Statistical Mechanics of Tethered Surfaces

Kantor, Yacov; Kardar, Mehran; Nelson, David R.

doi:10.1103/physrevlett.57.791

Cited by 311 publications

(238 citation statements)

References 17 publications

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“…Other problems related to the physics of crumpled structures with the topology of a sheet have been investigated in the last two decades, as examples one can mention studies on basic statistical aspects [11,12,13,14,15], on stress and strain relaxation in crumpled thin sheets [16], among others [17]. On the contrary, the physics of crushed structures with one-dimensional topology as exemplified by a squeezed ball of wire, has been much less studied.…”

Section: Introductionmentioning

confidence: 99%

Condensation of elastic energy in two-dimensional packing of wires

Donato

Gomes

2007

Phys. Rev. E

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Forced packing of a long metallic wire injected into a two-dimensional cavity leads to crushed structures involving a hierarchical cascade of loops with varying curvature radii. We study the distribution of elastic energy stored in such systems from experiments, and high-resolution digital techniques. It is found that the set where the elastic energy of curvature is concentrated has dimension DS = 1.0 ± 0.1, while the set where the mass is distributed, has dimension D = 1.9 ± 0.1.

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Section: Introductionmentioning

confidence: 99%

Condensation of elastic energy in two-dimensional packing of wires

Donato

Gomes

2007

Phys. Rev. E

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“…Our models have their origin in the "tethered network" model of Kantor, Kardar, and Nelson [4,18] [4,18]. With no bond-crossing allowed, the membrane is self-avoiding.…”

Section: Introductionmentioning

confidence: 99%

Negative Poisson ratio in two-dimensional networks under tension

1993

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The elastic properties of two-dimensional networks under tension are studied by the mean-Aeld approximation and Monte Carlo simulation. The networks are characterized by Axed (polymerized) connectivity and either a square-well or a Hooke s-law interaction among their components. Both selfavoiding and phantom networks are examined. The elastic properties of Hooke's-law networks at large equilibrium length are found to be well represented by a mean-field model. All the networks investigated show a negative Poisson ratio over a range of tension. At finite tension, the phantom networks exhibit a phase transition to a collapsed state. PACS number(s): 64.60. -i, OS.40. +j, 62.20.Dc, 87.22.Bt

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“…Generally, these are defined as follows: 12) where the expectation value · ⋄ is taken within the pinned ensemble as defined in (2.4). The quantity, which is accessible in perturbation theory, is the effective coupling as defined in (2.7).…”

Section: Plaquettes-density Correlation Functionsmentioning

confidence: 99%

Scaling behavior of tethered crumpled manifolds with inner dimension close to : Resumming the perturbation theory

Pinnow

Wiese

2005

Nuclear Physics B

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The field theory of self-avoiding tethered membranes still poses major challenges. In this article, we report progress on the toy-model of a manifold repelled by a single point. Our approach allows to sum the perturbation expansion in the strength g 0 of the interaction exactly in the limit of internal dimension D → 2, yielding an analytic solution for the strong-coupling limit. This analytic solution is the starting point for an expansion in 2 − D, which aims at connecting to the well studied case of polymers (D = 1). We give results to fourth order in 2 − D, where the dependence on g 0 is again summed exactly. As an application, we discuss plaquette density functions, and propose a Monte-Carlo experiment to test our results. These methods should also allow to shed light on the more complex problem of self-avoiding manifolds.

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Statistical Mechanics of Tethered Surfaces

Cited by 311 publications

References 17 publications

Condensation of elastic energy in two-dimensional packing of wires

Condensation of elastic energy in two-dimensional packing of wires

Negative Poisson ratio in two-dimensional networks under tension

Scaling behavior of tethered crumpled manifolds with inner dimension close to : Resumming the perturbation theory

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