Functional differential operators with involution and Dirac operators with periodic boundary conditions

2014 ◽  
Vol 89 (1) ◽  
pp. 8-10 ◽  
Author(s):  
M. Sh. Burlutskaya ◽  
A. P. Khromov
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Differential Operators ◽  
Dirac Operators ◽  
Periodic Boundary Conditions ◽  
Functional Differential

On the Determination of Eigenpairs of 2D Positive Differential Operators with Periodic Boundary Conditions

PIERS Online ◽  
2007 ◽  
Vol 3 (4) ◽  
pp. 490-493
Author(s):  
A. Rezaee ◽  
Alireza Baghai-Wadji
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Differential Operators ◽  
Periodic Boundary Conditions

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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