scholarly journals An Explanation of Metastability in the Viscous Burgers Equation with Periodic Boundary Conditions via a Spectral Analysis

2016 ◽  
Vol 15 (4) ◽  
pp. 1916-1961 ◽  
Author(s):  
Kelly McQuighan ◽  
C. Eugene Wayne
Keyword(s):  
Spectral Analysis ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Burgers Equation ◽  
Periodic Boundary Conditions

scholarly journals A MARKOV JUMP PROCESS APPROXIMATION OF THE STOCHASTIC BURGERS EQUATION

2004 ◽  
Vol 04 (02) ◽  
pp. 245-264 ◽  
Author(s):  
CHRISTOPH GUGG ◽  
JINQIAO DUAN
Keyword(s):  
Boundary Conditions ◽  
White Noise ◽  
Periodic Boundary ◽  
Burgers Equation ◽  
Jump Process ◽  
Periodic Boundary Conditions ◽  
Markov Jump ◽  
Markov Jump Process ◽  
Stochastic Burgers Equation ◽  
Process Approximation

We consider the stochastic Burgers equation [Formula: see text] with periodic boundary conditions, where t≥0, r∈[0,1], and η is some spacetime white noise. A certain Markov jump process is constructed to approximate a solution of this equation.

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

2019 ◽  
Author(s):  
Pier Paolo Poier ◽  
Louis Lagardere ◽  
Jean-Philip Piquemal ◽  
Frank Jensen
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Force Fields ◽  
Periodic Boundary Conditions ◽  
Computational Effort ◽  
Polarizable Force Fields ◽  
Energy Models ◽  
Capacity Model ◽  
Energy Gradient ◽  
Polarization Models

<div> <div> <div> <p>We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. </p><div> <div> <div> <p>By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p><div><div><div> </div> </div> </div> <p> </p><div> <div> <div> <p>variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p> </div> </div> </div> </div> </div> </div> </div> </div> </div>

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