Simulation techniques Langevin methods

Other promising FTS techniques have been devdoped recently, but they dther still lack the proof of correct statistical convergence, like the complex Langevin method, or still need to prove thdr effectiveness on systems, where multiple saddle points are important. Hie complex Langevin method is computationally demanding and it can run into imexpected difficulties in some cases. To improve the effidency of the method and permit study of larger systems, it is capable to use systematically CG fidd theories that can be simulated on coarsely spaced simulation lattices without tmncation of important short-wavdength contributions. ... 

To study protein folding theoretically, simulation methods have proved indispensable. The folding transition is ultimately governed by statistical thermodynamics and hence it is paramount to use sampling methods that are able to reproduce the canonical Boltzmann distribution. Common sampling techniques are molecular dynamics (MD), Langevin or Brownian dynamics (BD) and Monte Carlo (MC). 

Due to the size constrains of the simulations special boundary conditions are used in many cases to dissipate the energy produced by the high-energy particle. The method employed in most of the simulations is a thermal bath at the boundary of the simulation box. This thermal bath is forced to keep a constant temperature, and several techniques can be used for such purpose, for example, rescaling the velocities of those atoms in the thermal bath, or applying Langevin dynamics to those atoms at the boundary. 

MD is the most fundamental computational technique used for a direct simulation of temporal evolution of interacting particle ensembles [28,29]. Many other particle-based techniques, such as the Brownian and Langevin dynamics [28], constimte in fact the simplification of the MD method. They were devised to cover larger length, and time scales than MD. 

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