Langevin dynamics
In physics, Langevin dynamics is an approach to the mathematical modeling of the dynamics of molecular systems, originally developed by the French physicist Paul Langevin. The approach is characterized by the use of simplified models while accounting for omitted degrees of freedom by the use of stochastic differential equations.
A molecular system in the real world is unlikely to be present in vacuum. Jostling of solvent or air molecules causes friction, and the occasional high velocity collision will perturb the system. Langevin dynamics attempts to extend molecular dynamics to allow for these effects. Also, Langevin dynamics allows controlling the temperature like a thermostat, thus approximating the canonical ensemble.
Langevin dynamics mimics the viscous aspect of a solvent. It does not fully model an implicit solvent; specifically, the model does not account for the electrostatic screening and also not for the hydrophobic effect. It should also be noted that for denser solvents, hydrodynamic interactions are not captured via Langevin dynamics.
For a system of N particles with masses M, with coordinates X=X(t) that constitute a time-dependent random variable, the resulting Langevin equation is M\ddot{X} = - \nabla U(X) - \gamma M \dot{X} + \sqrt{2 \gamma k_B T M} R(t)\,,
where U(X) is the particle interaction potential; \nabla is the gradient operator such that -\nabla U(X) is the force calculated from the particle interaction potentials; the dot is a time derivative such that \dot{X} is the velocity and \ddot{X} is the acceleration; T is the temperature, kB is Boltzmann's constant; and R(t) is a delta-correlated stationary Gaussian process with zero-mean, satisfying
\left\langle R(t) \right\rangle =0
\left\langle R(t)R(t') \right\rangle = \delta(t-t')
Here, \delta is the Dirac delta.
If the main objective is to control temperature, care should be exercised to use a small damping constant \gamma. As \gamma grows, it spans the inertial all the way to the diffusive (Brownian) regime. The Langevin dynamics limit of non-inertia is commonly described as Brownian dynamics. Brownian dynamics can be considered as overdamped Langevin dynamics, i.e. Langevin dynamics where no average acceleration takes place.
The Langevin equation can be reformulated as a Fokker–Planck equation that governs the probability distribution of the random variable X.

This is an excerpt from the article Langevin dynamics from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
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Langevin dynamics - Wikipedia, the free encyclopedia
In physics, Langevin dynamics is an approach to the mathematical modeling of the dynamics of molecular systems, originally developed by the French physicist ...
en.wikipedia.org/wiki/Langevin_dynamics
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Langevin Dynamics (LD) Simulation - Center for Molecular Modeling
Langevin dynamics (LD) Simulation. The Langevin equation is a stochastic differential equation in which two force terms have been added to Newton's second ...
cmm.cit.nih.gov/intro_simulation/node24.html
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fix langevin - Lammps
This discretization has been shown to be consistent with the underlying physical model of Langevin dynamics and produces the correct statistical distribution of ...
lammps.sandia.gov/doc/fix_langevin.html
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Stability of complex Langevin dynamics in effective models
Dec 20, 2012 ... Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown that complex ...
arxiv.org/abs/1212.5231
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Phys. Rev. E 88, 032138 (2013): Relativistic Langevin dynamics in ...
Sep 27, 2013 ... Relativistic Langevin dynamics in expanding media. Abstract. References. No Citing Articles. Download: PDF (343 kB) Buy this article Export: ...
link.aps.org/doi/10.1103/PhysRevE.88.032138
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Langevin dynamics in NVT ensemble
Langevin dynamics in NVT ensemble. See Sec. 6.62.5 for brief description of Langevin thermostat. Set the standard MD-related flags: IBRION=0, TEBEG, POTIM ...
cms.mpi.univie.ac.at/vasp/vasp/Langevin_dynamics_in_NVT_ensemble.html
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Langevin dynamics - CHARMM forums
i want to simulate protein structure dynamic in solution and in order to save time i do 1ns Langevin dynamics simulation with timestp 0.002 ...
www.charmm.org/ubbthreads/ubbthreads.php?ubb=showflat&Number=31648
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Bayesian Learning via Stochastic Gradient Langevin Dynamics
Bayesian Learning via Stochastic Gradient Langevin dynamics. Max Welling welling@ics.uci.edu. D. Bren School of Information and Computer Science, ...
www.ece.duke.edu/~lcarin/398_icmlpaper.pdf
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Molecular dynamics simulation
•Potential energy function. •Newton's law of motion and integrations algorithms. • Running MD simulations. •other simulation methods: •Langevin dynamics.
www.weizmann.ac.il/sb/faculty_pages/Levy/sites/weizmann.ac.il.sb.faculty_pages.Levy/files/Molecular_dynamics_simulation.pdf
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Animatronic Hand Robot 3D printer…
Vid:4 You can follow the work in progress of "InMoov" at http://inmoov.blogspot.com http://www.thingiverse.com/thing:17773 This hand was printed on a 3D ...
