Generalized Brownian dynamics. I. Numerical integration of the generalized Langevin equation through autoregressive modeling of the memory function

1990 ◽  
Vol 92 (2) ◽  
pp. 1304-1311 ◽  
Author(s):  
D. E. Smith ◽  
C. B. Harris
Keyword(s):  
Numerical Integration ◽  
Langevin Equation ◽  
Brownian Dynamics ◽  
Memory Function ◽  
Generalized Langevin Equation ◽  
Autoregressive Modeling

Universal Trend of the Non-Exponential Rouse Mode Relaxation in Glass-Forming Polymers Systems: Experimental Facts, MD-Simulation Results and a Theoretical Approach Based on a Generalized Langevin Equation

MRS Advances ◽  
2016 ◽  
Vol 1 (26) ◽  
pp. 1903-1913 ◽  
Author(s):  
J. Colmenero
Keyword(s):  
Langevin Equation ◽  
Theoretical Approach ◽  
Md Simulation ◽  
Memory Function ◽  
Md Simulations ◽  
Generalized Langevin Equation ◽  
Exponential Behavior ◽  
Glass Forming ◽  
Chain Stiffness ◽  
Local Potentials

ABSTRACTNowadays there are clear evidences from both experiments and MD-simulations proving that the chain Rouse modes correlation functions are non-exponential in unentangled polymer blends and also in pure polymers at low temperature (with respect to that of the glass transition Tg) even for the long wavelengths modes where local potentials and chain stiffness should not play any role. In a recent paper [S. Arrese-Igor et al, Phys. Rev. Lett.113, 078302 (2014)] it has been proposed that this non-exponential behavior depends on the ratio between the so-called Rouse time - i.e., the characteristic time of the slowest chain mode relaxation - and the time scale of the α-relaxation. This parameter is in some way ‘universal’ in the meaning that it can encode many different experimental situations. In this paper, we show that this behavior can be quantitatively explained in the framework of a theoretical approach based on: (i) a generalized Langevin equation (GLE) formalism and (ii) a memory function which takes into account the effect of collective dynamics on the chain dynamics of a tagged chain and which was constructed taking inspirations from the original ideas of the reptation model proposed by de Gennes.

scholarly journals The study of dynamic singularities of seismic signals by the generalized Langevin equation

2009 ◽  
Vol 388 (17) ◽  
pp. 3629-3635 ◽  
Author(s):  
Renat Yulmetyev ◽  
Ramil Khusnutdinoff ◽  
Timur Tezel ◽  
Yildiz Iravul ◽  
Bekir Tuzel ◽  
...  
Keyword(s):  
Langevin Equation ◽  
Generalized Langevin Equation ◽  
Seismic Signals
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