1993, Probability and its applications., ISBN 0817635890, xiv, 425

Book

2013, 1. Aufl., Modern Birkhauser classics, ISBN 1461460247, 435

The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple...

Self-avoiding walks (Mathematics) | Mathematics | Chemistry, Physical and theoretical | Statistical physics

Self-avoiding walks (Mathematics) | Mathematics | Chemistry, Physical and theoretical | Statistical physics

eBook

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 01/2019, Volume 475, Issue 2221, p. 20180549

The self-avoiding walk, and lattice spin systems such as the phi(4) model, are models of interest both in mathematics and in physics. Many of their important...

Critical exponent | Renormalization | model | Self-avoiding walk | LONG-RANGE | critical exponent | RIGOROUS CONTROL | MULTIDISCIPLINARY SCIENCES | SUSCEPTIBILITY | self-avoiding walk | O(N) MODELS | CRITICAL EXPONENTS | phi model | FIELD BEHAVIOR | renormalization | LOGARITHMIC CORRECTIONS | FINITE-RANGE DECOMPOSITION | CONVERGENCE | CRITICAL-BEHAVIOR | 1008 | φ4 model | 120

Critical exponent | Renormalization | model | Self-avoiding walk | LONG-RANGE | critical exponent | RIGOROUS CONTROL | MULTIDISCIPLINARY SCIENCES | SUSCEPTIBILITY | self-avoiding walk | O(N) MODELS | CRITICAL EXPONENTS | phi model | FIELD BEHAVIOR | renormalization | LOGARITHMIC CORRECTIONS | FINITE-RANGE DECOMPOSITION | CONVERGENCE | CRITICAL-BEHAVIOR | 1008 | φ4 model | 120

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 2019

Journal Article

ANNALS OF PROBABILITY, ISSN 0091-1798, 09/2019, Volume 47, Issue 5, pp. 2801 - 2829

We study self-avoiding walk on graphs whose automorphism group has a transitive nonunimodular subgroup. We prove that self-avoiding walk is ballistic, that the...

transitive graph | nonunimodular | bubble diagram | PERCOLATION | STATISTICS & PROBABILITY | CONNECTIVE CONSTANTS | Self-avoiding walk | nonamenable | mean-field

transitive graph | nonunimodular | bubble diagram | PERCOLATION | STATISTICS & PROBABILITY | CONNECTIVE CONSTANTS | Self-avoiding walk | nonamenable | mean-field

Journal Article

Discrete and Continuous Dynamical Systems - Series S, ISSN 1937-1632, 04/2017, Volume 10, Issue 2, pp. 289 - 311

We show that the 'erasing-larger-loops-first' (ELLF) method, which was first introduced for erasing loops from the simple random walk on the Sierpinski gasket,...

Loop-erased random walk | Fractal | Fractal dimension | Scaling limit | Sierpinski gasket | Displacement exponent | Self-avoiding walk | Self-repelling walk | MATHEMATICS, APPLIED | UNIFORM SPANNING-TREES | scaling limit | fractal dimension | fractal | PATHS | self-avoiding walk | displacement exponent | self-repelling walk

Loop-erased random walk | Fractal | Fractal dimension | Scaling limit | Sierpinski gasket | Displacement exponent | Self-avoiding walk | Self-repelling walk | MATHEMATICS, APPLIED | UNIFORM SPANNING-TREES | scaling limit | fractal dimension | fractal | PATHS | self-avoiding walk | displacement exponent | self-repelling walk

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 10/2015, Volume 48, Issue 45, pp. 454001 - 27

We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is...

compressive force | bridges | self-avoiding walks | Schramm-Loewner evolution | self-avoiding polygons | EXPONENTS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Functions (mathematics) | Half spaces | Mathematical analysis | Evolution | Boundaries | Compressed | Saws | Polygons

compressive force | bridges | self-avoiding walks | Schramm-Loewner evolution | self-avoiding polygons | EXPONENTS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Functions (mathematics) | Half spaces | Mathematical analysis | Evolution | Boundaries | Compressed | Saws | Polygons

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2018, Volume 51, Issue 20, p. 204001

We consider a simple cubic lattice self-avoiding walk model of 3-star polymers adsorbed at a surface and then desorbed by pulling with an externally applied...

self-avoiding walk | phase diagram | pulled adsorbing lattice star | CHAIN | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics

self-avoiding walk | phase diagram | pulled adsorbing lattice star | CHAIN | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics

Journal Article

2006, ISBN 0444527354, 279

The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer...

Random walks (Mathematics) | Mathematics | Stochastic processes

Random walks (Mathematics) | Mathematics | Stochastic processes

eBook

Electronic Journal of Combinatorics, ISSN 1077-8926, 12/2017, Volume 24, Issue 4

The connective constant mu(G) of an infinite transitive graph G is the exponential growth rate of the number of self-avoiding walks from a given origin. The...

