Variational Lagrangian general formulation

Biot and Daughaday (B6) have improved an earlier application by Citron (C5) of the variational formulation given originally by Biot for the heat conduction problem which is exactly analogous to the classical dynamical scheme. In particular, a thermal potential V, a dissipation function D, and generalized thermal force Qi are defined which satisfy the Lagrangian heat flow equation... 

Parrinello-Rahman method. The constant pressure MD formulation of Andersen (4) provides a method for permitting the variation in the volume of the simulation cell. Parrinello and Rahman (5, 14, 15) generalized Andersen s method to include variations in the volume as well as the shape of the simulation cell. In the Parrinello-Rahman formulation, the simulation cell is represented by three vectors, a, b, and c. The lagrangian is given by... 

The END theory was proposed in 1988 [11] as a general approach to deal with time-dependent non-adiabatic processes in quantum chemistry. We have applied the END method to the study of time-dependent processes in energy loss [12-16]. The END method takes advantage of a coherent state representation of the molecular wave function. A quantum mechanical Lagrangian formulation is employed to approximate the Schrodinger equation, via the time-dependent variational principle, by a set of coupled first-order differential equations in time to describe the END. 

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