Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods
Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM)...
Ausführliche Beschreibung
Autor*in: |
Skoneczny, Szymon [verfasserIn] Cioch-Skoneczny, Monika [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2018 |
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Schlagwörter: |
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Übergeordnetes Werk: |
Enthalten in: Chemical engineering research and design - Amsterdam : Elsevier, 1983, 139, Seite 309-320 |
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Übergeordnetes Werk: |
volume:139 ; pages:309-320 |
DOI / URN: |
10.1016/j.cherd.2018.09.038 |
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Katalog-ID: |
ELV000997455 |
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245 | 1 | 0 | |a Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods |
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520 | |a Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM). Monod and Haldane kinetic models were taken into consideration. Some unknown properties of these methods are presented. It was show that third-order approximation by HAM is more accurate than the method by Abbas and Eberl (2011) and Valdés-Parada et al. (2005). Additionally, the former is the same as for second-order HAM approximation. The accuracy of homotopy-based approximations is considerably influenced by external mass transfer resistances, expressed by the Biot number. The methods are especially useful for modelling bioreactors in which biofilm thicknesses are relatively small and coefficients of mass transfer from liquid to biofilm are large. | ||
650 | 4 | |a Biofilm | |
650 | 4 | |a Approximation methods | |
650 | 4 | |a Homotopy analysis method | |
650 | 4 | |a Homotopy perturbation method | |
650 | 4 | |a Optimal homotopy analysis method | |
650 | 4 | |a Steady-states | |
700 | 1 | |a Cioch-Skoneczny, Monika |e verfasserin |4 aut | |
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2018 |
allfields |
10.1016/j.cherd.2018.09.038 doi (DE-627)ELV000997455 (ELSEVIER)S0263-8762(18)30516-1 DE-627 ger DE-627 rda eng 540 660 DE-600 58.10 bkl Skoneczny, Szymon verfasserin (orcid)0000-0002-4549-7167 aut Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM). Monod and Haldane kinetic models were taken into consideration. Some unknown properties of these methods are presented. It was show that third-order approximation by HAM is more accurate than the method by Abbas and Eberl (2011) and Valdés-Parada et al. (2005). Additionally, the former is the same as for second-order HAM approximation. The accuracy of homotopy-based approximations is considerably influenced by external mass transfer resistances, expressed by the Biot number. The methods are especially useful for modelling bioreactors in which biofilm thicknesses are relatively small and coefficients of mass transfer from liquid to biofilm are large. Biofilm Approximation methods Homotopy analysis method Homotopy perturbation method Optimal homotopy analysis method Steady-states Cioch-Skoneczny, Monika verfasserin aut Enthalten in Chemical engineering research and design Amsterdam : Elsevier, 1983 139, Seite 309-320 Online-Ressource (DE-627)312841965 (DE-600)2008006-2 (DE-576)090893190 1744-3563 nnns volume:139 pages:309-320 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_206 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 58.10 Verfahrenstechnik: Allgemeines AR 139 309-320 |
spelling |
10.1016/j.cherd.2018.09.038 doi (DE-627)ELV000997455 (ELSEVIER)S0263-8762(18)30516-1 DE-627 ger DE-627 rda eng 540 660 DE-600 58.10 bkl Skoneczny, Szymon verfasserin (orcid)0000-0002-4549-7167 aut Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM). Monod and Haldane kinetic models were taken into consideration. Some unknown properties of these methods are presented. It was show that third-order approximation by HAM is more accurate than the method by Abbas and Eberl (2011) and Valdés-Parada et al. (2005). Additionally, the former is the same as for second-order HAM approximation. The accuracy of homotopy-based approximations is considerably influenced by external mass transfer resistances, expressed by the Biot number. The methods are especially useful for modelling bioreactors in which biofilm thicknesses are relatively small and coefficients of mass transfer from liquid to biofilm are large. Biofilm Approximation methods Homotopy analysis method Homotopy perturbation method Optimal homotopy analysis method Steady-states Cioch-Skoneczny, Monika verfasserin aut Enthalten in Chemical engineering research and design Amsterdam : Elsevier, 1983 139, Seite 309-320 Online-Ressource (DE-627)312841965 (DE-600)2008006-2 (DE-576)090893190 1744-3563 nnns volume:139 pages:309-320 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_206 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 58.10 Verfahrenstechnik: Allgemeines AR 139 309-320 |
allfields_unstemmed |
10.1016/j.cherd.2018.09.038 doi (DE-627)ELV000997455 (ELSEVIER)S0263-8762(18)30516-1 DE-627 ger DE-627 rda eng 540 660 DE-600 58.10 bkl Skoneczny, Szymon verfasserin (orcid)0000-0002-4549-7167 aut Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM). Monod and Haldane kinetic models were taken into consideration. Some unknown properties of these methods are presented. It was show that third-order approximation by HAM is more accurate than the method by Abbas and Eberl (2011) and Valdés-Parada et al. (2005). Additionally, the former is the same as for second-order HAM approximation. The accuracy of homotopy-based approximations is considerably influenced by external mass transfer resistances, expressed by the Biot number. The methods are especially useful for modelling bioreactors in which biofilm thicknesses are relatively small and coefficients of mass transfer from liquid to biofilm are large. Biofilm Approximation methods Homotopy analysis method Homotopy perturbation method Optimal homotopy analysis method Steady-states Cioch-Skoneczny, Monika verfasserin aut Enthalten in Chemical engineering research and design Amsterdam : Elsevier, 1983 139, Seite 309-320 Online-Ressource (DE-627)312841965 (DE-600)2008006-2 (DE-576)090893190 1744-3563 nnns volume:139 pages:309-320 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_206 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 58.10 Verfahrenstechnik: Allgemeines AR 139 309-320 |
