The passive polymer problem

Journal of Statistical Physics

Volumn 101, Issue 3-4, 2000, Pages 843-891

  Wiese, Kay Jörg ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

Multiscaling; Passive advection; Passive scalar; Polymer; Polymerized membrane; Renormalization group; Turbulence

Indexed keywords

EID: 0034310029     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1026473504422     Document Type: Article

References (49)

1. A. N. Kolmogorov, On the energy distribution in the spectrum of a turbulent flow, C. R. Acad. Sci. URSS 30:301-305 (1941).
2. A. M. Oboukhov, Some specific featues of atmoshperic turbulence, J. Fluid Mech. 13: 77-81 (1962).
3. A. N. Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high reynolds number, J. Fluid Mech. 13:82-85 (1962).
4. A. M. Obukhov, Izv. Akad. Nauk. SSSR, Geogr. Geofiz. 13:58 (1949).
5. R. H. Kraichnan, Small-scale structure of a scalar field convected by turbulence, Phys. Fluids 11:945-953 (1968).
6. S. Chen and R. H. Kraichnan, Sweeping decorrelation in isotropic turbulence, Phys. Fluids A 1:2019-2024 (1998).
7. K. Gawedzki and A. Kupiainen, Anomalous scaling of the passive scalar, Phys. Rev. Lett. 75:3834 (1995).
8. K. Gawedzki and A. Kupiainen, Universality in turbulence: An exactly soluble model, cond-mat/9504002 (1995).
9. M. Chertkov, G. Falkovich, I. Kolokolov, and V Lebedev, Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar, Phys. Rev. E 52:4924-4941 (1995).
10. R. H. Kraichnan, V. Yakhot, and S. Chen, Scaling relations for a randomly advected passive scalar field, Phys. Rev. Lett. 75:240-243 (1995).
11. M. Chertkov and G. Falkovich, Anomalous scaling of a white advected passive scalar, Phys. Rev. Lett. 76:2706 (1996).
12. D. Bernard, K. Gawȩdzki, and A. Kupiainen, Anomalous scaling in the n-point functions of a passive scalar, Phys. Rev. E 54:2564-2572 (1996).
13. B. I. Shraiman and E. D. Siggia, Symmetry and scaling of turbulent mixing. Phys. Rev. Lett. 77:2466 (1996).
14. M. Chertkov, G. Falkovich, and V. Lebedev, Non-universality of the scaling exponents of a passive scalar converted by a random flow, Phys. Rev. E 52:4924 (1995).
15. E. Balkovsky and V. Lebedev, Instanton for the Kraichnan passive scalar problem, Phys. Rev. E 58:5776 (1998).
16. L. T. Adzhemyan, N. V. Antonov, and A. N. Vasil'ev, Renormalization group, operator product expansion, and anomalous scaling in a model of advected passive scalar. Phys. Rev. E 58:1823-1835 (1998).
17. VS. L'vov, I. Procaccia, and AL. Fairhall, Anomalous scaling in fluid mechanics: The case of the passive scalar, Phys. Rev. E 50:4684-4704 (1994).
18. AL. Fairhall, O. Gat, V L'vov, and I. Procaccia, Anomalous scaling in a model of passive scalar advection: Extict results, Phys. Rev. E 53:3518-3535 (1996).
19. O. Gat, VS. L'vov, and I. Procaccia, Perturbative and nonperturbative analysis of the third-order zero modes in the Kraichnan model for turbulent advection, Phys. Rev. E 56:406-416 (1997).
20. O. Gat, VS. L'vov, E. Podivilov, and I. Procaccia, Nonperturbative zero modes in the Kraichnan model for turbulent advection. Phys. Rev. E 55:R3836-3839 (1997).
21. AL. Fairhall, B. Galanti, VS. L'vov, and I. Procaccia, Direct numerical simulations of the Kraichnan model: Scaling exponents and fusion rules, Phys. Rev. Lett. 79:4166-4169 (1997).
22. D. Bernard, K. Gawedzki and A. Kupiainen, Slow modes in passive advection, J. Stat. Phys. 90:519-569 (1998).
23. S. Chen and RH. Kraichnan, Simulations of a randomly advected passive scalar field, Phys. Fluids 10:2867-2884 (1998).