Spectral bottom | Indicable group | Amenable group | Spectral radius | Cayley graph | Grigorchuk group | Harmonic function | Self-avoiding walk | Group height function | Unimodularity | Baumslag-Solitar group | Elementary amenable group | Connective constant | Graph height function | Higman group | MATHEMATICS, APPLIED | PERCOLATION | amenable group | harmonic function | indicable group | connective constant | group height function | CONNECTIVE CONSTANTS | unimodularity | MATHEMATICS | spectral bottom | AMENABLE-GROUPS | graph height function | spectral radius | elementary amenable group | LATTICE | CAYLEY-GRAPHS

Spectral bottom | Indicable group | Amenable group | Spectral radius | Cayley graph | Grigorchuk group | Harmonic function | Self-avoiding walk | Group height function | Unimodularity | Baumslag-Solitar group | Elementary amenable group | Connective constant | Graph height function | Higman group | MATHEMATICS, APPLIED | PERCOLATION | amenable group | harmonic function | indicable group | connective constant | group height function | CONNECTIVE CONSTANTS | unimodularity | MATHEMATICS | spectral bottom | AMENABLE-GROUPS | graph height function | spectral radius | elementary amenable group | LATTICE | CAYLEY-GRAPHS

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 02/2016, Volume 49, Issue 11, p. 11

We prove some theorems about self-avoiding walks attached to an impenetrable surface (i.e. positive walks) and subject to a force. Specifically we show the...

65C05 | adsorbing self-avoiding walk | free energy | 82B80 | phase diagram Mathematics Subject Classification: 82B41 | phase diagram | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Theorems | Mathematical models | Confining | Planes | Free energy | Convergence | Physics - Statistical Mechanics

65C05 | adsorbing self-avoiding walk | free energy | 82B80 | phase diagram Mathematics Subject Classification: 82B41 | phase diagram | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Theorems | Mathematical models | Confining | Planes | Free energy | Convergence | Physics - Statistical Mechanics

Journal Article

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 10/2019, Volume 52, Issue 40, p. 405001

We consider self-avoiding walks terminally attached to a surface at which they can adsorb. A force is applied, normal to the surface, to desorb the walk and we...

POLYMER-CHAIN | phase diagram | pulled self-avoiding walks | adsorbing self-avoiding walks | Monte Carlo | PHYSICS, MULTIDISCIPLINARY | SURFACE | PHYSICS, MATHEMATICAL

POLYMER-CHAIN | phase diagram | pulled self-avoiding walks | adsorbing self-avoiding walks | Monte Carlo | PHYSICS, MULTIDISCIPLINARY | SURFACE | PHYSICS, MATHEMATICAL

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 01/2019, Volume 52, Issue 2, p. 25004

Flory-Huggins theory (Flory 1942 J. Chem. Phys. 10 51-61; Huggins 1942 J. Am. Chem. Soc. 64 2716-8) is a mean field theory for modelling the free energy of...

Flory interaction parameter | Confined self-avoiding walk | Flory-Huggins theory | Self-avoiding walk | Dense polymer | Osmotic pressure of self-avoiding walk | flory interaction parameter | POLYMERS | confined self-avoiding walk | PHYSICS, MULTIDISCIPLINARY | HUGGINS INTERACTION PARAMETER | self-avoiding walk | PHYSICS, MATHEMATICAL | DEPENDENCE | CHAIN | THERMODYNAMICS | dense polymer | osmotic pressure of self-avoiding walk

Flory interaction parameter | Confined self-avoiding walk | Flory-Huggins theory | Self-avoiding walk | Dense polymer | Osmotic pressure of self-avoiding walk | flory interaction parameter | POLYMERS | confined self-avoiding walk | PHYSICS, MULTIDISCIPLINARY | HUGGINS INTERACTION PARAMETER | self-avoiding walk | PHYSICS, MATHEMATICAL | DEPENDENCE | CHAIN | THERMODYNAMICS | dense polymer | osmotic pressure of self-avoiding walk

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 4/2017, Volume 167, Issue 2, pp. 317 - 350

We consider the critical behaviour of the continuous-time weakly self-avoiding walk with contact self-attraction on $$\mathbb {Z}^4$$ Z 4 , for sufficiently...

