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Volumn 79, Issue 2, 2009, Pages

Nonalgebraic length dependence of transmission through a chain of barriers with a Lévy spacing distribution

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EID: 60349108346     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.024204     Document Type: Article
Times cited : (48)

References (26)
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    • The authors of Ref. calculate a lower bound to the mean-square displacement, with the result 〈 x2 〉 ≥ tmin (2,3-α) if the initial position of the particle is randomly chosen along the chain (so superdiffusion for any 0<α<2). If the particle starts at a barrier (which corresponds to the situation we consider in the present work), the result is 〈 x2 〉 ≥ t2-α (so superdiffusion for 0<α<1). Earlier papers gave different results for the mean-square displacement, but a direct comparison is problematic because those papers did not notice the dependence on the starting position.
    • The authors of Ref. calculate a lower bound to the mean-square displacement, with the result 〈 x2 〉 ≥ tmin (2,3-α) if the initial position of the particle is randomly chosen along the chain (so superdiffusion for any 0<α<2). If the particle starts at a barrier (which corresponds to the situation we consider in the present work), the result is 〈 x2 〉 ≥ t2-α (so superdiffusion for 0<α<1). Earlier papers gave different results for the mean-square displacement, but a direct comparison is problematic because those papers did not notice the dependence on the starting position.
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    • We cannot directly take the derivative of Eq. 5 because that would lead (for p≠1) to an undefined product of θ (L-x) and δ (L-x). No such complication arises if we take the derivative of Eq. 7.
    • We cannot directly take the derivative of Eq. 5 because that would lead (for p≠1) to an undefined product of θ (L-x) and δ (L-x). No such complication arises if we take the derivative of Eq. 7.
  • 23
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    • For efficient algorithms to generate random variables with a Lévy stable distribution, see 10.2307/2285309;
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    • (1976) J. Am. Stat. Assoc. , vol.71 , pp. 340
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.