allfieldsGer |
10.1016/j.cherd.2018.09.038 doi (DE-627)ELV000997455 (ELSEVIER)S0263-8762(18)30516-1 DE-627 ger DE-627 rda eng 540 660 DE-600 58.10 bkl Skoneczny, Szymon verfasserin (orcid)0000-0002-4549-7167 aut Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM). Monod and Haldane kinetic models were taken into consideration. Some unknown properties of these methods are presented. It was show that third-order approximation by HAM is more accurate than the method by Abbas and Eberl (2011) and Valdés-Parada et al. (2005). Additionally, the former is the same as for second-order HAM approximation. The accuracy of homotopy-based approximations is considerably influenced by external mass transfer resistances, expressed by the Biot number. The methods are especially useful for modelling bioreactors in which biofilm thicknesses are relatively small and coefficients of mass transfer from liquid to biofilm are large. Biofilm Approximation methods Homotopy analysis method Homotopy perturbation method Optimal homotopy analysis method Steady-states Cioch-Skoneczny, Monika verfasserin aut Enthalten in Chemical engineering research and design Amsterdam : Elsevier, 1983 139, Seite 309-320 Online-Ressource (DE-627)312841965 (DE-600)2008006-2 (DE-576)090893190 1744-3563 nnns volume:139 pages:309-320 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_206 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 58.10 Verfahrenstechnik: Allgemeines AR 139 309-320 |
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10.1016/j.cherd.2018.09.038 doi (DE-627)ELV000997455 (ELSEVIER)S0263-8762(18)30516-1 DE-627 ger DE-627 rda eng 540 660 DE-600 58.10 bkl Skoneczny, Szymon verfasserin (orcid)0000-0002-4549-7167 aut Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods 2018 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM). Monod and Haldane kinetic models were taken into consideration. Some unknown properties of these methods are presented. It was show that third-order approximation by HAM is more accurate than the method by Abbas and Eberl (2011) and Valdés-Parada et al. (2005). Additionally, the former is the same as for second-order HAM approximation. The accuracy of homotopy-based approximations is considerably influenced by external mass transfer resistances, expressed by the Biot number. The methods are especially useful for modelling bioreactors in which biofilm thicknesses are relatively small and coefficients of mass transfer from liquid to biofilm are large. Biofilm Approximation methods Homotopy analysis method Homotopy perturbation method Optimal homotopy analysis method Steady-states Cioch-Skoneczny, Monika verfasserin aut Enthalten in Chemical engineering research and design Amsterdam : Elsevier, 1983 139, Seite 309-320 Online-Ressource (DE-627)312841965 (DE-600)2008006-2 (DE-576)090893190 1744-3563 nnns volume:139 pages:309-320 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_206 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 58.10 Verfahrenstechnik: Allgemeines AR 139 309-320 |
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Skoneczny, Szymon ddc 540 bkl 58.10 misc Biofilm misc Approximation methods misc Homotopy analysis method misc Homotopy perturbation method misc Optimal homotopy analysis method misc Steady-states Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods |
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540 660 DE-600 58.10 bkl Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods Biofilm Approximation methods Homotopy analysis method Homotopy perturbation method Optimal homotopy analysis method Steady-states |
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mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods |
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Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods |
abstract |
Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM). Monod and Haldane kinetic models were taken into consideration. Some unknown properties of these methods are presented. It was show that third-order approximation by HAM is more accurate than the method by Abbas and Eberl (2011) and Valdés-Parada et al. (2005). Additionally, the former is the same as for second-order HAM approximation. The accuracy of homotopy-based approximations is considerably influenced by external mass transfer resistances, expressed by the Biot number. The methods are especially useful for modelling bioreactors in which biofilm thicknesses are relatively small and coefficients of mass transfer from liquid to biofilm are large. |
abstractGer |
Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM). Monod and Haldane kinetic models were taken into consideration. Some unknown properties of these methods are presented. It was show that third-order approximation by HAM is more accurate than the method by Abbas and Eberl (2011) and Valdés-Parada et al. (2005). Additionally, the former is the same as for second-order HAM approximation. The accuracy of homotopy-based approximations is considerably influenced by external mass transfer resistances, expressed by the Biot number. The methods are especially useful for modelling bioreactors in which biofilm thicknesses are relatively small and coefficients of mass transfer from liquid to biofilm are large. |
abstract_unstemmed |
Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM). Monod and Haldane kinetic models were taken into consideration. Some unknown properties of these methods are presented. It was show that third-order approximation by HAM is more accurate than the method by Abbas and Eberl (2011) and Valdés-Parada et al. (2005). Additionally, the former is the same as for second-order HAM approximation. The accuracy of homotopy-based approximations is considerably influenced by external mass transfer resistances, expressed by the Biot number. The methods are especially useful for modelling bioreactors in which biofilm thicknesses are relatively small and coefficients of mass transfer from liquid to biofilm are large. |
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Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods |
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|
score |
7.4003057 |