dorsal/arxiv
View SchemaDynamic and static limitation in multiscale reaction networks, revisited
| Authors | A. N. Gorban, O. Radulescu |
|---|---|
| Categories | |
| ArXiv ID | physics/0703278 |
| URL | https://arxiv.org/abs/physics/0703278 |
| DOI | 10.1016/S0065-2377(08)00003-3 |
| Journal | Advances in Chemical Engineering, Volume 34 (2008), 103-173 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
The concept of limiting step gives the limit simplification: the whole network behaves as a single step. However, in its simplest form this idea is applicable only to the simplest linear cycles in steady states. For such the simplest cycles the nonstationary behaviour is also limited by a single step, but not the same step that limits the stationary rate. We develop a general theory of static and dynamic limitation for all linear multiscale networks. New estimates of eigenvectors for diagonally dominant matrices are used. Multiscale ensembles of reaction networks with well separated constants are introduced and typical properties of such systems are studied. For any given ordering of reaction rate constants the explicit approximation of steady state, relaxation spectrum and related eigenvectors ("modes") is presented. The obtained multiscale approximations that we call "dominant systems" are computationally cheap and robust. These dominant systems can be used for direct computation of steady states and relaxation dynamics, especially when kinetic information is incomplete, for design of experiments and mining of experimental data, and could serve as a robust first approximation in perturbation theory or for preconditioning.
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"abstract": "The concept of limiting step gives the limit simplification: the whole\nnetwork behaves as a single step. However, in its simplest form this idea is\napplicable only to the simplest linear cycles in steady states. For such the\nsimplest cycles the nonstationary behaviour is also limited by a single step,\nbut not the same step that limits the stationary rate. We develop a general\ntheory of static and dynamic limitation for all linear multiscale networks. New\nestimates of eigenvectors for diagonally dominant matrices are used.\n Multiscale ensembles of reaction networks with well separated constants are\nintroduced and typical properties of such systems are studied. For any given\nordering of reaction rate constants the explicit approximation of steady state,\nrelaxation spectrum and related eigenvectors (\"modes\") is presented. The\nobtained multiscale approximations that we call \"dominant systems\" are\ncomputationally cheap and robust. These dominant systems can be used for direct\ncomputation of steady states and relaxation dynamics, especially when kinetic\ninformation is incomplete, for design of experiments and mining of experimental\ndata, and could serve as a robust first approximation in perturbation theory or\nfor preconditioning.",
"arxiv_id": "physics/0703278",
"authors": [
"A. N. Gorban",
"O. Radulescu"
],
"categories": [
"physics.chem-ph",
"physics.comp-ph"
],
"doi": "10.1016/S0065-2377(08)00003-3",
"journal_ref": "Advances in Chemical Engineering, Volume 34 (2008), 103-173",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Dynamic and static limitation in multiscale reaction networks, revisited",
"url": "https://arxiv.org/abs/physics/0703278"
},
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