Travelling waves in an open cubic autocatalytic system
Abstract A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spat...
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| Autor*in: |
Sadiq, M. A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1996 |
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| Schlagwörter: |
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| Anmerkung: |
© J.C. Baltzer AG, Science Publishers 1996 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of mathematical chemistry - Kluwer Academic Publishers, 1987, 20(1996), 2 vom: Sept., Seite 213-233 |
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| Übergeordnetes Werk: |
volume:20 ; year:1996 ; number:2 ; month:09 ; pages:213-233 |
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| DOI / URN: |
10.1007/BF01165344 |
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| 520 | |a Abstract A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter σ δDA/DB (DA,DB being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that σ≲4, a result confirmed by numerical integrations of an initial-value problem. For values of σ larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration. | ||
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10.1007/BF01165344 doi (DE-627)OLC2060402417 (DE-He213)BF01165344-p DE-627 ger DE-627 rakwb eng 510 540 VZ Sadiq, M. A. verfasserin aut Travelling waves in an open cubic autocatalytic system 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Science Publishers 1996 Abstract A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter σ δDA/DB (DA,DB being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that σ≲4, a result confirmed by numerical integrations of an initial-value problem. For values of σ larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration. Physical Chemistry Diffusion Coefficient Stationary State Front Wave Dimensionless Parameter Merkin, J. H. aut Enthalten in Journal of mathematical chemistry Kluwer Academic Publishers, 1987 20(1996), 2 vom: Sept., Seite 213-233 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:20 year:1996 number:2 month:09 pages:213-233 https://doi.org/10.1007/BF01165344 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_4012 GBV_ILN_4027 AR 20 1996 2 09 213-233 |
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10.1007/BF01165344 doi (DE-627)OLC2060402417 (DE-He213)BF01165344-p DE-627 ger DE-627 rakwb eng 510 540 VZ Sadiq, M. A. verfasserin aut Travelling waves in an open cubic autocatalytic system 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Science Publishers 1996 Abstract A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter σ δDA/DB (DA,DB being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that σ≲4, a result confirmed by numerical integrations of an initial-value problem. For values of σ larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration. Physical Chemistry Diffusion Coefficient Stationary State Front Wave Dimensionless Parameter Merkin, J. H. aut Enthalten in Journal of mathematical chemistry Kluwer Academic Publishers, 1987 20(1996), 2 vom: Sept., Seite 213-233 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:20 year:1996 number:2 month:09 pages:213-233 https://doi.org/10.1007/BF01165344 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_4012 GBV_ILN_4027 AR 20 1996 2 09 213-233 |
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10.1007/BF01165344 doi (DE-627)OLC2060402417 (DE-He213)BF01165344-p DE-627 ger DE-627 rakwb eng 510 540 VZ Sadiq, M. A. verfasserin aut Travelling waves in an open cubic autocatalytic system 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Science Publishers 1996 Abstract A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter σ δDA/DB (DA,DB being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that σ≲4, a result confirmed by numerical integrations of an initial-value problem. For values of σ larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration. Physical Chemistry Diffusion Coefficient Stationary State Front Wave Dimensionless Parameter Merkin, J. H. aut Enthalten in Journal of mathematical chemistry Kluwer Academic Publishers, 1987 20(1996), 2 vom: Sept., Seite 213-233 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:20 year:1996 number:2 month:09 pages:213-233 https://doi.org/10.1007/BF01165344 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_4012 GBV_ILN_4027 AR 20 1996 2 09 213-233 |
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10.1007/BF01165344 doi (DE-627)OLC2060402417 (DE-He213)BF01165344-p DE-627 ger DE-627 rakwb eng 510 540 VZ Sadiq, M. A. verfasserin aut Travelling waves in an open cubic autocatalytic system 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Science Publishers 1996 Abstract A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter σ δDA/DB (DA,DB being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that σ≲4, a result confirmed by numerical integrations of an initial-value problem. For values of σ larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration. Physical Chemistry Diffusion Coefficient Stationary State Front Wave Dimensionless Parameter Merkin, J. H. aut Enthalten in Journal of mathematical chemistry Kluwer Academic Publishers, 1987 20(1996), 2 vom: Sept., Seite 213-233 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:20 year:1996 number:2 month:09 pages:213-233 https://doi.org/10.1007/BF01165344 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_4012 GBV_ILN_4027 AR 20 1996 2 09 213-233 |
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10.1007/BF01165344 doi (DE-627)OLC2060402417 (DE-He213)BF01165344-p DE-627 ger DE-627 rakwb eng 510 540 VZ Sadiq, M. A. verfasserin aut Travelling waves in an open cubic autocatalytic system 1996 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © J.C. Baltzer AG, Science Publishers 1996 Abstract A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter σ δDA/DB (DA,DB being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that σ≲4, a result confirmed by numerical integrations of an initial-value problem. For values of σ larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration. Physical Chemistry Diffusion Coefficient Stationary State Front Wave Dimensionless Parameter Merkin, J. H. aut Enthalten in Journal of mathematical chemistry Kluwer Academic Publishers, 1987 20(1996), 2 vom: Sept., Seite 213-233 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:20 year:1996 number:2 month:09 pages:213-233 https://doi.org/10.1007/BF01165344 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_11 GBV_ILN_40 GBV_ILN_70 GBV_ILN_4012 GBV_ILN_4027 AR 20 1996 2 09 213-233 |
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Abstract A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter σ δDA/DB (DA,DB being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that σ≲4, a result confirmed by numerical integrations of an initial-value problem. For values of σ larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration. © J.C. Baltzer AG, Science Publishers 1996 |
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Abstract A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter σ δDA/DB (DA,DB being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that σ≲4, a result confirmed by numerical integrations of an initial-value problem. For values of σ larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration. © J.C. Baltzer AG, Science Publishers 1996 |
| abstract_unstemmed |
Abstract A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter σ δDA/DB (DA,DB being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that σ≲4, a result confirmed by numerical integrations of an initial-value problem. For values of σ larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration. © J.C. Baltzer AG, Science Publishers 1996 |
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Travelling waves in an open cubic autocatalytic system |
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Merkin, J. H. |
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