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Langevin dynamics in science
Phys. Rev. E 88, 032138 (2013): Relativistic Langevin dynamics in ...
Sep 27, 2013 ... Relativistic Langevin dynamics in expanding media ... 2Department of Applied Physics, Nanjing University of Science and Technology, Nanjing ...
Complex Langevin dynamics and other approaches at finite ...
Feb 13, 2013 ... Complex Langevin dynamics and other approaches at finite chemical potential. Gert Aarts (Swansea University). I review the presence of the ...
Adaptive stepsize and instabilities in complex Langevin dynamics
Dec 3, 2009 ... Title: Adaptive stepsize and instabilities in complex Langevin dynamics. Authors: Gert Aarts (Swansea University), Frank A. James (Swansea ...
[PDF]Langevin Stabilization of Multiscale Mollified Molecular Dynamics
Langevin Stabilization of Multiscale Mollified. Molecular Dynamics. Jes us A. Izaguirre. Department of Computer Science and Engineering. University of Notre ...
[PDF]An attempt toward the generalized Langevin dynamics simulation
1 Department of Physics, Changwon National University, Changwon 641–773, Korea ... An attempt to generalize the Langevin dynamics simulation method is ...
Stochastic Gradient Riemannian Langevin Dynamics on the ... - NIPS
UCL; University of Oxford. Poster: Stochastic Gradient Riemannian Langevin dynamics on the Probability Simplex. In this paper we investigate the use of ...
"Generalized Langevin dynamics of a nanoparticle using a finite ...
Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise. Uma Balakrishnan, University of ...
[PDF]Generalized Langevin dynamics of a nanoparticle using a finite ...
Sep 16, 2011 ... 1Department of Bioengineering, University of Pennsylvania, ... of an one- dimensional generalized Langevin equation, it is observed that where ...
[PDF]A simple and effective Verlet-type algorithm for simulating Langevin ...
Feb 14, 2013 ... Explicitly, the Langevin equation of motion is given by [5]. C 2013 Taylor & Francis. Downloaded by [University of California Davis] at 13:46 20 ...
[PDF]An impulse integrator for Langevin dynamics
1Department of Computer Science (and Beckman Institute), University of Illinois,. 1304 West ... The appropriate generalization to simple Langevin dynamics is.
Books on the term Langevin dynamics
The Langevin and Generalised Langevin Approach to the ...
The Langevin and Generalised Langevin Approach to the ...
Ian Snook, 2006
Extensive appendices are given to enable the reader to carry out computations to illustrate many of the points made in the main body of the book. * Starts from fundamental equations * Gives up-to-date illustration of the application of ...
Path Integral Formulation of Langevin Dynamics with ...
Path Integral Formulation of Langevin Dynamics with ...
Bradley Michael Dickson, 2006
Rather, this work offers a new formulation of an old idea while keeping in mind two key issues: first, whatever theory and methods are developed they should be accessible to those simply seeking methods and easy to implement, since the goal ...
The Molecular Dynamics of Liquid Crystals
The Molecular Dynamics of Liquid Crystals
G. R. Luckhurst, C. A. Veracini, 1994
even though formally a Langevin description implies that the solute suffers an infinite number of collisions with infmitesimally small momentum transfer. In comparing the results of Langevin dynamics with those of other stochastic methods ...
