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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 01/2020, Volume 53, Issue 1, p. 15002
A compressed knotted ring polymer in a confining cavity is modelled by a knotted lattice polygon confined in a cube in . The GAS algorithm (Janse van Rensburg... 
CHAIN | PROBABILITY | PHYSICS, MULTIDISCIPLINARY | DNA | ALGORITHM | RING POLYMERS | Flory?Huggins | compressed knots | PHYSICS, MATHEMATICAL | lattice knots | EFFECTIVE DIAMETER
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 04/2011, Volume 44, Issue 16, pp. 162002 - 8
Let p(n) denote the number of self-avoiding polygons of length n on a regular three-dimensional lattice, and let p(n)(K) be the number which have knot type K.... 
PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Cubic lattice | Amplitudes | Asymptotic properties | Lattices | Texts | Three dimensional | Knots | Polygons | Physics - Statistical Mechanics
Journal Article
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 08/2019, Volume 52, Issue 31, p. 315002
We investigate the phase diagram of a self-avoiding walk model of a 3-star polymer in two dimensions, adsorbing at a surface and being desorbed by the action... 
3-star polymer desorption | Monte Carlo | PHYSICS, MULTIDISCIPLINARY | SELF-AVOIDING WALKS | polymer statistical mechanics | polymer phase diagram | PHYSICS, MATHEMATICAL | polymer adsorption
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
Journal Article
Experimental Mathematics, ISSN 1058-6458, 10/2015, Volume 24, Issue 4, pp. 391 - 409
We describe a Metropolis Monte Carlo algorithm for random sampling of freely reduced words equal to the identity in a finitely presented group. The algorithm... 
Metropolis algorithm | R. Thompson's group F | amenable group | spectral radius | Baumslag-Solitar group | cogrowth | R. Thompson's group F | MONTE-CARLO | MATHEMATICS | RANDOM-WALKS | THOMPSONS GROUP-F | COGROWTH SERIES
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 03/2014, Volume 24, Issue 2, pp. 171 - 187
We compute the cogrowth series for Baumslag–Solitar groups BS(N, N) = 〈a,b|aNb = baN〉, which we show to be D-finite. It follows that their cogrowth rates are... 
Cogrowth series | Baumslag-Solitar group | D-finite generating function | Amenable group | Algebraic generating function | MATHEMATICS | WALKS | amenable group | algebraic generating function | Cytokinins | Computation | Algebra
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 05/2008, Volume 41, Issue 18, p. 185004
A polymer in a confined geometry may be modeled by a self-avoiding walk or a self-avoiding polygon confined between two parallel walls. In two dimensions, this... 
SUBJECT | CHAIN POLYMER | BOUNDARY | STRIPS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL
Journal Article
PHYSICAL REVIEW E, ISSN 2470-0045, 07/2019, Volume 100, Issue 1
A numerical simulation shows that the osmotic pressure of compressed lattice knots is a function of knot type, and so of entanglements. The osmotic pressure... 
STATISTICAL-MECHANICS | POLYMERS | DNA KNOTS | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS
Journal Article
PHYSICAL REVIEW E, ISSN 2470-0045, 01/2020, Volume 101, Issue 1
The free energy of a model of uniformly weighted lattice knots of length n and knot type K confined to a lattice cube of side length L-1 is given by F-L(phi) =... 
PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS
Journal Article
Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 09/2005, Volume 2005, Issue 9, pp. P09010 - 285
Consider fully directed paths from the origin in the square lattice and confined to the q/p-wedge formed by the Y-axis and the line Y = (q/p)X, where (p, q) is... 
Exact results | Polymers | Rigorous results in statistical mechanics | Solvable lattice models | rigorous results in statistical mechanics | STATISTICAL-MECHANICS | VESICLES | FINITE RANDOM COPOLYMERS | ADSORPTION | PHYSICS, MATHEMATICAL | exact results | AVOIDING WALK MODEL | POLYMER-CHAIN | solvable lattice models | MECHANICS | TREES | SURFACE | polymers
Journal Article
PHYSICAL REVIEW E, ISSN 1539-3755, 10/2001, Volume 64, Issue 4, p. 046101
Branched polymers interacting with an impenetrable wall can be modeled by lattice trees confined to a half space with a fugacity kappa conjugate to the number... 
