Robust and efficient configurational molecular sampling via Langevin Dynamics

Benedict Leimkuhler; Charles Matthews

doi:10.1063/1.4802990

Home/Archive/arXiv

arXiv · 1304.3269

Robust and efficient configurational molecular sampling via Langevin Dynamics

Benedict Leimkuhler·Charles Matthews

View original source ↗Read source document ↗Export metadata ↓

Abstract

A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian motions in some combination. The Baker-Campbell-Hausdorff expansion is used to study sampling accuracy following recent work by the authors, which allows determination of the stepsize-dependent bias in configurational averaging. For harmonic oscillators, configurational averaging is exact for certain schemes, which may result in improved performance in the modelling of biomolecules where bond stretches play a prominent role. For general systems, an optimal method can be identified that has very low bias compared to alternatives. In simulations of the alanine dipeptide reported here (both solvated and unsolvated), higher accuracy is obtained without loss of computational efficiency, while allowing large timestep, and with no impairment of the conformational exploration rate (the effective diffusion rate observed in simulation). The optimal scheme is a uniformly better performing algorithm for molecular sampling, with overall efficiency improvements of 25% or more in practical timestep size achievable in vacuum, and with reductions in the error of configurational averages of a factor of ten or more attainable in solvated simulations at large timestep.

Explore related subjects

physics.comp-ph cond-mat.stat-mech cs.NA math.NA physics.chem-ph

Keep this discovery

BibTeX RIS

Benedict Leimkuhler, Charles Matthews. 2013-04-11. Robust and efficient configurational molecular sampling via Langevin Dynamics. https://doi.org/10.1063/1.4802990

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Geometrically Parameterized Quasi-Stationary 3D Model for High-Frequency Induction Tube Welding

A three-dimensional multiphysics finite element framework for the simulation of high-frequency induction welding of tubes is presented. The model couples a time-harmonic magnetic scalar potential formulation with a stabilized quasi-stationary advection-diffusion heat transport equation, enabling accurate prediction of electromagnetic and thermal fields under industrial operating conditions. The framework incorporates parameterized geometry generation and semi-automated, physics-tailored mesh construction and is implemented using the open-source tools GetDP and Gmsh. Validation against measurements from a commercial induction welding line for AISI 304 stainless steel tubes demonstrates good agreement with operating data. The validated model is subsequently applied to investigate the influence of impeder material by comparing a conventional FeNiZnV ferrite with the soft magnetic composite Ferrotron 559H for the induction welding of AISI 304 stainless steel tubes.

physics.comp-ph↗

arXiv2026

Stress-Testing Dynamical and Generative Downscaling Using Subseasonal Extreme Precipitation Forecasts

Coarse spatial resolution limits the ability of subseasonal prediction models to resolve extreme precipitation. Downscaling with either dynamical or deep generative models can overcome this issue, but the comparative performance of these models for extremes across different atmospheric regimes remains poorly understood. In this work, we evaluate the Weather Research and Forecasting (WRF) model against a diffusion-based generative model by downscaling two physically distinct, extreme precipitation events up to lead times of 3 weeks. For a fair comparison with WRF, which can downscale boundary conditions from different driving models without model-specific training, the diffusion model is trained in an unpaired fashion. Both approaches improve upon the raw European Centre for Medium-Range Weather Forecasts forecasts, in comparison to fused rain gauge-radar observations in Switzerland (CombiPrecip), but exhibit regime-dependent strengths. WRF achieves the highest probabilistic skill for a multicell, non-stationary event. Conversely, the diffusion model is more consistent across different performance metrics for the two events, outperforming WRF in a more stationary supercell event. These results demonstrate that explicit dynamical modeling can add value for specific precipitation events for subseasonal lead times, and that generative downscaling adds value more broadly in different situations.

physics.comp-ph↗

arXiv2026

Nonlinear flame describing function and mean shift kinematics of slit flames under combined axial-transverse forcing

This study investigates the nonlinear kinematics of a premixed slit flame using a two-dimensional $G$-equation level-set framework. Results show that combined forcing induces nonlinear saturation in the FDF, characterized by early gain flattening and premature phase drops, which intensify with the transverse forcing amplitude. Kinematic analysis reveals that this geometric nonlinearity manifests as a reduction in the time-averaged flame height, defined as the mean shift. In the quasi-steady limit, this mean shift is analytically quantified via a multivariate asymptotic expansion, where fourth-order terms successfully capture the saturation mechanism at elevated amplitudes. By introducing a scaling parameter to account for transverse dominance, the frequency-dependent decay of the mean shift in the compact limit collapses onto a single master curve, enabling the derivation of a unified theoretical model that integrates this asymptotic response with a second-order low-pass filter. Furthermore, because the mean shift reduces the physical extent of the flame, it alters the wrinkle propagation time. Correcting the Strouhal number using the measured mean shift collapses the dispersed nonlinear FDF curves onto the linear theory prediction. The analysis is further extended to disturbances convected at a finite speed, for which the linear transfer function is derived analytically and the correction with the measured mean shift continues to collapse the nonlinear FDF. These findings establish that the nonlinear FDF behavior under multidimensional forcing is fundamentally governed by the kinematic mean shift, providing a theoretical baseline for decoupling geometric nonlinearities from other thermo-diffusive or hydrodynamic instabilities in turbulent flames.

physics.comp-ph↗