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Blog posts on the term
Langevin dynamics
Phys. Rev. E 88, 032138 (2013): Relativistic Langevin dynamics in expanding media
link.aps.org/doi/10.1103/PhysRevE.88.032138
"Computer simulation of viral-assembly and translocation" by Jyoti Prakash Mahalik
We investigated four different problems using coarse grained computational models : self-assembly of single stranded (ss) DNA virus, ejection dynamics of double stranded(ds) DNA from phages, translocation of ssDNA through MspA protein pore, and segmental dynamics of a polymer translocating through a synthetic nanopore. In the first part of the project, we investigated the self-assembly of a virus with and without its genome. A coarse-grained model was proposed for the viral subunit proteins and its genome (ssDNA). Langevin dynamics simulation, and replica exchange method were used to determine the kinetics and energetics of the self-assembly process, respectively. The self-assembly follows a nucleation-growth kind of mechanism. The ssDNA plays a crucial role in the self-assembly by acting as a template and enhancing the local concentration of the subunits. The presence of the genome does not changes the mechanism of the self-assembly but it reduces the nucleation time and enhances the growth rate by almost an order of magnitude. The second part of the project involves the investigation of the dynamics of the ejection of dsDNA from phages. A coarse-grained model was used for the phage and dsDNA. Langevin dynamics simulation was used to investigate the kinetics of the ejection. The ejection is a stochastic process and a slow intermediate rate kinetics was observed for most ejection trajectories. We discovered that the jamming of the DNA at the pore mouth at high packing fraction and for a disordered system is the reason for the intermediate slow kinetics. The third part of the project involves translocation of ssDNA through MspA protein pore. MspA protein pore has the potential for genome sequencing because of its ability to clearly distinguish the four different nucleotides based on their blockade current, but it is a challenge to use this pore for any practical application because of the very fast traslocation time. We resolved the state of DNA translocation reported in the recent experimental work . We also investigated two methods for slowing down the translocation process: pore mutation and use of alternating voltage. Langevin dynamics simulation and Poisson Nernst Planck solver were used for the investigation. We demonstrated that mutation of the protein pore or applying alternating voltage is not a perfect solution for increasing translocation time deterministically. Both strategies resulted in enhanced average translocation time as well as the width of the translocation time distribution. The increase in the width of the translocation time distribution
scholarworks.umass.edu/dissertations/AAI3589086/
Heavy Flavor Suppression: Boltzmann vs Langevin - INSPIRE-HEP
The propagation of heavy flavor through the quark gluon plasma has been treated commonly within the framework of Langevin dynamics, i.e. assuming the heavy flavor momentum transfer is much smaller than the light one. On the other hand a similar suppression factor $R_{AA}$ has been observed experimentally for light and heavy flavors. We present a thorough study of the approximations involved by Langevin equation by mean of a direct comparison with the full collisional integral within the framework of Boltzmann transport equation. We have compared the results obtained in both approaches which can differ substantially for charm quark leading to quite different values extracted for the heavy quark diffusion coefficient. In the case of bottom quark the approximation appears to be quite reasonable. Das, Santosh K.; Scardina, Francesco; Plumari, Salvatore; Greco, Vincenzo
inspirehep.net/record/1256164
"Generalized Langevin dynamics of a nanoparticle using a finite element" by Uma Balakrishnan, T. N. Swaminathan et al.
A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.
repository.upenn.edu/be_papers/183/
Bayesian Learning via Stochastic Gradient Langevin Dynamics | StatsBlogs.com | All About Statistics
(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs. ) Burak Bayramli writes: In this paper by Sunjin Ahn, Anoop Korattikara, and Max Welling and this paper by Welling and Yee Whye The, there are some arguments on big data and the use of MCMC.
www.statsblogs.com/2012/08/04/bayesian-learning-via-stochastic-gradient-langevin-dynamics/
5 Instructional Techniques to Promote Positive Group Dynamics | Langevin - Blog
Group dynamics is too large a topic to cover in this blog, so I am just going to focus on the four stages of group formation and how this relates to training.
www.langevin.com/blog/2012/08/02/5-instructional-techniques-to-promote-positive-group-dynamics/
Preprint: Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems | Gavin E. Crooks
Posted on 2013-01-16 by gec.
threeplusone.com/gec/news/sivak2013b
Stochastic trailing string and Langevin dynamics from AdS/CFT - CERN Document Server
Using the gauge/string duality, we derive a set of Langevin equations describing the dynamics of a relativistic heavy quark moving with constant average speed through the strongly-coupled N=4 SYM plasma at finite temperature. We show that the stochasticity arises at the string world-sheet horizon, and thus is causally disconnected from the black hole horizon in the space-time metric. This hints at the non-thermal nature of the fluctuations, as further supported by the fact that the noise term and the drag force in the Langevin equations do not obey the Einstein relation. We propose a physical picture for the dynamics of the heavy quark in which dissipation and fluctuations are interpreted as medium-induced radiation and the associated quantum-mechanical fluctuations. This picture provides the right parametric estimates for the drag force and the (longitudinal and transverse) momentum broadening coefficients. Giecold, G C; Iancu, E; Müller, A H
cds.cern.ch/record/1166288
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