`a`
Kinetic and Related Models (KRM)
 

Kinetic theory and numerical simulations of two-species coagulation
Pages: 253 - 290, Issue 2, June 2014

doi:10.3934/krm.2014.7.253      Abstract        References        Full text (757.6K)           Related Articles

Carlos Escudero - Departamento de Matemáticas & ICMAT (CSIC-UAM-UC3M-UCM), Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain (email)
Fabricio Macià - Universidad Politécnica de Madrid, ETSI Navales, Avda. Arco de la Victoria s/n, 28040 Madrid, Spain (email)
Raúl Toral - IFISC (Instituto de Física Interdisciplinar y Sistemas Complejos), CSIC-UIB, Campus UIB, 07122 Palma de Mallorca, Spain (email)
Juan J. L. Velázquez - Hausdorff Center for Mathematics, Rheinischen Friedrich-Wilhelms-Universität Bonn, 53115 Bonn, Germany (email)

1 G. Arfken, Mathematical Methods for Physicists, 3rd edition, Academic Press, Orlando, 1985.       
2 J. M. Ball and J. Carr, The discrete coagulation-fragmentation equations: Existence, uniqueness, and density conservation, J. Stat. Phys., 61 (1990), 203-234.       
3 M. Bodnar and J. J. L. Velázquez, An integro-differential equation arising as a limit of individual cell-based models, J. Diff. Eqs., 222 (2006), 341-380.       
4 J. Buhl, D. J. T. Sumpter, I. D. Couzin, J. J. Hale, E. Despland, E. R. Miller and S. J. Simpson, From disorder to order in marching locusts, Science, 312 (2006), 1402-1406.
5 J. A. Carrillo, M. R. D'Orsogna and V. Panferov, Double milling in self-propelled swarms from kinetic theory, Kin. Rel. Mod., 2 (2009), 363-378.       
6 C. Castellano, S. Fortunato and V. Loreto, Statistical physics of social dynamics, Rev. Mod. Phys., 81 (2009), 591-646.
7 P. Clifford and A. Sudbury, A model for spatial conflict, Biometrika, 60 (1973), 581-588.       
8 M. Conti, B. Meerson, A. Peleg and P. V. Sasorov, Phase ordering with a global conservation law: Ostwald ripening and coalescence, Phys. Rev. E, 65 (2002), 046117.
9 R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey and D. E. Knuth, On the Lambert $W$ function, Adv. Comput. Math., 5 (1996), 329-359.       
10 A. Czirók, A.-L. Barabási and T. Vicsek, Collective motion of self-propelled particles: Kinetic phase transition in one dimension, Phys. Rev. Lett., 82 (1999), 209-212.
11 M. R. D'Orsogna, Y. L. Chuang, A. L. Bertozzi and L. S. Chayes, Self-propelled particles with soft-core interactions: Patterns, stability and collapse, Phys. Rev. Lett., 96 (2006), 104302.
12 G. Deffuant, D. Neu, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents, Adv. Complex Syst., 3 (2000), 87-98.
13 C. Escudero, F. Macià and J. J. L. Velázquez, Two-species coagulation approach to consensus by group level interactions, Phys. Rev. E, 82 (2010), 016113.       
14 C. Escudero, C. A. Yates, J. Buhl, I. D. Couzin, R. Erban, I. G. Kevrekidis and P. K. Maini, Ergodic directional switching in mobile insect groups, Phys. Rev. E, 82 (2010), 011926.
15 O. Al Hammal, H. Chaté, I. Dornic and M. A. Muñoz, Langevin description of critical phenomena with two symmetric absorbing states, Phys. Rev. Lett., 94 (2005), 230601.
16 E. Hernández-García and C. López, Clustering, advection and patterns in a model of population dynamics, Phys. Rev. E, 70 (2004), 016216.
17 R. A. Holley and T. M. Liggett, Ergodic theorems for weakly interacting infinite systems and the voter model, Ann. Probab., 3 (1975), 573-739.       
18 C. Huepe and M. Aldana, Intermittency and clustering in a system of self-driven particles, Phys. Rev. Lett., 92 (2004), 168701.
19 S. Janson, D. E. Knuth, T. Luczak and B. Pittel, The birth of the giant component, Rand. Struct. Alg., 4 (1993), 233-358.       
20 M. Kreer and O. Penrose, Proof of dynamical scaling in Smoluchowski's coagulation equation with constant kernel, J. Stat. Phys., 75 (1994), 389-407.       
21 I. M. Lifshitz and V. V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Solids, 19 (1961), 35-50.
22 T. M. Liggett, Interacting Particle Systems, Springer-Verlag, New York, 1985.       
23 J. B. McLeod, On the scalar transport equation, Proc. London Math. Soc., 14 (1964), 445-458.       
24 G. Menon and R. L. Pego, Approach to self-similarity in Smoluchowski's coagulation equations, Commun. Pure Appl. Math., 57 (2004), 1197-1232.       
25 H. S. Niwa, School size statistics of fish, J. Theor. Biol., 195 (1998), 351-361.
26 F. Peruani, A. Deutsch and M. Bär, Nonequilibrium clustering of self-propelled rods, Phys. Rev. E, 74 (2006), 030904(R).
27 M. Pineda, R. Toral and E. Hernández-García, Noisy continuous-opinion dynamics, J. Stat. Mech., (2009), P08001.
28 J. Seinfeld, Atmospheric Chemistry and Physics of Air Polution, Wiley, New York, 1986.
29 J. Silk and S. D. White, The development of structure in the expanding universe, Astrophys. J., 223 (1978), L59-L62.
30 T. Sintes, R. Toral and A. Chakrabarti, Reversible aggregation in self-associating polymer systems, Phys. Rev. E, 50 (1994), 2967-2976.
31 R. Toral and J. Marro, Cluster kinetics in the lattice gas model: The Becker-Doring type of equations, J. Phys. C: Solid State Phys., 20 (1987), 2491-2500.
32 R. Toral and C. J. Tessone, Finite size effects in the dynamics of opinion formation, Commun. Comput. Phys., 2 (2007), 177-195.       
33 F. Vázquez and C. López, Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior, Phys. Rev. E, 78 (2008), 061127.
34 C. A. Yates, R. Erban, C. Escudero, I. D. Couzin, J. Buhl, I. G. Kevrekidis, P. K. Maini and D. J. T. Sumpter, Inherent noise can facilitate coherence in collective swarm motion, Proc. Nat. Acad. Sci. USA, 106 (2009), 5464-5469.
35 R. M. Ziff, Kinetics of polymerization, J. Stat. Phys., 23 (1980), 241-263.       

Go to top