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

Gespeichert in:

Autor*in:	Skoneczny, Szymon [verfasserIn] Cioch-Skoneczny, Monika [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Biofilm Approximation methods Homotopy analysis method Homotopy perturbation method Optimal homotopy analysis method Steady-states

Übergeordnetes Werk:	Enthalten in: Chemical engineering research and design - Amsterdam : Elsevier, 1983, 139, Seite 309-320
Übergeordnetes Werk:	volume:139 ; pages:309-320

DOI / URN:	10.1016/j.cherd.2018.09.038

Katalog-ID:	ELV000997455

Internformat


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245	1	0	\|a Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods
264		1	\|c 2018
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337			\|a Computermedien \|b c \|2 rdamedia
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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
773	0	8	\|i Enthalten in \|t Chemical engineering research and design \|d Amsterdam : Elsevier, 1983 \|g 139, Seite 309-320 \|h Online-Ressource \|w (DE-627)312841965 \|w (DE-600)2008006-2 \|w (DE-576)090893190 \|x 1744-3563 \|7 nnns
773	1	8	\|g volume:139 \|g pages:309-320
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912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_101
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_206
912			\|a GBV_ILN_224
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
936	b	k	\|a 58.10 \|j Verfahrenstechnik: Allgemeines
951			\|a AR
952			\|d 139 \|h 309-320

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publishDate	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
allfieldsSound	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
language	English
source	Enthalten in Chemical engineering research and design 139, Seite 309-320 volume:139 pages:309-320
sourceStr	Enthalten in Chemical engineering research and design 139, Seite 309-320 volume:139 pages:309-320
format_phy_str_mv	Article
bklname	Verfahrenstechnik: Allgemeines
institution	findex.gbv.de
topic_facet	Biofilm Approximation methods Homotopy analysis method Homotopy perturbation method Optimal homotopy analysis method Steady-states
dewey-raw	540
isfreeaccess_bool	false
container_title	Chemical engineering research and design
authorswithroles_txt_mv	Skoneczny, Szymon @@aut@@ Cioch-Skoneczny, Monika @@aut@@
publishDateDaySort_date	2018-01-01T00:00:00Z
hierarchy_top_id	312841965
dewey-sort	3540
id	ELV000997455
language_de	englisch
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author	Skoneczny, Szymon
spellingShingle	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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topic_title	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
topic	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
topic_unstemmed	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
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title	Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods
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title_full	Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods
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title_sort	mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods
title_auth	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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title_short	Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods
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up_date	2024-07-06T19:52:41.405Z
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Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods

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