The statistical mechanics of random copolymers

Soteros, C E; Whittington, S G

doi:10.1088/0305-4470/37/41/r01

Cited by 60 publications

(68 citation statements)

References 120 publications

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“…In the literature one finds also a large number of numerical works on copolymers, we mention here for example [9], [25] and references therein. As far as we have seen, the attention is often shifted toward different aspects, notably of course the issue of critical exponents, and the more complex model in which the polymer is not directed but rather self-avoiding, see [9] and [25] also for some rigorous results and references in such a direction.…”

Section: 4mentioning

confidence: 99%

A Numerical Approach to Copolymers at Selective Interfaces

2006

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Abstract. We consider a model of a random copolymer at a selective interface which undergoes a localization/delocalization transition. In spite of the several rigorous results available for this model, the theoretical characterization of the phase transition has remained elusive and there is still no agreement about several important issues, for example the behavior of the polymer near the phase transition line. From a rigorous viewpoint non coinciding upper and lower bounds on the critical line are known.In this paper we combine numerical computations with rigorous arguments to get to a better understanding of the phase diagram. Our main results include: -Various numerical observations that suggest that the critical line lies strictly in between the two bounds.-A rigorous statistical test based on concentration inequalities and super-additivity, for determining whether a given point of the phase diagram is in the localized phase. This is applied in particular to show that, with a very low level of error, the lower bound does not coincide with the critical line. -An analysis of the precise asymptotic behavior of the partition function in the delocalized phase, with particular attention to the effect of rare atypical stretches in the disorder sequence and on whether or not in the delocalized regime the polymer path has a Brownian scaling. -A new proof of the lower bound on the critical line. This proof relies on a characterization of the localized regime which is more appealing for interpreting the numerical data.

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Section: 4mentioning

confidence: 99%

A Numerical Approach to Copolymers at Selective Interfaces

2006

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“…where we recall that K(n) is the P-probability that first return to 0 of an excursion of the free process occurs at step n, as in (1.2), while L r 's, the (possibly vanishing) lengths of the excursions of the process between two blocks B i , B i ′ with i, i ′ ∈ I(ω), are defined as 26) with the convention that j 0 = −1, j |I(ω)|+1 = k, see Figure 1. Taking the expectation with respect to the disorder and using (1.3), one obtains then 27) for ℓ sufficiently large.…”

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confidence: 99%

Smoothing Effect of Quenched Disorder on Polymer Depinning Transitions

Giacomin

Toninelli

2006

Commun. Math. Phys.

191

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Abstract. We consider general disordered models of pinning of directed polymers on a defect line. This class contains in particular the (1 + 1)-dimensional interface wetting model, the disordered Poland-Scheraga model of DNA denaturation and other (1 + d)-dimensional polymers in interaction with flat interfaces. We consider also the case of copolymers with adsorption at a selective interface. Under quite general conditions, these models are known to have a (de)localization transition at some critical line in the phase diagram. In this work we prove in particular that, as soon as disorder is present, the transition is at least of second order, in the sense that the free energy is differentiable at the critical line, so that the order parameter vanishes continuously at the transition. On the other hand, it is known that the corresponding non-disordered models can have a first order (de)localization transition, with a discontinuous first derivative. Our result shows therefore that the presence of the disorder has really a smoothing effect on the transition. The relation with the predictions based on the Harris criterion is discussed.2000 Mathematics Subject Classification: 60K35, 82B41, 82B44

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“…[19], which in light of the given mapping may now be useful in understanding population dynamics. On the other hand, the connectivity between phenotypes in realistic biological problems is generally more complex than the one we have considered here, and the numbers of phenotypes and environments are often greater than two.…”

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confidence: 99%

Polymer-Population Mapping and Localization in the Space of Phenotypes

2006

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We present a mapping between the thermodynamics of an ideal heteropolymer in an external field and the dynamics of structured populations in fluctuating environments. We employ a population model in which individuals may adopt different phenotypes, each of which may be optimal in a different environment. Using this mapping, we develop a path integral formulation for populations and predict the existence of a biological counterpart for the well-known heteropolymer localization phase transition.

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The statistical mechanics of random copolymers

Cited by 60 publications

References 120 publications

A Numerical Approach to Copolymers at Selective Interfaces

A Numerical Approach to Copolymers at Selective Interfaces

Smoothing Effect of Quenched Disorder on Polymer Depinning Transitions

Polymer-Population Mapping and Localization in the Space of Phenotypes

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