| 53 |
|
time $t_2$. To find out, we need the classical equations of |
| 54 |
|
motion, and one useful formulation of them is the Lagrangian form. |
| 55 |
|
|
| 56 |
< |
The Lagrangian ($L$) is a function of the positions and velocites that |
| 56 |
> |
The Lagrangian ($L$) is a function of the positions and velocities that |
| 57 |
|
takes the form, |
| 58 |
|
\begin{equation} |
| 59 |
|
L = K - V, |
| 542 |
|
that the higher the order of the polynomial, the more abrupt the |
| 543 |
|
switching transition. |
| 544 |
|
|
| 545 |
< |
\subsection{Long-Range Interaction Corrections} |
| 545 |
> |
\subsection{\label{sec:LJCorrections}Long-Range Interaction Corrections} |
| 546 |
|
|
| 547 |
|
While a good approximation, accumulating interaction only from the |
| 548 |
|
nearby particles can lead to some issues, because the further away |
| 574 |
|
\subsection{Periodic Boundary Conditions} |
| 575 |
|
|
| 576 |
|
In typical molecular dynamics simulations there are no restrictions |
| 577 |
< |
placed on the motion of particles outside of what the interparticle |
| 577 |
> |
placed on the motion of particles outside of what the inter-particle |
| 578 |
|
interactions dictate. This means that if a particle collides with |
| 579 |
|
other particles, it is free to move away from the site of the |
| 580 |
|
collision. If we consider the entire system as a collection of |
| 666 |
|
property can be determined via the standard deviation. Fluctuations |
| 667 |
|
are useful for measuring various thermodynamic properties in computer |
| 668 |
|
simulations. In section \ref{sec:t5peThermo}, we use fluctuations in |
| 669 |
< |
propeties like the enthalpy and volume to calculate various |
| 669 |
> |
properties like the enthalpy and volume to calculate various |
| 670 |
|
thermodynamic properties, such as the constant pressure heat capacity |
| 671 |
|
and the isothermal compressibility. |
| 672 |
|
|
