Interacting particle systems in time-dependent geometries

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2013, Issue 9, 2013, Pages

  Ali, A ^a   Ball, R ^a   Grosskinsky, S ^a   Somfai, E ^a,b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

coarsening processes (theory); diffusion; kinetic growth processes (theory); stochastic particle dynamics (theory)

Indexed keywords

EID: 84885128420     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2013/09/P09006     Document Type: Article

References (51)

1. Witten T A and Sander L M 1981 Diffusion-limited aggregation, a kinetic critical phenomenon Phys. Rev. Lett. 47 1400
2. Stanley H E, Bunde A, Havlin S, Lee J, Roman E and Schwarzer S 1990 Dynamic mechanisms of disorderly growth: recent approaches to understanding diffusion limited aggregation Physica A 168 23
3. Stanley H E, Coniglio A, Havlin S, Lee J, Schwarzer S and Wolf M 1994 Diffusion limited aggregation: a paradigm of disorderly cluster growth Physica A 205 254
4. Saito Y and Müller-Krumbhaar H 1995 Critical phenomena in morphology transitions of growth models with competition Phys. Rev. Lett. 74 4325
5. Saffman P G and Taylor G 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous fluid Proc. R. Soc. A 245 312
6. Paterson L 1981 Radial fingering in a Hele Shaw cell J. Fluid Mech. 113 513
7. Thome H, Rabaud M, Hakim V and Couder Y 1989 The Saffman-Taylor instability: from the linear to the circular geometry Phys. Fluids A 1 224
8. Hallatschek O, Hersen P, Ramanathan S and Nelson D R 2007 Genetic drift at expanding frontiers promotes gene segregation Proc. Nat. Acad. Sci. USA 104 19926
9. Korolev K S, Avlund M, Hallatschek O and Nelson D R 2010 Genetic demixing and evolution in linear stepping stone models Rev. Mod. Phys. 82 1691
10. Somfai E and Sander L M 1997 Scaling and river networks: a Landau theory for erosion Phys. Rev. E 56 R5
11. Barabasi A L and Stanley H E 1995 Fractal Concepts in Surface Growth 1st edn (Cambridge: Cambridge University Press)
12. Ali A and Grosskinsky S 2010 Pattern formation through genetic drift at expanding population fronts Adv. Complex Syst. 13 349
13. Ali A, Somfai E and Grosskinsky S 2012 Reproduction-time statistics and segregation patterns in growing populations Phys. Rev. E 85 021923
14. Bunde A and Havlin S 1995 Fractals and Disordered Systems 2nd edn (Berlin: Springer)
15. Kopelman R 1988 Fractal reaction kinetics Science 241 1620
16. Kurz W and Fisher D J 1989 Fundamentals of Solidification 1st edn
17. Jacob C 2010 Branching processes: their role in epidemiology Int. J. Environ. Res. Public Health 7 1186
18. Murray J D 2003 Mathematical Biology II: Spatial Models and Biomedical Applications 3rd edn (Berlin: Springer)
19. Mandelbrot B B 1982 The Fractal Geometry of Nature 1st edn (San Francisco: Freeman)
20. Lehe R, Hallatschek O and Peliti L 2012 The rate of beneficial mutations surfing on the wave of a range expansion PLoS Comput. Biol. 8 e1002447
21. Lebovka N I and Vygornitskii N V 1998 How does the geometry affect the criticality in two-component spreading phenomena? J. Phys. A: Math. Gen. 31 9199 (Pubitemid 128160987)
22. Eden M 1961 A two-dimensional growth process Proc. 4th Berkeley Symp. on Maths, Statistics and Probility vol 4 pp 223-39
23. Munasinghe R, Rajesh R, Tribe R and Zaboronski O 2006 Multi-scaling of the n-point density function for coalescing brownian motions Commun. Math. Phys. 268 717 (Pubitemid 44630354)
