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Title:

The passive polymer problem

Description:

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity cor...

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity correlations which are uncorrelated in time and grow with the distance x as |x | ε, and ε small. This relation gets modified in the case of polymers and membranes (the marginal advecting flow has correlations which are shorter ranged.) The construction is done in three steps: First, we reconsider the treatment of the passive scalar problem using the most convenient treatment via field theory and renormalization group. We explicitly show why IR-divergences and thus the system-size appear in physical observables, which is rather unusual in the context of ordinary field-theories, like the φ 4-model. We also discuss, why the renormalization group can nevertheless be used to sum these divergences and leads to anomalous scaling of 2n-point correlation functions as e.g. S 2n (x): = ⟨[Θ(x,t) − Θ(0,t)] 2n ⟩. In a second step, we reformulate the problem in terms of a Langevin equation. This is interesting in its own, since it allows for a distinction between single-particle and multi-particle contributions, which is not obvious in the Focker-Planck treatment. It also gives an efficient algorithm to determine S 2n numerically, by measuring the diffusion of particles in a random velocity field. In a third and final step, we generalize the Langevin treatment of a particle to polymers and membranes, or more generally to an elastic object of inner dimension D with 0 ≤ D ≤ 2. These objects can intersect each other. We also analyze what happens when self-intersections are no longer allowed. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-05

Source:

http://arxiv.org/pdf/chao-dyn/9911005v3.pdf

http://arxiv.org/pdf/chao-dyn/9911005v3.pdf Minimize

Document Type:

text

Language:

en

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Accepted for publication in J. Stat. Phys

Accepted for publication in J. Stat. Phys Minimize

DDC:

532 Fluid mechanics; liquid mechanics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

DISORDERED SYSTEMS AND THE FUNCTIONAL RENORMALIZATION GROUP, A PEDAGOGICAL INTRODUCTION

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-26

Source:

http://arxiv.org/pdf/cond-mat/0205116v1.pdf

http://arxiv.org/pdf/cond-mat/0205116v1.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Principles of non-local field theories and their application to polymerized membranes

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-26

Source:

http://arxiv.org/pdf/cond-mat/0106361v1.pdf

http://arxiv.org/pdf/cond-mat/0106361v1.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

The functional renormalization group treatment of disordered systems: a review

Description:

We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group treatment is necessary, contrary to pure systems, where renormalization of a single coupling constant is s...

We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group treatment is necessary, contrary to pure systems, where renormalization of a single coupling constant is sufficient. This leads to a disorder distribution, which after a finite renomalization becomes non-analytic, thus overcoming the predictions of the seemingly exact dimensional reduction. We discuss, how a renormalizable field theory can be constructed, even beyond 1-loop order. We then discuss an elastic manifold imbedded in N dimensions, and give the exact solution for N → ∞. This is compared to predictions of the Gaussian replica variational ansatz, using replica symmetry breaking. We finally discuss depinning, both isotropic and anisotropic, and the scaling Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-26

Source:

http://arxiv.org/pdf/cond-mat/0302322v1.pdf

http://arxiv.org/pdf/cond-mat/0302322v1.pdf Minimize

Document Type:

text

Language:

en

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Contents

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DDC:

539 Modern physics *(computed)*

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Title:

The passive polymer problem

Description:

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity cor...

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity correlations which are uncorrelated in time and grow with the distance x as |x | ε, and ε small. This relation gets modified in the case of polymers and membranes (the marginal advecting flow has correlations which are shorter ranged.) The construction is done in three steps: First, we reconsider the treatment of the passive scalar problem using the most convenient treatment via field theory and renormalization group. We explicitly show why IR-divergences and thus the system-size appear in physical observables, which is rather unusual in the context of ordinary field-theories, like the φ 4-model. We also discuss, why the renormalization group can nevertheless be used to sum these divergences and leads to anomalous scaling of 2n-point correlation functions as e.g. S 2n (x): = ⟨[Θ(x,t) − Θ(0,t)] 2n ⟩. In a second step, we reformulate the problem in terms of a Langevin equation. This is interesting in its own Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-05

Source:

http://arxiv.org/pdf/chao-dyn/9911005v1.pdf

http://arxiv.org/pdf/chao-dyn/9911005v1.pdf Minimize

Document Type:

text

Language:

en

DDC:

532 Fluid mechanics; liquid mechanics *(computed)*

Rights:

Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

The passive polymer problem

Description:

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity cor...

