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Novel size effect in mesoscopic chemical oscillation systems

Novel size effect in mesoscopic chemical oscillation systems. Zhonghuai Hou ( 侯中怀 ) Sep. 2008, Hefei Department of Chemical Physics Hefei National Lab for Physical Sciences at Microscale University of Science & Technology of China. Our Research Interests.

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Novel size effect in mesoscopic chemical oscillation systems

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  1. Novel size effect in mesoscopic chemical oscillation systems Zhonghuai Hou (侯中怀) Sep. 2008, Hefei Department of Chemical Physics Hefei National Lab for Physical Sciences at Microscale University of Science & Technology of China

  2. Our Research Interests • Nonlinear Dynamics in Mesoscopic Chemical Systems • Dynamics of Complex Networks • Nonequilibrium Thermodynamics of Small Systems (Fluctuation Theorem) • Multiscale Modeling of Complex Systems Nonequilibrium +Nonlinear+ Complexity

  3. Outline • Introduction  the question • Optimal Size Effect • Stochastic Normal Form Theory • Conclusion

  4. 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 Nonequilibrium Statistical Mechanics

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

  6. We already know ... • Noise Induced Pattern Transition • Disorder sustained spiral waves • Taming Chaos by Topological Disorder • Ordering Bursting Chaos in Neuron Networks • Y. Gong,Z.Hou, H.Xin. ChemPhysChem 6，1042（2005）；M. M.Wang, Z.Hou, H.Xin. ChemPhysChem7，579( 2006); 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 systems

  7. Modeling of Chemical Oscillations • Macroscopic level: Deterministic, Cont. N Species, M reaction channels, well-stirred in V Reaction j: Rate: Hopf bifurcation leads to oscillation

  8. Modeling of Chemical Oscillations Exactly Kinetic Monte Carlo Simulation (KMC) Gillespie’s algorithm Approximately Internal Noise Deterministic equation • Mesoscopic Level: Stochastic, Discrete Master Equation

  9. New: Noise Induced Oscillation • A model system: The Brusselator Stochastic Deterministic FFT Noisy Oscillation

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

  11. Seems to be common … • Internal Noise Stochastic Resonance in a Circadian Clock SystemJ.Chem.Phys.119, 11508(2003) ? Common mechanism • 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) Analytical Study • Internal Noise Stochastic Resonance of syntheticgenenetwork Chem.Phys.Lett. 401,307(2005)

  12. Analytical study • Main idea Fact: all happens close to the HB Question: common features near HB? Answer: normal form on center manifold

  13. Analytical study • Stochastic Normal Form

  14. Analytical study • Stochastic Averaging

  15. Analytical study(…) • Probability distribution of r Fokker-Planck equation Stationary distribution Most probable radius Noise induced oscillation

  16. Analytical study(…) • Auto-correlation function

  17. Analytical study(…) • Power spectrum and SNR Optimal system size:

  18. Analytical study(…) Universal near HB System Dependent ChemPhysChem 7, 1520(July 2006) ; J. Phys.Chem.A 111, 11500(Nov. 2007); New J. Phys. 9, 403(Nov. 2007) ;

  19. System Size Bi-resonance System Size Biresonance for Intracellular Calcium Signaling J. Zhang, Z.H.Hou, H.W.Xin, ChemPhysChem 5, 1041(2004)

  20. System Size Bi-resonance Effects of Internal Noise for Rate Oscillation During CO Oxidation Z.Hou, T. Rao, H.Xin. J.Chem.Phys. 122，134708(2005)

  21. N个HH神经元的耦合体系 …… S S S S N Double System Size Resonance Log(S) Coupled Neuron Network: ChemPhysChem 5，1062(2004) Coupled Calcium Oscillation: Phye.Rev.E 74 031901(2006)

  22. 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 • System Bi-Resonance and Double System Size Resonance are observed

  23. Acknowledgements Supported by: National science foundation (NSF) Prof. Yubing Gong (龚玉兵 鲁东大学) Prof. Jiqian Zhang (张季谦 安徽师范大学) Maosheng Wang (汪茂胜 安徽师范大学) Zhiwei Wang (王志伟 天津科技大学) Tiejun Xiao (肖铁军) Juan Ma(马娟) Ting Rao(饶汀)

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