24. K. Gawȩdzki and M. Vergassola, Phase transition in the passive scalar advection, Physica D 138:63 (2000).
25. O. Gat and R. Zeitak, Multiscaling in passive scalar advection as stochastic shape dynamics, Phys. Rev. E 57:5511-5519 (1998).
26. O. Gat, I. Procaccia, and R. Zeitak, Anomalous scaling in passive scalar advection: Monte carlo Lagrangian trajectories, Phys. Rev. Lett. 80:5536-5539 (1998).
27. U. Frisch, A. Mazzino, A. Noullez, and M. Vergassola, Lagrangian method for multiple correlations in passive scalar advection, Phys. Fluids 11:2178-2186 (1999).
28. L. D. Landau and I. M. Lifshitz, Hydrodynamik, Lehrbuch der Theoretischen Physik (Akademie-Verlag, Berlin, 1991), Vol. 6.
29. P. C. Martin, E. D. Siggia, and H. A. Rose, Statistical dynamics of classical systems, Phys. Rev. A 8:423-437 (1973).
30. H. K. Janssen, On the renormalized field theory of nonlinear critical relaxation, in From Phase Transitions to Chaos. Topics in Modern Statistical Physics (World Scientific, Singapore, 1992), pp. 68-117.
31. K. J. Wiese, On the perturbation expansion of the KPZ-equation, J. Stat. Phys. 93: 143-154 (1998).
32. N. V. Antonov, Anomalous scaling regimes of a passive scalar advected by the synthetic velocity Held. Phys. Rev. E 60:6691 (1999).
33. J. Zinn-Justin. Quantum Field Theory and Critical Phenomena (Oxford University Press, Oxford, 1989).
34. F. David, B. Duplantier, and E. Guitter, Renormalization and hyperscaling for self-avoiding manifold models, Phys. Rev. Lett. 72:311 (1994).
35. F. David, B. Duplantier, and E. Guitter, Renormalization theory for the self-avoiding polymerized membranes, cond-mat/9702136 (1997).
36. K. J. Wiese and K. David, New renormalization group results for scaling of sell-avoiding tethered membranes, Nucl. Phys. B 487:529-632 (1997).
37. K. J. Wiese, Dynamics of selfavoiding tethered membranes I, model A dynamics (Rouse model), Eur. Phys. J. B 1:269-272 (1998).
38. K. J. Wiese, Dynamics of selfavoiding tethered membranes II, inclusion of hydrodynamic interactions (Zimm model), Eur. Phys. J. B 1:273-276 (1998).
39. K. J. Wiese and P. Le Doussal, Polymers and manifolds in static random flows: A RG study, Nucl. Phys. B 552:529-598 (1999).
40. K. J. Wiese, Polymerized Membranes, a Review, Habilitations-Schrift, Universität Essen, published in Vol. 19 of Phase Transitions and Critical Phenomena, C. Domb and J. Lobowitz, eds. (Acadamic Press, London, 2000).
41. U. Frisch, A. Mazzino, and M. Vergassola, Intermittency in passive scalar advection, Phys. Rev. Lett. 80:5532-5535 (1998).
42. Y Kantor, M. Kardar, and D. R. Nelson, Statistical mechanics of tethered surfaces, Phys. Rev. Lett. 57:791-795 (1986).
43. Y Kantor, M. Kardar, and D. R. Nelson, Tethered surfaces: Statics and dynamics, Phys. Rev. A 35:3056-3071 (1987).
44. S. F. Edwards, The statistical mechanics of polymers with excluded volume, Proc. Phys. Soc. 85:613 (1965).
45. D. Bonn, Y. Couder, P. H. J. van Dam, and S. Douady, From small scales to large scales in three-dimensional turbulence: The effect of diluted polymers, Phys. Rev. 47-R28-31 (1993).
46. O. Cadot, D. Bonn, and S. Douady, Turbulent drag reduction in a closed flow system: Boundary layer versus bulk effects, Phys. of Fluids 10:426-436 (1998).
47. D. Nelson, in ref. 49.
48. B. H. Zimm, Dynamics of polymer molecules in dilute solutions: Viscoelasticity, flow birefringence and dielectric loss, J. Chem. Phys. 24:269 (1956).
49. D. R. Nelson, T. Piran, and S. Weinberg, eds., Statistical mechanics of membranes and surfaces, in Proceedings of the Fifth Jerusalem Winter School for Theoretical Physics (World Scientific, Singapore, 1989).