Numerické řešení inverzních integrálních rovnic matematického modelování ve výzkumu biopaliv
| Thesis title in Czech: | Numerické řešení inverzních integrálních rovnic matematického modelování ve výzkumu biopaliv |
|---|---|
| Thesis title in English: | Numerical solution of inverse integral equations arising in mathematical modeling for biofuel research |
| Key words: | inverzní integrální rovnice, kvadratura, konvergence, odhad chyby |
| English key words: | inverse integral equation, quadrature, convergence, error estimates |
| Academic year of topic announcement: | 2011/2012 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Department of Numerical Mathematics (32-KNM) |
| Supervisor: | doc. RNDr. Iveta Hnětynková, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 18.10.2011 |
| Date of assignment: | 09.11.2011 |
| Confirmed by Study dept. on: | 02.12.2011 |
| Date and time of defence: | 22.06.2012 00:00 |
| Date of electronic submission: | 25.05.2012 |
| Date of submission of printed version: | 25.05.2012 |
| Date of proceeded defence: | 22.06.2012 |
| Opponents: | doc. RNDr. Josef Kofroň, CSc. |
| Advisors: | prof. Rosemary Renaut |
| Guidelines |
| Anode-respiring bacteria (ARB) are unique in their capacity to transfer electrons from organic substrates to a solid anode. The result of anode respiration is an electrical current that can be used for various bioenergy applications in microbial electrochemical cells (MXCs). Fuel cell research relies on electrochemical impedance spectroscopy (EIS). The underlying mathematical model requires the numerical solution of an inverse integral equation. Two approaches have been proposed in the literature, one using a basic numerical quadrature (Weese, 1992) and the other based on Fourier analysis (Schichlein et al, 2002). This thesis concerns the study of these two approaches, including Matlab comparison for simulated and real data, as well as a theoretical analysis to determine the minimum number of measurement data required for each experiment. |
| References |
| Logan, B. E., B. Hamelers, et al. (2006). Environ Sci Technol 40(17): 5181-5192.
Rittmann, B. E., R. Krajmalnik-Brown, et al. (2008). Nat Rev Microbiol 6(8): 604-612. Schichlein, H., A. C. Muller, et al. (2002). J Appl Electrochem 32(8): 875-882. Weese, J. (1992). Comput. Phys. Commun. 69(1): 99-111. |