Mass-Dependent Solvent Friction of a Hydrophobic Molecule

Daldrop, Jan O.; Netz, Roland R.

doi:10.1021/acs.jpcb.9b08295

Cited by 9 publications

(5 citation statements)

References 53 publications

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“…Figures 1 and 2 show the calculations of the MSD of the harmonically trapped BP experimentally studied in reference [16]. In [16], the system was correctly considered as an overdamped one and it is well seen that if the mass of the followed silica BP with a diameter of 2.73 μm is taken into account, the underdamped solution (17) can hardly be distinguished from the overdamped one (13), which very well describes the experiment. Another example is taken from the computer simulations study [17] of the BM of a solute (methane molecule) in water.…”

Section: Transition Between Overdamped and Underdamped Regimesmentioning

confidence: 63%

“…The assumption of the infinitely rapid change of the fluctuation force brings a serious limitation for possible applications of the SLE to real systems [7,8]. A variety of phenomena, e.g., in liquid-state physics and chemistry, as well as in biology and other areas [9][10][11][12][13] are more effectively described with the use of the generalized Langevin equation (GLE) [7,14]…”

Section: Introductionmentioning

confidence: 99%

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Overdamped and underdamped Langevin equations in the interpretation of experiments and simulations

Tóthová¹,

Lisý²

2022

Eur. J. Phys.

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The Brownian motion (BM) is not only a natural phenomenon but also a fundamental concept in several scientific fields. The mathematical description of the BM for students of various disciplines is most often based on Langevin's equation with the Stokes friction force and the random force modeling Brownian particle (BP) collisions with surrounding molecules. For many phenomena, such a description is insufficient, as it assumes an infinitesimal correlation time of random force. This shortcoming is overcome by the generalized Langevin equation (GLE), which is now one of the most widely used equations in physics. In the present work, we offer a simple way of solving this equation, consisting of its transformation into an integro-differential equation for the mean square displacement of the BP, which is then effectively solved using the Laplace transform (LT). We demonstrate the use of this method to solve both the standard Langevin equation and the GLE for the BP in an external harmonic field. We analyze the cases of overdamped (when frictional forces prevail over inertial forces and the BP mass is considered zero in the equation) and underdamped (inertial effects are not neglected) equations. We show under what conditions an overdamped solution can be used instead of complicated solutions of the underdamped equation. We also demonstrate the effectiveness of the use of the LT on a microscopic approach to the derivation of the GLE. Graduate students are offered several problems in which the internal shortcomings of the overdamped Langevin equations manifest themselves.

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Section: Transition Between Overdamped and Underdamped Regimesmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Overdamped and underdamped Langevin equations in the interpretation of experiments and simulations

Tóthová¹,

Lisý²

2022

Eur. J. Phys.

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“…However, the confinement of the methane molecule influences the relaxation of the water molecules in the hydration shell, effectively increasing the local viscosity in the first hydration shell. They observed a similar effect when artificially increasing the mass of the methane molecule . Higher solute masses also resulted in a slowdown of hydration shell dynamics and a local increase of the viscosity.…”

Section: Reconstruction Of Memory Kernelsmentioning

confidence: 71%

“…They observed a similar effect when artificially increasing the mass of the methane molecule. 78 Higher solute masses also resulted in a slowdown of hydration shell dynamics and a local increase of the viscosity.…”

Section: Reconstruction Of Memory Kernelsmentioning

confidence: 99%

Introducing Memory in Coarse-Grained Molecular Simulations

et al. 2021

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Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori−Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In this Review, we describe some of the recent studies in this regard. We focus on the construction and simulation of dynamically consistent systematic CG models based on the GLE, both in the simple Markovian limit and the non-Markovian case. Some recent studies of physical effects of memory are also discussed. The Review is aimed at summarizing recent developments in the field while highlighting the major challenges and possible future directions.

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“…Despite the difficulty of such a task, the calculation of memory kernels from microscopic dynamics can be performed reliably and efficiently by inverting the Volterra equations obtained from the Generalized Langevin Equation (GLE) [4][5][6][7][8][9][10][11][12][13][14] , although more complex methods exist [15][16][17][18][19][20] . The simple yet efficient method based on the inversion of Volterra equations has, however, only been applied to the computation of the memory kernel appearing in the GLE.…”

Section: Introductionmentioning

confidence: 99%

Simple and efficient algorithms based on Volterra equations to compute memory kernels and projected cross-correlation functions from molecular dynamics

Obliger

2023

The Journal of Chemical Physics

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Starting from the orthogonal dynamics of any given set of variables with respect to the projection variable used to derive the Mori–Zwanzig equation, a set of coupled Volterra equations is obtained that relate the projected time correlation functions between all the variables of interest. This set of equations can be solved using standard numerical inversion methods for Volterra equations, leading to a very convenient yet efficient strategy to obtain any projected time correlation function or contribution to the memory kernel entering a generalized Langevin equation. Using this strategy, the memory kernel related to the diffusion of tagged particles in a bulk Lennard–Jones fluid is investigated up to the long-term regime to show that the repulsive–attractive cross-contribution to memory effects represents a small but non-zero contribution to the self-diffusion coefficient.

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Mass-Dependent Solvent Friction of a Hydrophobic Molecule

Cited by 9 publications

References 53 publications

Overdamped and underdamped Langevin equations in the interpretation of experiments and simulations

Overdamped and underdamped Langevin equations in the interpretation of experiments and simulations

Introducing Memory in Coarse-Grained Molecular Simulations

Simple and efficient algorithms based on Volterra equations to compute memory kernels and projected cross-correlation functions from molecular dynamics

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