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity correlations which are uncorrelated in time and grow with the distance x as |x | ε, and ε small. This relation gets modified in the case of polymers and membranes (the marginal advecting flow has correlations which are shorter ranged.) The construction is done in three steps: First, we reconsider the treatment of the passive scalar problem using the most convenient treatment via field theory and renormalization group. We explicitly show why IR-divergences and thus the system-size appear in physical observables, which is rather unusual in the context of ordinary field-theories, like the φ 4-model. We also discuss, why the renormalization group can nevertheless be used to sum these divergences and leads to anomalous scaling of 2n-point correlation functions as e.g. S 2n (x): = ⟨[Θ(x,t) − Θ(0,t)] 2n ⟩. In a second step, we reformulate the problem in terms of a Langevin equation. This is interesting in its own Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-05

Source:

http://arxiv.org/pdf/chao-dyn/9911005v2.pdf

http://arxiv.org/pdf/chao-dyn/9911005v2.pdf Minimize

Document Type:

text

Language:

en

DDC:

532 Fluid mechanics; liquid mechanics *(computed)*

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Title:

Why one needs a functional RG to survive in a disordered world

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-26

Source:

http://arxiv.org/pdf/cond-mat/0511529v1.pdf

http://arxiv.org/pdf/cond-mat/0511529v1.pdf Minimize

Document Type:

text

Language:

en

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Title:

Supersymmetry Breaking in Disordered Systems and Relation to Functional Renormalization and Replica-Symmetry Breaking

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-15

Source:

http://arxiv.org/pdf/cond-mat/0411656v1.pdf

http://arxiv.org/pdf/cond-mat/0411656v1.pdf Minimize

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text

Language:

en

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Title:

To be published in Journal of Statistical Physics 1 On the Perturbation Expansion of the KPZ- Equation

Description:

We present a simple argument to show that the β-function of the d-dimensional KPZ-equation (d ≥ 2) is to all orders in perturbation theory given by β(gR) = (d − 2)gR − 2 (8π) d/2 Γ(2 − d/2)g2 R. Neither the dynamical exponent z nor the roughness-exponent ζ have any correction in any order of perturbation theory. This shows that standard perturba...

We present a simple argument to show that the β-function of the d-dimensional KPZ-equation (d ≥ 2) is to all orders in perturbation theory given by β(gR) = (d − 2)gR − 2 (8π) d/2 Γ(2 − d/2)g2 R. Neither the dynamical exponent z nor the roughness-exponent ζ have any correction in any order of perturbation theory. This shows that standard perturbation theory cannot attain the strong-coupling regime and in addition breaks down at d = 4. We also calculate a class of correlation-functions exactly. KEY WORDS: KPZ-equation, growth processes 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-15

Source:

http://arxiv.org/pdf/cond-mat/9802068v2.pdf

http://arxiv.org/pdf/cond-mat/9802068v2.pdf Minimize

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text

Language:

en

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Title:

Perturbative Linearization of Reaction-Diffusion Equations

Description:

We develop perturbative expansions to obtain solutions for the initial-value problems of two important reaction-diffusion systems, viz., the Fisher equation and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of our expansion is the corresponding singular-perturbation solution. This approach transforms the solution of nonl...

We develop perturbative expansions to obtain solutions for the initial-value problems of two important reaction-diffusion systems, viz., the Fisher equation and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of our expansion is the corresponding singular-perturbation solution. This approach transforms the solution of nonlinear reaction-diffusion equations into the solution of a hierarchy of linear equations. Our numerical results demonstrate that this hierarchy rapidly converges to the exact solution. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-30

Source:

http://arxiv.org/pdf/cond-mat/0209524v1.pdf

http://arxiv.org/pdf/cond-mat/0209524v1.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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