No Access

EXPONENTIAL AND POWER LAW DISTRIBUTION OF MASS CLUSTERS IN A (MAGNETIC-LIKE) DEPOSITION MODEL OF ELONGATED GRAINS IN 2D PILES

SUPRATECS (SUPRATECS = Services Universitaires Pour la Recherche et les Applications Technologiques de matériaux Electro-céramiques, Composites, Supraconducteurs.), Institute of Physics, B5, University of Liège, B-4000 Liège, Euroland

Institute of Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50-204 Wrocław, Poland

Search for more papers by this author

M. AUSLOOS

Search for more papers by this author

, and

R. CLOOTS

LCIS (LCIS = Laboratoire de Chimie Inorganique Structurale, a member of the SUPRATECS Centre.), Institute of Chemistry, B6, University of Liège, B-4000 Liège, Euroland

Search for more papers by this author

https://doi.org/10.1142/S0129183104006571Cited by:3 (Source: Crossref)

Abstract

A generalized magnetically controlled ballistic rain-like deposition (MBD) model of granular piles has been numerically investigated in 2D. The grains are taken to be elongated disks whence characterized by a two-state scalar degree of freedom, called "nip", their interaction being described through a Hamiltonian. The results are discussed in order to search for the effect of nip flip (or grain rotation from vertical to horizontal and conversely) probability in building a granular pile. The characteristics of creation of + (or -) nip's clusters and clusters of holes (missing nips) are analyzed. Two different cluster-mass regimes have been identified, through the cluster-mass distribution function which can be exponential or have a power law form depending on whether the nip flip (or grain rotation) probability is large or small. Analytical forms of the exponent are empirically found in terms of the Hamiltonian parameters.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

