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Nonlinear Dynamics in Mesoscopic Chemical Systems

Nonlinear Dynamics in Mesoscopic Chemical Systems. Zhonghuai Hou ( 侯中怀 ) Department of Chemical Physics Hefei National Lab of Physical Science at Microscale University of Science & Technology of China. Nonlinear Chemical Dynamics. Stationary spatial structures in reaction-diffusion systems.

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Nonlinear Dynamics in Mesoscopic Chemical Systems

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  1. Nonlinear Dynamics in Mesoscopic Chemical Systems Zhonghuai Hou (侯中怀) Department of Chemical Physics Hefei National Lab of Physical Science at Microscale University of Science & Technology of China

  2. Nonlinear Chemical Dynamics Stationary spatial structures in reaction-diffusion systems Two or more stable states under same external constraints Travelling/Target/Spiral/Soliton … waves Temporally Periodic Variations of Concentrations Aperiodic/Initial condition sensitivity/strange attractor… Strange Attractor The Lorenz System Chemical turbulence CO+O2 on Pt Surface Science 2001 Turing Pattern BZ Reaction System PNAS 2003 Synthetic transcriptional oscillator (Repressilator) Nature 2002 Calcium Spiral Wave in Cardiac Tissues Nature 1998 Reactive/Inactive bistabe CO+O2 on Pt filed tip PRL1999 Genetic Toggle Switch In E. Coli Nature 2000 Cellular Pattern CO Oxidation on Pt PRL 2001 Rate Oscillation CO+O2 Nano-particle Catal.Today 2003 PEEM Image CO Oxidation on Pt PRL 1995 • far-from equilibrium, self-organized, complex, spatio-temporal structures • Oscillation • Multistability • Patterns • Waves • Chaos Collective behavior involving many molecular units

  3. Mesoscopic Reaction Systems Molecular Fluctuation N, V (Small) ? Nonlinear Chemical Dynamics • Heterogeneous catalysis - field emitter tips - nanostructured composite surface - small metal particles • Sub-cellular reactions - gene expression - ion-channel gating - calcium signaling ……

  4. Noise/Disorder • Noise Induced Pattern Transition • Disorder sustained spiral waves • Taming Chaos by Topological Disorder Z.Hou, et al., PRL 81, 2854 (1998) Z.Hou, et al., PRL 89, 280601 (2002) F. Qi, Z.Hou, H. Xin, PRL 91, 064102 (2003) • Noise and disorder play constructive roles in nonlinear dynamical systems

  5. Stochastic Chemical Kinetics stochastic state variable probability distribution • chemical reactions are essentially stochastic, discrete processes Discrete Brownian Motion of X : Prob. Evolution: Master equation Sample Trajectory: Langevin equation

  6. Chemical Langevin equation (CLE) • Molecular fluctuation (Internal noise) N Species, M reaction channels, well-stirred in V Reaction j: Rate: • Deterministic kinetics for • Each channel contributes independently to internal noise: • Fast numerical simulation

  7. The Brusselator • Deterministic bifurcation Fixed Point: Hopf bifurcation:

  8. Noise Induced Oscillation • Stochastic dynamics FFT

  9. Optimal System Size Optimal System size for mesoscopic chemical oscillation Z. Hou, H. Xin. ChemPhysChem 5, 407(2004)

  10. Seems to be common … • Internal Noise Stochastic Resonance in a Circadian Clock SystemJ.Chem.Phys.119, 11508(2003) • System size bi-resonance for intracellularcalcium signaling ChemPhysChem 5, 1041(2004) • Double-System-Size resonance for spiking activity of coupledHHneurons ChemPhysChem 5, 1602(2004) • Optimal Particle Size for Rate Oscillation in COOxidationonNanometer-SizedPalladium(Pd) Particles J.Phys.Chem.B 108, 17796(2004) • Effects of Internal Noise for rate oscillations during CO oxidation on platinum(Pt) surfaces J.Chem.Phys.122, 134708(2005) • Internal Noise Stochastic Resonance of syntheticgenenetwork Chem.Phys.Lett. 401,307(2005)

  11. Analytical study • Stochastic Normal Form

  12. Analytical study • Stochastic Averaging

  13. Analytical study • Probability distribution of r Fokker-Planck equation Stationary distribution Most probable radius Noise induced oscillation

  14. Analytical study • Auto-correlation function

  15. Analytical study • Power spectrum and SNR Optimal system size:

  16. Analytical study Universal near HB System Dependent Internal Noise Coherent Resonance for Mesoscopic Chemical oscillations: a Fundamental Study. Z. Hou, … ChemPhysChem 7, 1520(2006)

  17. Summary • In mesoscopic chemical systems, molecular fluctuations can induce oscillation even outside the deterministic oscillatory region • Optimal system size exists, where the noise-induced oscillation shows the best performance, characterized by a maximal SNR, a trade off between strength and regularity • Based on stochastic normal form, analytical studies show rather good agreements with the simulation results, uncovering the mechanism of NIO and OSS

  18. Further questions

  19. Acknowledgements Supported by: National science foundation (NSF) Fok Yin Dong education foundation Thank you

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