Related papers: Application of Projection Operator Method to Coars…
This work presents a systematic methodology for describing the transient dynamics of coarse-grained molecular systems inferred from all-atom simulated data. We suggest Langevin-type dynamics where the coarse-grained interaction potential…
We show that a mesoscopic coarse-grained dynamics model which incorporates the transient potential can be formally derived from an underlying microscopic dynamics model. As a microscopic dynamics model, we employ the overdamped Langevin…
We develop a formalism to carry out coarse-grainings in quantum field theoretical systems by using a time-dependent projection operator in the Heisenberg picture. A systematic perturbative expansion with respect to the interaction part of…
The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can…
In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of…
Complex microscopic many-body processes are often interpreted in terms of so-called `reaction coordinates', i.e. in terms of the evolution of a small set of coarse-grained observables. A rigorous method to produce the equation of motion of…
To investigate the impact of non-linear interactions on dynamic coarse graining, we study a simplified model system, featuring a tracer particle in a complex environment. Using a projection operator formalism and computer simulations, we…
In the field of machine learning coarse-grained potentials in molecular dynamics, many propagators require that the effective Hamiltonian is quadratic in momentum, thus limiting the family of coarse-graining functions. In this paper, we…
We present a numerical method to produce stochastic dynamics according to the generalized Langevin equation with a non-stationary memory kernel. This type of dynamics occurs when a microscopic system with an explicitly time-dependent…
Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter extensive efforts have been made but…
Coarse graining (CG) is an important task for efficient modeling and simulation of complex multi-scale systems, such as the conformational dynamics of biomolecules. This work presents a projection-based coarse-graining formalism for general…
A careful derivation of the generalized Langevin equation using "Zwanzig flavor" projection operator formalism is presented. We provide arguments why this formalism has better properties compared to alternative projection-operator…
We investigate two different types of non-Markovian coarse-grained models extracted from a linear, non-equilibrium microscopic system, featuring a tagged particle coupled to underdamped oscillators. The first model is obtained by…
By exact projection in phase space we derive the generalized Langevin equation (GLE) for time-filtered observables. We employ a general convolution filter that directly acts on arbitrary phase-space observables and can involve low-pass,…
Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations, since sufficiently large portions of the bath have to be included in the computation to…
We introduce a general framework for deriving effective dynamics from arbitrary time-dependent generators, based on a systematic operator cumulant expansion. Unlike traditional approaches, which typically assume periodic or adiabatic…
We present a derivation of a coarse-grained model from the Langevin dynamics. The focus is placed on the memory kernel function and the fluctuation-dissipation theorem. Also presented is an hierarchy of approximations for the memory and…
We present a new framework for coarse-graining molecular dynamics models for crystalline solids. The reduction method is based on a Galerkin projection to a subspace, whose dimension is much smaller than that of the full atomistic model.…
This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The…
We recently showed that the dynamics of coarse-grained observables in systems out of thermal equilibrium are governed by the non-stationary generalized Langevin equation [J. Chem. Phys. 147, 214110 (2017), J. Chem. Phys. 150, 174118…