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Volumn 66, Issue 2, 2002, Pages

Survival and residence times in disordered chains with bias

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; DIFFUSION; MATRIX ALGEBRA; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; RANDOM PROCESSES; SET THEORY;

EID: 41349116753     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.021112     Document Type: Article
Times cited : (18)

References (53)
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    • E.W. Montroll and B.J. West, in Fluctuation Phenomena, 2nd ed., edited by E. W. Montroll and J. L. Lebowitz (North-Holland, Amsterdam, 1987), Chap. 2.
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    • J.P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990);B.D. Hughes, Random Walks and Random Environments (Oxford Univesity Press, New York, 1995);D. ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, U.K., 2000).
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    • Bouchaud, J.P.1    Georges, A.2
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    • N.G. van Kampen, Stochastic Processes in Physics and Chemistry, 2nd ed. (North-Holland, Amsterdam, 1992), Chap. XII.
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    • 85036217090 scopus 로고    scopus 로고
    • N.G. van Kampen, Stochastic Processes in Physics and Chemistry (Ref. 4), Chap. V, Sec. 9
    • N.G. van Kampen, Stochastic Processes in Physics and Chemistry (Ref. 4), Chap. V, Sec. 9.
  • 49
    • 85036420856 scopus 로고    scopus 로고
    • We are considering only one-step processes. For general processes with large jumps allowed the boundary condition must be extended over all sites (Formula presented) out of D
    • We are considering only one-step processes. For general processes with large jumps allowed the boundary condition must be extended over all sites (Formula presented) out of D.
  • 50
    • 85036425423 scopus 로고    scopus 로고
    • From Eq. (2.8) the general expression for MFPT is given by (Formula presented)
    • From Eq. (2.8) the general expression for MFPT is given by (Formula presented).
  • 51
    • 85036334246 scopus 로고    scopus 로고
    • A related interesting model is the multiplicative one: (Formula presented) and (Formula presented) where (Formula presented). Thus, (Formula presented) and the corresponding evolution equation that results from Eq. (2.6) is (Formula presented). Here, we can also obtain the symmetrical disordered system and the ordered biased chain as limit cases
    • A related interesting model is the multiplicative one: (Formula presented) and (Formula presented) where (Formula presented). Thus, (Formula presented) and the corresponding evolution equation that results from Eq. (2.6) is (Formula presented). Here, we can also obtain the symmetrical disordered system and the ordered biased chain as limit cases.
  • 52
    • 85036287061 scopus 로고    scopus 로고
    • We must note that from Eqs. (2.3) and (2.10), the MRT is defined only if (Formula presented) is an integrable function in the interval (Formula presented). This condition is only fulfilled in the presence of bias
    • We must note that from Eqs. (2.3) and (2.10), the MRT is defined only if (Formula presented) is an integrable function in the interval (Formula presented). This condition is only fulfilled in the presence of bias.


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