B. J. Alder and T. E. Wainwright, J. Chem. Phys. 27, 1208 (1957). Crossref, Web of Science, ADS, Google Scholar
A. Santos, M. L. de Haro and S. B. Yuste, J. Chem. Phys. 103, 4622 (1995). Crossref, Web of Science, ADS, Google Scholar
J. M. Kosterlitz and D. J. Thouless, J. Phys. C 76, 1181 (1973). Web of Science, Google Scholar
B. I. Halperin and D. R. Nelson, Phys. Rev. Lett. 41, 121 (1978). Crossref, Web of Science, ADS, Google Scholar
A. P. Young, Phys. Rev. B 19, 1855 (1979). Crossref, Web of Science, Google Scholar
A. Jaster, Phys. Rev. E 59, 2594 (1999); Phys. Lett. A 330, 120 (2004) . Google Scholar
H. A. Makse , J. Brujic and S. F. Edwards , The Physics of Granular Media , eds. H. Hinrichsen and D. E. Wolf ( Wiley-VCH , Weinheim , 2004 ) . Google Scholar
T. Unger and J. Kertesz, Int. J. Mod. Phys. B 17, 5623 (2003). Link, Web of Science, ADS, Google Scholar
M. Niemiecet al., Physica A 248, 365 (1998). Crossref, Web of Science, ADS, Google Scholar
J. M. Rubí and A. Gadomski, Physica A 326, 333 (2003). Crossref, Web of Science, ADS, Google Scholar
A. Gadomski and J. M. Rubí, Chem. Phys. 293, 169 (2003). Crossref, Web of Science, ADS, Google Scholar
D. Helbing, Physica A 219, 375 (1995). Crossref, Web of Science, ADS, Google Scholar
M. Kaulke and S. Trimper, J. Phys. A: Mathematical and General 28, 5445 (1995). Crossref, ADS, Google Scholar
B. S. Kerner and H. Rehborn, Phys. Rev. E 53, R1297 (1996). Crossref, Web of Science, ADS, Google Scholar
N. Pieretet al., Traffic and Granular Flow 97, eds. M. Schreckenberg and D. E. Wolf (Springer, Singapore, 1998) pp. 447–452. Google Scholar
M. Schreckenberg and D. E. Wolf (eds.) , Traffic and Granular Flow 97 ( Springer , Singapore , 1998 ) . Google Scholar
S. F. Edwards and P. W. Anderson, J. Phys. F: Metal Phys. 5, 965 (1975). Crossref, Web of Science, ADS, Google Scholar
P. Meakin and R. Jullien, J. Chem. Phys. 89, 246 (1988). Crossref, Web of Science, ADS, Google Scholar
P. Meakin, Zh.-Y. Chen and P. Evesque, J. Chem. Phys. 87, 630 (1987). Crossref, Web of Science, ADS, Google Scholar
F. Family, P. Meakin and T. Vicsek, J. Chem. Phys. 83, 4144 (1985). Crossref, Web of Science, ADS, Google Scholar
M. Ausloos, J. Chem. Phys. 64, 3490 (1976). Crossref, Web of Science, ADS, Google Scholar
M. Ausloos and P. Clippe, J. Chem. Phys. 67, 624 (1977). Crossref, Web of Science, ADS, Google Scholar
N. Vandewalle, S. Galam and M. Kramer, Eur. Phys. J. B 14, 407 (2000). Crossref, Web of Science, ADS, Google Scholar
A. R. Kansal, S. Torquato and F. H. Stillinger, J. Chem. Phys. 117, 8212 (2002). Crossref, Web of Science, ADS, Google Scholar
F. H. Stillinger, H. Sakai and S. Torquato, Phys. Rev. E 67, 031107 (2003). Crossref, Web of Science, Google Scholar
H. J. Herrmann, Physica A 191, 263 (1992). Crossref, Web of Science, ADS, Google Scholar
V. Fretteet al., Nature 379, 49 (1996). Crossref, Web of Science, ADS, Google Scholar
K. Christensenet al., Phys. Rev. Lett. 77, 107 (1996). Crossref, Web of Science, ADS, Google Scholar
S. R. Nagel, Rev. Mod. Phys. 64, 321 (1992). Crossref, Web of Science, ADS, Google Scholar
N. Vandewalle, R. D'hulst and M. Ausloos, Phys. Rev. E 59, 631 (1999). Crossref, Web of Science, ADS, Google Scholar
J. J. Alonso, J.-P. Hovi and H. J. Herrmann, Phys. Rev. E 58, 672 (1998). Crossref, Web of Science, ADS, Google Scholar
H. J. Herrmann , Physics of Dry Granular Media , eds. H. J. Herrmann , J.-P. Hovi and S. Luding ( Kluwer , Dordrecht , 1998 ) . Crossref, Google Scholar
J. Schäfer, S. Dippel and D. E. Wolf, J. Phys. I France 6, 5 (1996). Crossref, Google Scholar
J. Duran, E. Kolb and L. Vanel, Phys. Rev. E 58, 805 (1998). Crossref, Web of Science, ADS, Google Scholar
I. Zuriguel, L. A. Pugnaloni, A. Garcimartin and D. Maza, arXiv:cond-mat/0301006 . Google Scholar
S. Luding, T.A.S.K. Quarterly, Scientific Bulletin of Academic Computer Centre of the Technical University of Gdansk 2, 417 (1998). Google Scholar
P. J. Flory, J. Am. Chem. Soc. 63, 3083 (1941); 63, 3091 (1941); 63, 3096 (1941) . Google Scholar