COLLAPSING TREES | SQUARE | BRANCHED POLYMERS | PHYSICS, FLUIDS & PLASMAS | SELF-AVOIDING WALKS | BEHAVIOR | SURFACE | PHYSICS, MATHEMATICAL | LATTICE TREES | CRITICAL EXPONENTS | 2 DIMENSIONS
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 10/2001, Volume 105, Issue 1, pp. 49 - 91
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 2002, Volume 9, Issue 1 R, pp. 1 - 24
In a previous work [26], by considering paths that are partially weighted, the generating function of Dyck paths was shown to possess a type of symmetry,... 
MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 03/2002, Volume 11, Issue 2, pp. 199 - 210
The maximum of the linking number between two lattice polygons of lengths n1, n2 (with n1 ≤ n2) is proven to be the order of n1 (n2)⅓. This result is... 
Lattice Polygons | Links | Lattice Links | Linking Number | Knots | MATHEMATICS | lattice links | COMPLEXITY | links | linking number | knots | LATTICE | lattice polygons
Journal Article
Mathematical Proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 3/1999, Volume 126, Issue 2, pp. 293 - 310
In this paper we define a set of radii called thickness for simple closed curves denoted by K, which are assumed to be differentiable. These radii capture a... 
MATHEMATICS | ENERGY
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 12/1997, Volume 6, Issue 6, pp. 799 - 807
An energy function for smooth knots is defined using the concept of thickness and proved to be a good indicator of the complexity of knots. This energy... 
Energy of Knots | Thickness of Knots | Knot Complexity | Knots | knot complexity | MATHEMATICS | CUBIC LATTICE | energy of knots | knots | thickness of knots
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 06/1999, Volume 8, Issue 4, pp. 463 - 490
A result of Milnor [1] states that the infimum of the total curvature of a tame knot K is given by 2πμ(K), where μ(K) is the crookedness of the knot K. It is... 
MATHEMATICS | CUBIC LATTICE
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 1996, Volume 82, Issue 1-2, pp. 155 - 181
We consider self-avoiding walks on the simple cubic lattice in which neighboring pairs of vertices of the walk (not connected by an edge) have an associated... 
Lattice models | Markov chains | Self-avoiding walks | Monte Carlo | Phase transitions | GLOBULE TRANSITION | lattice models | EXPONENTS | BEHAVIOR | phase transitions | 3 DIMENSIONS | PHYSICS, MATHEMATICAL | POLYMER-CHAIN | POLYSTYRENE | THETA-POINT | COLLAPSE | self-avoiding walks | LINEAR POLYMER | 2 DIMENSIONS
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 10/1997, Volume 6, Issue 5, pp. 633 - 657
An energy function on knots is a scale-invariant function from knot conformations into non-negative real numbers. The infimum of an energy function is an... 
Equilateral polygons | Polygonal knots | Energies of knots | Simulated annealing | Knots | polygonal knots | MATHEMATICS | simulated annealing | knots | equilateral polygons | energies of knots
Journal Article
Journal of Physics A: Mathematical and General, ISSN 0305-4470, 07/2004, Volume 37, Issue 27, pp. 6875 - 6898
A self-avoiding walk adsorbing on a line in the square lattice, and on a plane in the cubic lattice, is studied numerically as a model of an adsorbing polymer... 
POLYMER-CHAIN | NUMBER | COLLAPSE | PHYSICS, MULTIDISCIPLINARY | SQUARE LATTICE | SURFACE | COMPUTER-SIMULATION | POLYGONS | MODEL | ADSORPTION | PHYSICS, MATHEMATICAL | CRITICAL EXPONENTS
Journal Article
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