24. Alemany P A and ben-Avraham D 1995 Inter-particle distribution functions for one-species diffusion-limited annihilation, A + A → 0 Phys. Lett. A 206 18
25. Kazuo S and Tomohiro N 2000 Exact results for a diffusion-limited pair annihilation process on a one-dimensional lattice J. Phys. Soc. Japan 69 1341
26. Masser T O and ben-Avraham D 2001 Method of intervals for the study of diffusion-limited annihilation, A + A → 0 Phys. Rev. E 63 066108
27. Ali A, Ball R C, Grosskinsky S and Somfai E 2013 Scale-invariant growth processes in expanding space Phys. Rev. E 87 020102
28. Pazsit I and Pal L 2007 Neutron Fluctuations: A Treatise on the Physics of Branching Processes 1st edn
29. Biagini F, Hu Y, Øksendal B and Zhang T 2008 Stochastic Calculus for Fractional Brownian Motion and Applications 1st edn (Berlin: Springer)
30. Chechkin A V, Metzler R, Klafter J and Gonchar V Y 2008 Introduction to the Theory of Lévy Flights Wiley-VCH
31. Lavrentovich M O, Korolev K S and Nelson D R 2013 Radial Domany-Kinzel models with mutation and selection Phys. Rev. E 87 012103
32. Abe S and Okamoto Y 2001 Nonextensive Statistical Mechanics and its Applications (Berlin: Springer)
33. Øksendal B 2003 Stochastic Differential Equations: An Introduction with Applications 6th edn (Berlin: Springer)
34. Cáceres M O 1999 Lévy noise, Lévy flights, Lévy fluctuations J. Phys. A: Math. Gen. 32 6009
35. Fogedby H C 1994 Lévy flights in random environments Phys. Rev. Lett. 73 2517
36. Applebaum D 2009 Lévy Processes and Stochastic Calculus 2nd edn (Cambridge: Cambridge University Press)
37. Hahn M, Kobayashi K and Umarov S 2011 Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion Proc. Am. Math. Soc. 139 691
38. Hu Y, Nualart D and Song J 2009 Fractional martingales and characterization of the fractional Brownian motion Ann. Probab. 37 2404
39. Derrida B and Dickman R 1991 On the interface between two growing Eden clusters J. Phys. A: Math. Gen. 24 L191
40. Kirkpatrick S, Gelatt C D and Vecchi M P 1983 Optimization by simulated annealing Science 220 671
41. Serino C A and Redner S 2010 The Pearson walk with shrinking steps in two dimensions J. Stat. Mech. P01006
42. Krapivsky P L and Redner S 2004 Random walk with shrinking steps Am. J. Phys. 72 591 (Pubitemid 38614070)
43. de la Torre A C, Maltz A, Mártin H O, Catuogno P and García-Mata I 2000 Random walk with an exponentially varying step Phys. Rev. E 62 7748 (Pubitemid 32087995)
44. Rador T 2006 Random walkers with shrinking steps in d dimensions and their long term memory Phys. Rev. E 74 051105 (Pubitemid 44703859)
45. Bressler A and Pemantle R 2007 Quantum random walks in one dimension via generating functions Discrete Mathematics and Theoretical Computer Science www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/viewArticle/dmAH0130
46. Popovic L 2004 Asymptotic genealogy of a critical branching process Ann. Appl. Probab. 14 2120 (Pubitemid 41449208)
47. Bohr T and Pikovsky A 1993 Anomalous diffusion in the Kuramoto-Sivashinsky equation Phys. Rev. Lett. 70 2892
48. Rador T and Taneri S 2006 Random walks with shrinking steps: first-passage characteristics Phys. Rev. E 73 036118
49. Amar J G, Lam P-M and Family F 1991 Surface growth with long-range correlated noise Phys. Rev. A 43 4548
50. ben-Avraham D, Burschka M A and Doering C R 1990 Statics and dynamics of a diffusion-limited reaction: anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition J. Stat. Phys. 60 695
51. Samko S G, Kilbas A A and Marichev O I 1993 Fractional Integrals and Derivatives: Theory and Applications 1st edn (London: Taylor and Francis)