# Mean Field Approximation in Conformation Dynamics

@article{Friesecke2009MeanFA,
title={Mean Field Approximation in Conformation Dynamics},
author={Gero Friesecke and Oliver Junge and P{\'e}ter Koltai},
journal={Multiscale Model. Simul.},
year={2009},
volume={8},
pages={254-268}
}
• Published 10 July 2009
• Physics
• Multiscale Model. Simul.
We propose a new approach to the transfer operator based analysis of the conformation dynamics of molecules. It is based on a statistical independence ansatz for the eigenfunctions of the operator related to a partitioning into subsystems. Numerical tests performed on small systems show excellent qualitative agreement between mean field and exact model, at greatly reduced computational cost.
13 Citations

## Figures from this paper

Efficient Approximation Methods for the Global Long-Term Behavior of Dynamical Systems - Theory, Algorithms and Examples
Efficient numerical algorithms are developed in order to analyze the long-term behavior of dynamical systems by transfer operator methods, and mean field theory is used to approximate the marginal dynamics on low-dimensional subsystems.
A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems
• Mathematics
Multiscale Model. Simul.
• 2013
A variational principle is derived that is based on the maximization of a Rayleigh coefficient that forms a basis for the development of adaptive and efficient computational algorithms for simulating and analyzing metastable Markov processes while avoiding the sampling problem.
Mathematical study of quantum and classical models for random materials in the atomic scale
The contributions of this thesis concern two topics. The ﬁrst part is dedicated to the study of mean-ﬁeld models for the electronic structure of materials with defects. In Chapter 2, we introduce and
Effective dynamics using conditional expectations
• Mathematics
• 2009
The question of coarse-graining is ubiquitous in molecular dynamics. In this paper, we are interested in deriving effective properties for the dynamics of a coarse-grained variable ξ(x), where x
Effective Dynamics for a Kinetic Monte–Carlo Model with Slow and Fast Time Scales
• Physics, Mathematics
• 2013
We consider several multiscale-in-time kinetic Monte Carlo models, in which some variables evolve on a fast time scale, while the others evolve on a slow time scale. In the first two models we
Pseudogenerators of Spatial Transfer Operators
• Mathematics
SIAM J. Appl. Dyn. Syst.
• 2015
It is shown that even though the family of spatial transfer operators is not a semigroup, it possesses a well-defined generating structure and makes collocation methods particularly easy to implement and computationally efficient, which in turn may open the door for furt...
Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator
• Computer Science
• 2016
A tensor-based reformulation of two numerical methods for computing finite-dimensional approximations of the aforementioned infinite-dimensional operators, namely Ulam's method and Extended Dynamic Mode Decomposition (EDMD).
Transition-path theory and path-finding algorithms for the study of rare events.
• Computer Science
Annual review of physical chemistry
• 2010
The basic components of transition-path theory and path-finding algorithms are reviewed and connections with the classical transition-state theory are discussed.
A direction preserving discretization for computing phase-space densities
• Physics
SIAM J. Sci. Comput.
• 2021
A Petrov-Galerkin discretization of a phase-space boundary integral equation for transporting wave energy densities on two-dimensional surfaces is proposed, where the directional dependence of the energy density is approximated at each point on the boundary in terms of a finite local set of directions propagating into the domain.
Standard coupling unification in SO(10), hybrid seesaw neutrino mass and leptogenesis, dark matter, and proton lifetime predictions
• Physics
• 2016
A bstractWe discuss gauge coupling unification of SU(3)C × SU(2)L × U(1)Y descending directly from non-supersymmetric SO(10) while providing solutions to the three out-standing problems of the

## References

SHOWING 1-10 OF 15 REFERENCES
Macroscopic Dynamics of Complex Metastable Systems: Theory, Algorithms, and Application to B-DNA
• Chemistry
SIAM J. Appl. Dyn. Syst.
• 2008
The algorithmic aspects are illustrated by means of several examples of various degrees of complexity, culminating in their application to a full-scale molecular dynamics simulation of a B-DNA oligomer.
Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules
The function of many important biomolecules comes from their dynamic properties and their ability to switch between different {\em conformations}. In a conformation, the large scale geometric
CHARMM: A program for macromolecular energy, minimization, and dynamics calculations
• Chemistry
• 1983
CHARMM (Chemistry at HARvard Macromolecular Mechanics) is a highly flexible computer program which uses empirical energy functions to model macromolecular systems. The program can read or model build
Computation of Essential Molecular Dynamics by Subdivision Techniques
• Mathematics
Computational Molecular Dynamics
• 1999
The paper suggests the direct computation of these objects via eigenmodes of the associated Frobenius-Perron operator by means of a multilevel subdivision algorithm.
Molecular Conformation Dynamics and Computational Drug Design
• Mathematics
• 2004
The paper surveys recent progress in the mathematical modelling and simulation of essential molecular dynamics. Particular emphasis is put on computational drug design wherein time scales of $msec$
From Molecular Dynamics to Conformation Dynamics in Drug Design
The design of pharmaceuticals, briefly called drug design, is a pyramidal multistage process, from a broad basis to an extremely narrow tip:
On the Approximation of Complicated Dynamical Behavior
• Mathematics
• 1999
We present efficient techniques for the numerical approximation of complicated dynamical behavior. In particular, we develop numerical methods which allow us to approximate Sinai--Ruelle--Bowen
Transport in Dynamical Astronomy and Multibody Problems
• Physics
Int. J. Bifurc. Chaos
• 2005
This paper combines the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques to compute transport rates between two resonance regions for the three-body system consisting of the Sun, Jupiter and a third body.
Conformational dynamics: Modelling theory algorithm and applicatioconformational dynamics: Modelling, theory, algorithm, and application to biomolecules. Habilitation thesis
• Conformational dynamics: Modelling theory algorithm and applicatioconformational dynamics: Modelling, theory, algorithm, and application to biomolecules. Habilitation thesis
• 1999