D. Stauffer and A. Aharony , Introduction to Percolation Theory ( Taylor and Francis , London , 1994 ) . Google Scholar
R. L. Brown and P. G. W. Hawksley, The Institute of Fuel 27, 159 (1947). Google Scholar
Y. Grasselli and H. J. Herrmann, Granular Matter 1, 43 (1998). Crossref, Google Scholar
J. M. Ottino and D. V. Khakhar, Ann. Rev. Fluid Mech. 32, 55 (2000). Crossref, Web of Science, ADS, Google Scholar
A. Samadani, A. Pradhan and A. Kudrolli, Phys. Rev. E 60, 7203 (1999). Crossref, Web of Science, ADS, Google Scholar
G. Oron and H. J. Herrmann, Phys. Rev. E 58, 2079 (1998). Crossref, Web of Science, Google Scholar
A. L. Stella and M. D. Menech, Physica A 295, 101 (2001). Crossref, Web of Science, ADS, Google Scholar
A. Coniglio and H. J. Herrmann, Physica A 225, 1 (1996). Crossref, Web of Science, ADS, Google Scholar
H. J. Herrmann and S. Luding, Continuum Mechanics and Thermodynamics 10, 189 (1998). Crossref, Web of Science, ADS, Google Scholar
E. Cagliotiet al., Phys. Rev. Lett. 79, 1575 (1997). Crossref, Web of Science, ADS, Google Scholar
K. Trojan and M. Ausloos, Physica A 326, 491 (2003). Web of Science, Google Scholar
K. Trojan and M. Ausloos, Phys. Rev. E 69, 052301 (2004). Crossref, Web of Science, Google Scholar
H. J. Herrmann , J.-P. Hovi and S. Luding , Physics of Granular Media ( Kluwer , Dordrecht , 1998 ) . Crossref, Google Scholar
A. U. Hassanet al., Phys. Rev. E 58, 4461 (1998). Web of Science, Google Scholar
C. M. Horowitz, R. A. Monetti and E. V. Albano, Phys. Rev. E 63, 066132 (2001). Crossref, Web of Science, Google Scholar
R. Pandeyet al., Physica A 310, 325 (2002). Crossref, Web of Science, ADS, Google Scholar
S. N. Majumdar and D. S. Dean, Phys. Rev. E 66, 056114 (2002). Crossref, Web of Science, Google Scholar
M. Auslooset al., Phys. Rev. A 22, 2218 (1980). Crossref, Web of Science, ADS, Google Scholar
M. Blume, V. J. Emery and R. B. Griffiths, Phys. Rev. A 4, 1071 (1971). Crossref, Web of Science, Google Scholar
M. J. Vold, J. Coll. Sci. 18, 684 (1963). Crossref, Google Scholar
D. N. Sutherland, J. Colloid Interf. Sci. 22, 300 (1966). Crossref, Web of Science, ADS, Google Scholar
G. F. Carnevale, Y. Pomeau and W. R. Young, Phys. Rev. Lett. 64, 2913 (1990). Crossref, Web of Science, Google Scholar
H. J. Herrmann, Phys. Rep. 136, 153 (1986). Crossref, Web of Science, ADS, Google Scholar
Y. Saito and H. Müller-Krumbhaar, Phys. Rev. Lett. 74, 4325 (1995). Crossref, Web of Science, ADS, Google Scholar
N. Vandewalle and M. Ausloos, Phys. Rev. E 52, 3447 (1995). Crossref, Web of Science, ADS, Google Scholar
N. Vandewalle and M. Ausloos, Phys. Rev. E 51, 597 (1995). Crossref, Web of Science, ADS, Google Scholar
M. Ausloos and N. Vandewalle, Acta Phys. Pol. B 27, 737 (1996). Web of Science, Google Scholar
M. Schroeder , Fractals, Chaos and Power Laws ( W. H. Freeman and Co. , New York , 1991 ) . Google Scholar
B. West and B. Deering , The Lure of Modern Science ( World Scientific , Singapore , 1995 ) . Crossref, Google Scholar
Y. Gefen, A. Aharony and B. B. Mandelbrot, J. Phys. A 17, 1277 (1984). Crossref, ADS, Google Scholar
B. Lin and Z. R. Yang, J. Phys. A 19, L49 (1986). Crossref, Google Scholar
R. A. Feagin, Physica A 328, 315 (2003). Crossref, Web of Science, ADS, Google Scholar
C. M. Horowitz, R. A. Monetti and E. V. Albano, Phys. Rev. E 63, 066132 (2001). Crossref, Web of Science, Google Scholar
J. Candia and E. V. Albano, Phys. Rev. Lett. 88, 016103 (2002). Crossref, Web of Science, Google Scholar
R. Pastor-Satorras and J. M. Rubí, Phys. Rev. E 1, 5994 (1995). Google Scholar
M. Ausloos, N. Vandewalle and R. Cloots, Europhys. Lett. 24, 629 (1993). Crossref, ADS, Google Scholar
N. Vandewalle and M. Ausloos, Phys. Rev. E 50, R635 (1994). Crossref, Web of Science, ADS, Google Scholar
J. Candia and E. V. Albano, Phys. Rev. E 63, 066127 (2001). Crossref, Web of Science, Google Scholar
M. Mueller, K. Binder and E. V. Albano, Physica A 274, 188 (2000). Crossref, Web of Science, Google Scholar