14:00
Forthcoming events in this series
14:00
14:00
Modelling interactions in spatially-structured systems to understand the division of labour in nitrification
14:00
The buckling of an axisymmetric vesicle under compression
14:00
Mathematical modelling of cancer and radiotherapy
14:00
Sickle hemoglobin fibers - the “Ising model” for fibrillisation diseases?
14:00
14:00
Swimming micro-organisms: bioconvection, flowfields and hydrogen
14:00
Natural variation modulates pattern formation mechanisms during skin development
14:00
Dynamics on networks: synchronization of oscillators in biology
14:00
Multiphase flow - a variety of applications, and some simple numerical techniques
14:00
Agent-based modelling of cell migration and angiogenesis
14:00
14:00
Stochastic models of cell cycle regulation in eukaryotes
14:00
13:00
Self-simplification and 0-1 laws in multiscale reaction networks
Abstract
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 are computationally cheap and robust. Some of results obtained are rather surprising and unexpected. First of all is the zero-one asymptotic of eigenvectors (asymptotically exact lumping; but these asymptotic lumps could intersect). Our main mathematical tools are auxiliary discrete dynamical systems on finite sets and specially developed algorithms of ``cycles surgery"
for reaction graphs. Roughly speaking, the dynamics of linear multiscale networks transforms into the dynamics on finite sets of reagent names.
A.N. Gorban and O. Radulescu, Dynamic and static limitation in multiscale reaction networks, Advances in Chemical Engineering, 2008 (in press), arXiv e-print: http://arxiv.org/abs/physics/0703278
A.N. Gorban and O. Radulescu, Dynamical robustness of biological networks with hierarchical distribution of time scales, IET Syst.
Biol., 2007, 1, (4), pp. 238-246.
13:00
Angiogenesis and vascular remodelling in normal and cancerous tissues
13:00