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5
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-
0003911843
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-
Springer-Verlag, New York
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W. M. Gelbart, A. Ben-Shaoul, and D. Roux, Eds., Micelles, Membranes, Microemulsions and Monolayers (Springer-Verlag, New York, 1994).
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(1994)
Micelles, Membranes, Microemulsions and Monolayers
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-
Gelbart, W.M.1
Ben-Shaoul, A.2
Roux, D.3
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9
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0003879578
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Addison-Wesley, Reading, PA
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S. A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes (Addison-Wesley, Reading, PA, 1994).
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(1994)
Statistical Thermodynamics of Surfaces, Interfaces, and Membranes
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Safran, S.A.1
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24
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57649136073
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note
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∞ dω/2π.
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-
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29
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36149049574
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M. Doi, J. Phys. A 9, 1465 (1976).
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(1976)
J. Phys. A
, vol.9
, pp. 1465
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Doi, M.1
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30
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5544314407
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In fact, in the classical case (in the absence of the fluctuating potential) the fluctuation corrections induced by the exact description of the reaction diffusion system has been shown to be relevant only for d ≤ 2 - cf. B. P. Lee and J. Cardy, J. Stat. Phys. 80, 971 (1995).
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(1995)
J. Stat. Phys.
, vol.80
, pp. 971
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-
Lee, B.P.1
Cardy, J.2
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38
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-
57649136075
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note
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In the case of diffusion in the absence of the potential and reactions, we have z = 2, thereby yielding the results of Refs. 25 and 37.
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-
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-
41
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-
57649133186
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-
note
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These equations convey an important aspect regarding the renormalization procedure. Namely, it indicates that even if the bare value of the parameter u is irrelevant compared to the other parameters v and w, the renormalized version of the theory generates a correction to it, making it the most relevant parameter at the longest length scales. Thus, it would be erroneous to make an assumption at the outset regarding the magnitudes of the different terms present in the free energy functional Eq. (1) and work subsequently within such a framework. Rather, the framework of renormalization always works in favor of u at the longest length scales, thereby rendering the other parameters irrelevant. This feature of the analysis renders our theory restrictive in that it cannot study intermediate length scales or wavelengths wherein the effect of other modes of energy (represented by the parameters v and w) prove relevant.
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-
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42
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0001131105
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A. de Masi, P. A. Ferrari, S. Goldstein, and W. D. Wick, J. Stat. Phys. 55, 787 (1989).
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(1989)
J. Stat. Phys.
, vol.55
, pp. 787
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-
De Masi, A.1
Ferrari, P.A.2
Goldstein, S.3
Wick, W.D.4
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50
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57649116816
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-
note
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-sth(t).
-
-
-
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51
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-
57649119303
-
-
note
-
2(t) had in contrast possessed secular terms, then as t → ∞ it would be impossible to choose an ∈ small enough to maintain the perturbative nature of the correction - necessitating a renormalization procedure.
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-
-
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55
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57649113325
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-
note
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The presence of more than one sink would lead to hydrodynamic interactions arising from their fluctuations, and would modify the fluctuation spectra.
-
-
-
-
57
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-
57649128637
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-
note
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The path integral technique of Golestanian and Kardar (Ref. 54) is also perturbative and is restricted to small amplitude fluctuations. However, in view of its field theoretic nature, renormalization effects can be accounted within this approach.
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-
-
-
60
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-
57649124057
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-
note
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Since 〈φ〉 = 0, there is no net drift of the particle.
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-
-
-
61
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-
57649136072
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-
note
-
-1 (Refs. 10 and 20). The regime in which the above functional form for the potential is valid corresponds to q ≫ q*.
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