Random paths and random surfaces on a digital computer

Berg, Bernd A.; Foêrster, D.

doi:10.1016/0370-2693(81)90545-1

Cited by 149 publications

(130 citation statements)

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“…Besides the translocation processes, of central importance for biology, the study of topological spectra of DNA extracted from viral capsids is a typical context where the knowledge of spectra for specific models of random polymers is very valuable. 11,12,14 Model calculations like those carried out in the present work Figure 1: Example of a collapsed interacting selfavoiding ring with N = 500 steps on the cubic lattice, and its shortened form after the BFACF 39,40 reduction procedure with a low fugacity per step. The latter reveals that the ring holds a 5 2 knot, whose projection with the minimal crossing number n c = 5 is also shown.…”

Section: Introductionmentioning

confidence: 83%

“…This simplification is achieved with a grand-canonical algorithm of the BFACF type, 39,40,52 which has the property of preserving the knot type because it lets the configurations evolve only with local and crankshaft deletion/insertion moves. In our case the simplification is achieved with a bias toward deletion that emerges from choosing a low fugacity K per step.…”

Section: Variable Topologymentioning

confidence: 99%

See 1 more Smart Citation

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

2014

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The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter depending on the knot kind is an amplitude such that relative probabilities of knots do not vary with the temperature T , in the limit of long chains. We arrive at this conclusion by simulating interacting self-avoiding rings at low T on the cubic lattice, both with unrestricted topology and with setups where the globule is divided by a slip link in two loops (preserving their topology) which compete for the chain length, either in contact or separated by a wall as for translocation through a membrane pore. These findings suggest that in macromolecular environments there may be entropic forces with a purely topological origin, whence portions of polymers holding complex knots should tend to expand at the expense of significantly shrinking other topologically simpler portions. 1

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Section: Introductionmentioning

confidence: 83%

Section: Variable Topologymentioning

confidence: 99%

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

2014

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“…This algorithm was implemented using BFACF-style elementary moves [5] (see figure 8) Figure 8. BFACF moves in the square lattice [5].…”

Section: Numerical Results From Monte Carlo Datamentioning

confidence: 99%

“…This algorithm was implemented using BFACF-style elementary moves [5] (see figure 8) Figure 8. BFACF moves in the square lattice [5]. A positive move (or a positive BFACF move) increases the length of a polygon by 2 steps by replacing an edge with three edges.…”

Section: Numerical Results From Monte Carlo Datamentioning

confidence: 99%

Polygons pulled from an adsorbing surface

Guttmann¹,

Rensburg²,

Jensen³

et al. 2018

J. Phys. A: Math. Theor.

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Abstract. We consider self-avoiding lattice polygons, in the hypercubic lattice, as a model of a ring polymer adsorbed at a surface and either being desorbed by the action of a force, or pushed towards the surface. We show that, when there is no interaction with the surface, then the response of the polygon to the applied force is identical (in the thermodynamic limit) for two ways in which we apply the force. When the polygon is attracted to the surface then, when the dimension is at least 3, we have a complete characterization of the critical force-temperature curve in terms of the behaviour, (a) when there is no force, and, (b) when there is no surface interaction. For the 2-dimensional case we have upper and lower bounds on the free energy. We use both Monte Carlo and exact enumeration and series analysis methods to investigate the form of the phase diagram in two dimensions. We find evidence for the existence of a mixed phase where the free energy depends on the strength of the interaction with the adsorbing line and on the applied force.

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“…Several methods proposed recently, like the pseudo-fermion method [1][2][3], stochastic method [4,5] or the microcanonical method [6] are promising, but it is usually difficult to control their accuracy due to some approximations which affect the results only rather indirectly. In a recently proposed method based on high order numerical hopping parameter expansion [7,8] the committed errors are easier to control.…”

mentioning

confidence: 99%

Monte Carlo calculation with unquenched Wilson fermions

Montvay

1984

Physics Letters B

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A Monte Carlo updating procedure taking into account the virtual quark loops is described. It is based on high-order hopping parameter expansion of the quark determinant for Wilson fermions. In a first test run Wilson loop expectation values are measured on a 64 lattice at 13 = 5.70 using 16th order hopping parameter expansion for the quark determinant.The inclusion of the effects of virtual fermion loops in Monte Carlo simulations of lattice gauge theories is an important and challenging problem. At present it is to a large extent unknown how much the Monte Carlo resuks obtained in the pure colour gauge sector or in the "quenched approximation" will be changed once light dynamical quarks are properly included in the computations of lattice quantum chromodynamics. There is a class of problems, like the screening of (fundamental) colour charge or the fragmentation of fast quarks into hadrons etc., which cannot even be formulated without virtual quark loops.From the computational point of view the inclusion of dynamical fermions is, however, rather difficult because of the long range interaction induced by the virtual light fermion loops. Several methods proposed recently, like the pseudo-fermion method [1][2][3], stochastic method [4,5] or the microcanonical method [6] are promising, but it is usually difficult to control their accuracy due to some approximations which affect the results only rather indirectly. In a recently proposed method based on high order numerical hopping parameter expansion [7,8] the committed errors are easier to control. The fermion determinant is, however, not included in the updating but it is treated essentially as a part of the expectation value. In the case of light fermions this is the source of large fluctuations prohibiting the collection of enough statistics in a reasonable amount of computer time.i Supported by Bundesministerium f~ir Forschung und Technologie, Bonn, Germany. 70In the present letter I describe an updating procedure with the fermion determinant evaluated to high order in the hopping parameter expansion at every link and included in the Monte Carlo updating. The use of the hopping parameter expansion of fermion determinant in the updating was already attempted previously in a different way by Lang and Nicolai [9]. They, however, sorted out the contributions of the fermion determinant to the effective action according to closed curves passing through a given link. The number of such curves increases very rapidly with the length (i.e. with the order of expansion): at 12th order there are more than 4 × 106 such curves and e.g. at 16th order already more than 6 × 109 [10]. (Actually, these numbers refer to an infinite lattice. On a finite periodic lattice the number is still increased by the curves wrapping around the lattice.) It is clearly impossible to handle such large numbers of curves with any reasonable approximation (in ref.[9] typically 20 curves with length not more than 12 were taken). The solution I have chosen is to use the fast iterative method [11] for ...

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Random paths and random surfaces on a digital computer

Cited by 149 publications

References 10 publications

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

Polygons pulled from an adsorbing surface

Monte Carlo calculation with unquenched Wilson fermions

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