We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free-boundary, constrained by the condition of incompressibility. Two methods are used to obtain the bracket, both based on Dirac’s procedure for incorporating constraints. First, the Poisson bracket of moments of the u...

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations-an area of active research-is necessary for studying integrated functions of large systems of biological importance. Following perspectives of ...

We demonstrate that reciprocal Maupertuis' Principle is the classical limit of Schrödinger's Variational Principle in Quantum Mechanics. Misha Marinov loved analytical mechanics and understood its beauty. Canonical transformations, Poisson structures, symplectic geometry etc. were the notions that he constantly used in his original papers, and in his famous review on path integral. One of the a...

A method, called beatification, is presented for rapidly extracting weakly nonlinear Hamiltonian systems that describe the dynamics near equilibria of systems possessing Hamiltonian form in terms of noncanonical Poisson brackets. The procedure applies to systems like fluids and plasmas in terms of Eulerian variables that have such noncanonical Poisson brackets, i.e., brackets with nonstandard a...

The virial coefficients can be obtained from statistical mechanics in connection with the intermolecular potentials. The intermolecular potential of polyatomic molecules is usually assumed to consist of a spherically symmetric component plus a contribution due to asphericaity of the molecular charge distribution. In this study, the second virial coefficients have been calculated for N2...