Skip to main content

Discrete and Continuum Dynamics of Reacting and Interacting Individuals

  • Chapter
Collective Dynamics from Bacteria to Crowds

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 553))

  • 1063 Accesses

Abstract

These lectures review some recent decades’ research on non equilibrium statistical mechanics models of reaction and interaction kinetics. Lectures 1-4 focus on macroscopic kinetics of microscopically transport-limited interactions, while lectures 5 and 6 are concerned with discreteness and stochastic effects in reaction-diffusion fronts. The final lecture 7 considers demographic stochasticity in evolutionary population dynamics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • D. ben Avraham. Complete exact solution of a diffusion-limited coalescence, A + A → A. Physical Review Letters, 81(21):4756–4759, 1998.

    Google Scholar 

  • D. ben Avraham and C. R. Doering. Equilibrium of two-species annihilation with input. Physical Review A, 37(12):5007–5009, 1988.

    Google Scholar 

  • D. ben Avraham, M. A. Burschka, and C. R. Doering. Statics and dynamics of a diffusion-limited reaction: Anomalous kinetics, nonequilibrium selfordering, and a dynamic transition. Journal of Statistical Physics, 60: 695–728, 1990.

    Google Scholar 

  • O. BĂ©nichou, C. Chevalier, J. Klafter, B. Meyer, and R. Voituriez. Geometry-controlled kinetics. Nature Chemistry, 2:472, 2010.

    Google Scholar 

  • M. Bramson. Convergence of solutions of the Kolmogorov equations to traveling waves. Memoires of the American Mathematical Society, 44, 1983.

    Google Scholar 

  • M. Bramson and L. Lebowitz. Asymptotic behavior of densities for twoparticle annihilating random walks. Journal of Statistical Physics, 62: 297–372, 1991.

    Google Scholar 

  • E. Brunet and B. Derrida. Shift in the velocity of a front due to a cutoff. Physical Review E, 56(3):2597–2604, 1997.

    Google Scholar 

  • E. ClĂ©ment, L. M. Sander, and R. Kopelman. Steady-state diffusioncontrolled A + B → 0 reactions in two and three dimensions: Rate laws and particle distributions. Physical Review A, 39(12):6466–6471, 1989.

    Google Scholar 

  • C. R. Doering and M. A. Burschka. Long crossover times in a finite system. Physical Review Letters, 64(3):245–248, 1990.

    Google Scholar 

  • C. R. Doering, M. A. Burschka, and W. Horsthemke. Fluctuations and correlations in a diffusion-reaction system: Exact hydrodynamics. Journal of Statistical Physics, 65:953–970, 1991.

    Google Scholar 

  • C. R. Doering, C. Mueller, and P. Smereka. Interacting particles, the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, and duality. Physica A, 325:243–259, 2003.

    Google Scholar 

  • C. R. Doering, K. V. Sargsyan, and L. M. Sander. Extinction times for birthdeath processes. SIAM Journal on Multiscale Modeling and Simulation, 3:283–299, 2005a.

    Google Scholar 

  • C. R. Doering, K. V. Sargsyan, and P. Smereka. A numerical method for some stochastic differential equations with multiplicative noise. Physics Letters A, 344:149–155, 2005b.

    Google Scholar 

  • U. Ebert and W. van Saarloos. Front propagation into unstable states: universal algebraic convergence toward uniformly translating pulled fronts. Physica D, 146:1–99, 2000.

    Google Scholar 

  • D. A. Kessler, Z. Ner, and L. M. Sander. Front propagation: Precursors, cutoffs, and structural stability. Physical Review E, 58(1):107–114, 1998.

    Google Scholar 

  • R. Kopelman. Fractal reaction kinetics. Science, 241:1620–1626, 1988.

    Google Scholar 

  • R. Kroon, H. Fleurent, and R. Sprik. Diffusion-limited exciton fusion reaction in one-dimensional tetramethylammonium manganese trichloride (TMMC). Physical Review E, 47:2462–2472, 1993.

    Google Scholar 

  • Y. T. Lin, H. Kim, and C. R. Doering. Features of fast living: On the weak selection for longevity in degenerate birth-death progresses. Journal of Statistical Physics, 148:646–662, 2012.

    Google Scholar 

  • E. Monson and Raoul Kopelman. Observation of laser speckle effects and nonclassical kinetics in an elementary chemical reaction. Physical Review Letters, 85(3):666–669, 2000.

    Google Scholar 

  • C. Mueller and R. B. Sowers. Random traveling waves for the KPP equation with noise. Journal of Functional Analysis, 128, 1995.

    Google Scholar 

  • C. Mueller, L. Mytnik, and J. Quastel. Effect of noise on front propagation in reaction-diffusion equations of KPP type. Inventiones Mathematicae, 184:405–453, 2011.

    Google Scholar 

  • A. A. Ovchinnikov and Ya. B. Zeldovich. Role of density fluctuations in bimolecular reaction kinetics. Chemical Physics, 28:215–218, 1978.

    Google Scholar 

  • L. Pechenik and H. Levine. Interfacial velocity corrections due to multiplicative noise. Physical Review E, 59(4):3893–3900, 1999.

    Google Scholar 

  • D. Toussaint and F. Wilczek. Particle-antiparticle annihilation in diffusive motion. J. Chem. Phys., 78:2642–2647, 1983.

    Google Scholar 

  • J. N. Waddell, L. M. Sander, and C. R. Doering. Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers. Theoretical Population Biology, 77:279–286, 2010.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 CISM, Udine

About this chapter

Cite this chapter

Tesser, F., Doering, C.R. (2014). Discrete and Continuum Dynamics of Reacting and Interacting Individuals. In: Muntean, A., Toschi, F. (eds) Collective Dynamics from Bacteria to Crowds. CISM International Centre for Mechanical Sciences, vol 553. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1785-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-1785-9_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-1784-2

  • Online ISBN: 978-3-7091-1785-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics