NDLI: Beyond Flory theory: Distribution functions for interacting lattice trees

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Year: 2017 Volume: 95

Year: 2017 Volume: 95 Issue: 1-1

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Large deviations in Taylor dispersion.

Long-range interacting systems in the unconstrained ensemble.

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Ising spin glasses in dimension five.

Upper and lower critical decay exponents of Ising ferromagnets with long-range interaction

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One-loop diagrams in the random Euclidean matching problem.

Effects of flexoelectricity and weak anchoring on a Freedericksz transition cell.

Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method.

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Richtmyer-Meshkov instability of a flat interface subjected to a rippled shock wave

Stochastic Liouville equation for particles driven by dichotomous environmental noise.

Impact dynamics of particle-coated droplets

Reynolds number effects on the single-mode Richtmyer-Meshkov instability.

Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential

Synchronization and long-time memory in neural networks with inhibitory hubs and synaptic plasticity

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Scaling features of the tribology of polymer brushes of increasing grafting density around the mushroom-to-brush transition

Effect of similarity between patterns in associative memory.

Phase reduction theory for hybrid nonlinear oscillators.

Collective colloid diffusion under soft two-dimensional confinement

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Density of states from mode expansion of the self-dynamic structure factor of a liquid metal.

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Simple diffusion hopping model with convection.

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Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrödinger equation.

Effects of hydrodynamic interactions on rectified transport of self-propelled particles.

Analysis of the classical phase space and energy transfer for two rotating dipoles with and without external electric field.

Reconstructing links in directed networks from noisy dynamics.

Prediction of the moments in advection-diffusion lattice Boltzmann method. I. Truncation dispersion, skewness, and kurtosis

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Peak-height formula for higher-order breathers of the nonlinear Schrödinger equation on nonuniform backgrounds.

Criticality of colloids with three distinct interaction patches: As simple as $ A , B , C $ ?

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Statistical model of a flexible inextensible polymer chain: The effect of kinetic energy.

Network clustering and community detection using modulus of families of loops.

Nonequilibrium Markov state modeling of the globule-stretch transition.

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Geometry and design of origami bellows with tunable response.

Band instability in near-critical fluids subjected to vibration under weightlessness

Physics of negative absolute temperatures.

Nonvariational mechanism of front propagation: Theory and experiments.

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Collective dynamics of time-delay-coupled phase oscillators in a frustrated geometry.

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Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation.

Experimental observation of oscillatory cellular patterns in three-dimensional directional solidification

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Beyond Flory theory: Distribution functions for interacting lattice trees

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Acoustic streaming in two-dimensional freely suspended smectic liquid crystal films.

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Dynamic shear jamming in dense granular suspensions under extension.

Nonequilibrium temperature measurement in a thermal conduction process.

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Feynman-Kac formula for stochastic hybrid systems.

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Orientational action of edge dislocations on the director field in antiferroelectric smectic- $ C _{ A }^{ * } $ films

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Beyond Flory theory: Distribution functions for interacting lattice trees

Content Provider	World Health Organization (WHO)-Global Index Medicus
Author	Rosa, Angelo Everaers, Ralf
Description	Country affiliation: Italy Author Affiliation: Rosa A ( SISSA-Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy.); Everaers R ( Univ Lyon, Ens de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique and Centre Blaise Pascal, F-69342 Lyon, France.)
Abstract	While Flory theories [J. Isaacson and T. C. Lubensky, J. Physique Lett. 41, 469 (1980); M. Daoud and J. F. Joanny, J. Physique 42, 1359 (1981); A. M. Gutin et al., Macromolecules 26, 1293 (1993)] provide an extremely useful framework for understanding the behavior of interacting, randomly branching polymers, the approach is inherently limited. Here we use a combination of scaling arguments and computer simulations to go beyond a Gaussian description. We analyze distribution functions for a wide variety of quantities characterizing the tree connectivities and conformations for the four different statistical ensembles, which we have studied numerically in [A. Rosa and R. Everaers, J. Phys. A: Math. Theor. 49, 345001 (2016) and J. Chem. Phys. 145, 164906 (2016)]: (a) ideal randomly branching polymers, (b) $ 2 d $ and $ 3 d $ melts of interacting randomly branching polymers, (c) $ 3 d $ self-avoiding trees with annealed connectivity, and (d) $ 3 d $ self-avoiding trees with quenched ideal connectivity. In particular, we investigate the distributions (i) $ p _{ N } ( n ) $ of the weight, $ n $ , of branches cut from trees of mass $ N $ by severing randomly chosen bonds; (ii) $ p _{ N } ( l ) $ of the contour distances, $ l $ , between monomers; (iii) $ p _{ N } ( { ⃗ \atop r } ) $ of spatial distances, $ { ⃗ \atop r } $ , between monomers, and (iv) $ p _{ N } ( { ⃗ \atop r } \| l ) $ of the end-to-end distance of paths of length $ l $ . Data for different tree sizes superimpose, when expressed as functions of suitably rescaled observables $ { ⃗ \atop x } = { ⃗ \atop r } / 〈 r ^{ 2 } ( N ) 〉 $ or $ x = l / 〈 l ( N ) 〉 $ . In particular, we observe a generalized Kramers relation for the branch weight distributions (i) and find that all the other distributions (ii–iv) are of Redner-des Cloizeaux type, $ q ( { ⃗ \atop x } ) = C \| x \| ^{ θ } exp − ( K \| x \| ) ^{ t } $ . We propose a coherent framework, including generalized Fisher-Pincus relations, relating most of the RdC exponents to each other and to the contact and Flory exponents for interacting trees.
File Format	HTM / HTML
ISSN	24700045
e-ISSN	24700053
Journal	Physical Review E
Issue Number	1-1
Volume Number	95
Language	English
Publisher	American Physical Society
Publisher Date	2017-01-01
Publisher Place	United States
Access Restriction	Open
Subject Keyword	Statistical and Nonlinear Physics many-body systems Condensed Matter Physics
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistical and Nonlinear Physics Condensed Matter Physics

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