Comparison of modern Langevin integrators for simulations of coarse-grained polymer melts

Finkelstein, Joshua; Fiorin, Giacomo; Seibold, Benjamin

doi:10.1080/00268976.2019.1649493

Cited by 13 publications

(15 citation statements)

References 37 publications

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“…FIG. 3: Coarse-grained polyethylene system [48] inside a periodic box with dimensions 58.065 Å × 58.065 Å × 58.065 Å. This figure was made using VMD [50].…”

Section: Numerical Resultsmentioning

confidence: 99%

The Challenge of Stochastic Størmer-Verlet Thermostats Generating Correct Statistics

Finkelstein,

Cheng,

Fiorin

et al. 2020

Preprint

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In light of the recently developed complete GJ set of single random variable stochastic, discrete-time Størmer-Verlet algorithms for statistically accurate simulations of Langevin equations, we investigate two outstanding questions: 1) Are there any algorithmic or statistical benefits from including multiple random variables per time-step, and 2) are there objective reasons for using one or more methods from the available set of statistically correct algorithms? To address the first question, we assume a general form for the discrete-time equations with two random variables and then follow the systematic, brute-force GJ methodology by enforcing correct thermodynamics in linear systems. It is concluded that correct configurational Boltzmann sampling of a particle in a harmonic potential implies correct configurational freeparticle diffusion, and that these requirements only can be accomplished if the two random variables per time step are identical. We consequently submit that the GJ set represents all possible stochastic Størmer-Verlet methods that can reproduce timestep-independent statistics of linear systems. The second question is thus addressed within the GJ set. Based in part on numerical simulations of complex molecular systems, and in part on analytic scaling of time, we analyze the apparent difference in stability between different methods. We attribute this difference to the inherent time scaling in each method, and suggest that this scaling may lead to inconsistencies in the interpretation of dynamical and statistical simulation results. We therefore suggest that the method with the least inherent time-scaling, the GJ-I/GJF-2GJ method, be preferred for statistical applications where spurious rescaling of time is undesirable.

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“…FIG. 3: Coarse-grained polyethylene system [48] inside a periodic box with dimensions 58.065 Å × 58.065 Å × 58.065 Å. This figure was made using VMD [50].…”

Section: Numerical Resultsmentioning

confidence: 99%

The Challenge of Stochastic Størmer-Verlet Thermostats Generating Correct Statistics

Finkelstein,

Cheng,

Fiorin

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Several previous publications have already demonstrated the statistical accuracy of the GJ methods for both configurational and kinetic measures for both simple nonlinear and complex molecular dynamics systems [28,29,[32][33][34]. Of course, for linear systems these methods are designed to be statistically exact for any stable time step, but nonlinearities can create completely new dynamical features that dominate the system behavior for relatively large time steps [42].…”

Section: Numerical Simulations a Simple Non-linear Systemmentioning

confidence: 99%

“…Numerous direct simulations of both simple nonlinear and complex molecular dynamics systems have since confirmed these attractive features (see, e.g., Refs. [28][29][30][31][32][33][34]) and two variants of this method [26,28] are included in the public distribution of the molecular dynamics simulation suite LAMMPS [35,36].…”

Section: Introductionmentioning

confidence: 99%

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Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

Finkelstein,

Cheng,

Fiorin

et al. 2021

Preprint

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In light of the recently published complete set of statistically correct GJ methods for discrete-time thermodynamics, we revise the differential operator splitting method for the Langevin equation in order to comply with the basic GJ thermodynamic sampling features, namely the Boltzmann distribution and Einstein diffusion, in linear systems. This revision, which is based on the introduction of time scaling along with flexibility of a discrete-time velocity attenuation parameter, provides a direct link between the ABO splitting formalism and the GJ methods. This link brings about the conclusion that any GJ method has

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“…The GJF integrator is chosen because of its unusual robustness against such errors, which is critical for achieving accurate statistics of configurational results even when the integration time step dt is not vanishingly small. More specifically, the GJF integrator accomplishes statistical accuracy for configurational sampling of the Boltzmann distribution in closed systems; and it also provides the correct Einstein diffusion, x 2 = 2Dt (with D = k B T /α), of a freely diffusing particle in an unbounded system [17,18,25,26]. Note that on time scales…”

Section: Diffusion In Homogeneous Mediummentioning

confidence: 99%

Algorithms for Brownian dynamics across discontinuities

Farago

2020

Preprint

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The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of model systems is to match the solutions of the time-dependent diffusion equation in each layer, such that the boundary conditions at the interfaces between them are satisfied. As the number of layers increases, the solutions may become increasingly complicated. Here, we describe an alternative computational approach to multi-layer diffusion problems, which is based on the description of the overdamped Brownian motion of particles via the underdamped Langevin equation. In this approach, the probability distribution function is computed from the statistics of an ensemble of independent single particle trajectories. To allow for simulations of Langevin dynamics in layered systems, the numerical integrator must be supplemented with algorithms for the transitions across the discontinuous interfaces. Algorithms for three common types of discontinuities are presented: (i) A discontinuity in the friction coefficient, (ii) a semi-permeable membrane, and (iii) a step-function chemical potential. The general case of an interface where all three discontinuities are present (Kedem-Katchalsky boundary) is also discussed. We demonstrate the validity and accuracy of the derived algorithms by considering a simple two-layer model system and comparing the Langevin dynamics statistics with analytical solutions and alternative computational results.

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Comparison of modern Langevin integrators for simulations of coarse-grained polymer melts

Cited by 13 publications

References 37 publications

The Challenge of Stochastic Størmer-Verlet Thermostats Generating Correct Statistics

The Challenge of Stochastic Størmer-Verlet Thermostats Generating Correct Statistics

Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

Algorithms for Brownian dynamics across discontinuities

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