesised t...
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