The importance of introducing a waiting time for Lattice Monte Carlo simulations of a polymer translocation process

Haan, Hendrick W. de; Gauthier, Michel G.; Chubynsky, Mykyta V.; Slater, Gary W.

doi:10.1016/j.cpc.2010.07.045

Cited by 8 publications

(4 citation statements)

References 13 publications

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“…II A, our 1D optimal algorithm is the zero-field limit of a previously de- rived algorithm for biased diffusion [19]. We have recently applied the latter algorithm to a 1D model of polymer translocation through a nanopore [27] and showed that this algorithm gives very different widths of the translocation time distributions compared to the ordinary algorithm without waiting times, thus demonstrating the importance of introducing waiting times [28]. It is true, though, that the utility of the new algorithms will be further enhanced when the issues described above are taken care of, as well as when the approach is extended to biased diffusion in 2D and 3D as well.…”

Section: Discussionmentioning

confidence: 99%

Section: A Comparison To the Continuum Equationmentioning

confidence: 99%

“…By expanding both sides in the Taylor series in k we can verify that this equality is satisfied to O(k 4 ) only when the probabilities and the time step are given by Eqs. (26)- (28). For the maximum possible time step, τ = τ max = a 2 /2D, the decay rate diverges at ka = π/2, and for larger ka it is complex becoming purely imaginary (Re α = 0) at ka = π.…”

Section: A Comparison To the Continuum Equationmentioning

confidence: 99%

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Optimizing the accuracy of lattice Monte Carlo algorithms for simulating diffusion

Chubynsky

Slater

2012

Phys. Rev. E

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The behavior of a Lattice Monte Carlo algorithm (if it is designed correctly) must approach that of the continuum system that it is designed to simulate as the time step and the mesh step tend to zero. However, we show for an algorithm for unbiased particle diffusion that if one of these two parameters remains fixed, the accuracy of the algorithm is optimal for a certain finite value of the other parameter. In one dimension, the optimal algorithm with moves to the two nearest neighbor sites reproduces the correct second and fourth moments (and minimizes the error for the higher moments at large times) of the particle distribution and preserves the first two moments of the first-passage time distributions. In two and three dimensions, the same level of accuracy requires simultaneous moves along two axes ("diagonal" moves). Such moves attempting to cross an impenetrable boundary should be projected along the boundary, rather than simply rejected.We also treat the case of absorbing boundaries.

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Section: Discussionmentioning

confidence: 99%

Section: A Comparison To the Continuum Equationmentioning

confidence: 99%

Section: A Comparison To the Continuum Equationmentioning

confidence: 99%

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Optimizing the accuracy of lattice Monte Carlo algorithms for simulating diffusion

Chubynsky

Slater

2012

Phys. Rev. E

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“…Monte Carlo simulation is more popular among computer simulation methods. Many researchers paid attention to the study of macromolecular configurations by various Monte-Carlo (MC) devices [13][14][15][16][17] . Currently, few papers have been published on Monte Carlo study of isothermal crystallization kinetics.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Simulation Study of Isothermal Crystallization Kinetics of Polyethylene Glycol

Sun

Feng

Wang

et al. 2011

Polymer-Plastics Technology and Engineering

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Isothermal crystallization kinetics of polyethylene glycol (PEG) was investigated by use of Monte Carlo computer simulation. Nucleation mechanism, some crystallization parameters used in simulation and the crystalline morphology of PEG were first measured with a hot stage polarizing microscope (HSPOM). The results showed that under an instantaneous nucleation condition, PEG exhibited well-defined and large spherulites as being crystallized from the melt at various crystallization temperatures. The linear growth rate of PEG decreased as the crystallization temperature increased. The Avrami equation was suitable to describe the primary simulated isothermal crystallization process of PEG. With the increase of crystallization temperature, the overall crystallization rate decreased, while the Avrami exponent, approaching 3, almost remained unchanged. Differential scanning calorimetry (DSC) was employed to confirm the validity of the established simulation model. INTRODUCTIONUnderstanding the crystallization kinetics of polymer is important for assessing their processing-property interrelationship. The physical and mechanical properties of polymer are dependent on the developed crystallinity governed by the combined influence. The morphology of polymer can vary depending upon the relative crystallization times and the extent of crystallization as a function of temperature of the component polymers. Information regarding these parameters is necessary in order to understand the microstructure development in melt processing. Therefore, study of the crystallization kinetics is necessary for optimizing industrial processes and establishing the

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A theoretical study on entropy-driven polymer translocation through a finite-sized nanochannel

Meng

Zhou

et al. 2013

Chemical Physics Letters

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The importance of introducing a waiting time for Lattice Monte Carlo simulations of a polymer translocation process

Cited by 8 publications

References 13 publications

Optimizing the accuracy of lattice Monte Carlo algorithms for simulating diffusion

Optimizing the accuracy of lattice Monte Carlo algorithms for simulating diffusion

Monte Carlo Simulation Study of Isothermal Crystallization Kinetics of Polyethylene Glycol

A theoretical study on entropy-driven polymer translocation through a finite-sized nanochannel

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