scholarly journals Numerical integration of the extended variable generalized Langevin equation with a positive Prony representable memory kernel

2013 ◽  
Vol 139 (4) ◽  
pp. 044107 ◽  
Author(s):  
Andrew D. Baczewski ◽  
Stephen D. Bond
Keyword(s):  
Numerical Integration ◽  
Langevin Equation ◽  
Generalized Langevin Equation ◽  
Memory Kernel

ANALYSIS OF A GENERALIZED LANGEVIN EQUATION WITH FRACTIONAL DERIVATIVE, NONLOCAL DISSIPATIVE FORCE AND LINEAR EXTERNAL FORCE

2008 ◽  
Vol 08 (03n04) ◽  
pp. L381-L391 ◽  
Author(s):  
KWOK SAU FA
Keyword(s):  
Fractional Derivative ◽  
External Force ◽  
Langevin Equation ◽  
Relaxation Function ◽  
Dissipative Force ◽  
Generalized Langevin Equation ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Memory Kernel ◽  
Long Time

We analyze the motion of a particle governed by a generalized Langevin equation with fractional derivative, nonlocal dissipative force and linear external force. We consider the dissipative memory kernel given by the exponential and power-law functions. For these cases, one can obtain exact results for the relaxation function. The long-time behavior of this function is also investigated. Our results show that the inertial term has no significant influence on the long-time behavior.

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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