Collapse transition | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Renormalisation group | Weakly self-avoiding walk | Physics | Statistical Physics and Dynamical Systems | DIMENSIONS | FINITE-RANGE DECOMPOSITION | PHYSICS, MATHEMATICAL | LATTICE

Collapse transition | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Renormalisation group | Weakly self-avoiding walk | Physics | Statistical Physics and Dynamical Systems | DIMENSIONS | FINITE-RANGE DECOMPOSITION | PHYSICS, MATHEMATICAL | LATTICE

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 06/2017, Volume 50, Issue 26, p. 264002

We study self-avoiding walks on critical percolation clusters by means of a recently developed exact enumeration method, which can handle walks of several...

exact enumeration | self-avoiding walks | percolation clusters | THRESHOLD | SERIES | PHYSICS, MULTIDISCIPLINARY | DISORDERED MEDIA | DILUTED LATTICES | CRITICAL-BEHAVIOR | BACKBONE | PHYSICS, MATHEMATICAL | RANDOM-ENVIRONMENTS

exact enumeration | self-avoiding walks | percolation clusters | THRESHOLD | SERIES | PHYSICS, MULTIDISCIPLINARY | DISORDERED MEDIA | DILUTED LATTICES | CRITICAL-BEHAVIOR | BACKBONE | PHYSICS, MATHEMATICAL | RANDOM-ENVIRONMENTS

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2015, Volume 48, Issue 16, pp. 16 - 8

Self-avoiding walks (SAWs) are a simple and well-known model of long, flexible polymers in a good solvent. Polymers being pulled away from a surface by an...

Self-avoiding walks | phase transition | polymers | DIMENSIONS | MACROMOLECULES | PHYSICS, MULTIDISCIPLINARY | self-avoiding walks | SURFACE | PHYSICS, MATHEMATICAL | Solvents | Phases | Half spaces | Mathematical analysis | Mathematical models | Polymers | Saws | Free energy

Self-avoiding walks | phase transition | polymers | DIMENSIONS | MACROMOLECULES | PHYSICS, MULTIDISCIPLINARY | self-avoiding walks | SURFACE | PHYSICS, MATHEMATICAL | Solvents | Phases | Half spaces | Mathematical analysis | Mathematical models | Polymers | Saws | Free energy

Journal Article

ISSN 0022-4715, 2017

We consider the critical behaviour of the continuous-time weakly self-avoiding walk with contact self-attraction on $\mathbb{Z}$$^{4}$, for sufficiently small...

renormalisation group | weakly self-avoiding walk | collapse transition

renormalisation group | weakly self-avoiding walk | collapse transition

Journal Article

18.
The study of unfoldable self-avoiding walks-Application to protein structure prediction software

Journal of Bioinformatics and Computational Biology, ISSN 0219-7200, 08/2015, Volume 13, Issue 4, pp. 155000 - 1-155000-36

Self-avoiding walks (SAWs) are the source of very difficult problems in probability and enumerative combinatorics. They are of great interest as, for example,...

discrete structures | protein folding | Protein structure prediction | combinatorics algorithms | self-avoiding walks | problem complexity | SQUARE LATTICE | ALGORITHM | MATHEMATICAL & COMPUTATIONAL BIOLOGY | MODEL

discrete structures | protein folding | Protein structure prediction | combinatorics algorithms | self-avoiding walks | problem complexity | SQUARE LATTICE | ALGORITHM | MATHEMATICAL & COMPUTATIONAL BIOLOGY | MODEL

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 12/2015, Volume 49, Issue 1, p. 15004

We study terminally attached self-avoiding walks (SAWs) and bridges on the simple cubic lattice, both by series analysis and Monte Carlo methods. We provide...

pivot algorithm | critical exponents | self-avoiding walk | Monte Carlo | universal amplitude ratio | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Bridges (structures) | Monte Carlo methods | Cubic lattice | Amplitudes | Mathematical models | Saws | Three dimensional

pivot algorithm | critical exponents | self-avoiding walk | Monte Carlo | universal amplitude ratio | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Bridges (structures) | Monte Carlo methods | Cubic lattice | Amplitudes | Mathematical models | Saws | Three dimensional

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 1/2014, Volume 52, Issue 1, pp. 355 - 367

The Growing self avoiding walk model (GSAW) was proposed to explain statistical mechanics of the growth process in polymerization. Close examination of the...

Theoretical and Computational Chemistry | Chemistry | Depth first search trees | Physical Chemistry | Growing self avoiding walk | Condensation polymerization | Math. Applications in Chemistry | Growth process in polymerization | CARLO SERIES ANALYSIS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | GROWTH | PERCOLATION | CHEMISTRY, MULTIDISCIPLINARY | Polymerization | Trees (Graph theory) | Research | Statistical mechanics

Theoretical and Computational Chemistry | Chemistry | Depth first search trees | Physical Chemistry | Growing self avoiding walk | Condensation polymerization | Math. Applications in Chemistry | Growth process in polymerization | CARLO SERIES ANALYSIS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | GROWTH | PERCOLATION | CHEMISTRY, MULTIDISCIPLINARY | Polymerization | Trees (Graph theory) | Research | Statistical mechanics

Journal Article

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