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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 ) Department of Chemical Physics Hefei National Lab of Physical Science at Microscale University of Science & Technology of China. 电子结构理论 量子力学 结果 ：反应个体的物理化学性质；基本参数. 统计行为 统计 + 唯象 结果 ：宏观量时空演化行为 －实际体系功能.

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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) Department of Chemical Physics Hefei National Lab of Physical Science at Microscale University of Science & Technology of China

  2. 电子结构理论 量子力学 结果：反应个体的物理化学性质；基本参数 统计行为 统计+唯象 结果：宏观量时空演化行为 －实际体系功能 理论化学的三个层面 • 反应动力学 量子+统计 结果：反应势能面，反应途径，速率常数 夸克 美洲豹

  3. 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

  4. 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 ……

  5. Why 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 nonequilibrium systems

  6. 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

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

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

  9. Optimal System Size Best performance 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) ? 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)

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

  12. Analytical study • Stochastic Normal Form

  13. Analytical study • Stochastic Averaging

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

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

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

  17. 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) ;

  18. Entropy Production? • Macroscopic Level: Nonequilibrium Statistical Thermodynamics I. Prigogine 1970s

  19. Entropy Production? • Mesoscopic Level: Stochastic Thermodynamics Luo,Nicolis 1984; P.Gaspard 2004

  20. Entropy Production? • Single Trajectory Level: Dynamic Irreversibity A Random Trajectory Trajectory Entropy Total Entropy Change U. Seifert, PRL 2005

  21. Fluctuation Theorems ! • Integrate FT • Detailed FT(NESS)

  22. Application to Brusselator • Detailed FT holds

  23. Application to Brusselator • System Size Dependence Simulation SNF Theory

  24. Summary • Noise Induced Oscillation  Stochastic Modeling is important • Optimal system size  Noise + Nonlinearity • Success Analytical Study  Universality + Underlying mechanism • Fluctuation Theorem  Single Trajectory Thermodynamics + Dynamic Irreversibility

  25. Future directions Thermodynamics Size dependence Jarzynski equality Fluctuation theorems… Dynamics Nucleation and growth Transport/relaxation Nonlinear dynamics… • How does fluctuation influence the properties of small chemical systems Statistical physics in mesoscopic chemical systems

  26. Acknowledgements Supported by: National science foundation (NSF) Thank you

  27. Details

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