Related papers: Extended Lagrangian free energy molecular dynamics
We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear evolution equations that admit multi- Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a…
Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that…
Non-equilibrium electrochemistry raises new challenges for atomistic simulation: we need to perform molecular dynamics for the nuclear degrees of freedom with an explicit description of the electrons, which in turn must be free to enter and…
This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out…
We present a time-dependent formulation of coupled cluster theory. This theory allows for direct computation of the free energy of quantum systems at finite temperature by imaginary time integration and is closely related to the thermal…
The complete form of the high-temperature expansion of the one-loop contribution to the free energy of a scalar field on a stationary gravitational background is derived. The explicit expressions for the divergent and finite parts of the…
These notes were delivered as a series of NIMROD lectures at the Rutherford Appleton Laboratory by the author in February 1976 (RL-76-022). The purpose of these lectures was primarily two-fold: to discuss the classical theory of free point…
A rational expansion of the Fermi density operator is proposed. This approach allows to calculate efficiently physical properties of fermionic systems at finite temperatures without solving an eigenvalue problem. Using N evaluations of the…
We explore the application of the reference map technique, originally developed for the Eulerian simulation of solid mechanics, in Lagrangian kinematics of fluid flows. Unlike traditional methods based on explicit particle tracking, the…
The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and…
Variational integrators are a special kind of geometric discretisation methods applicable to any system of differential equations that obeys a Lagrangian formulation. In this thesis, variational integrators are developed for several…
The simulation of thermochemical nonequilibrium for the atomic and molecular energy level populations in plasma flows requires a comprehensive modeling of all the elementary collisional and radiative processes involved. Coupling detailed…
We compute the effective Lagrangian of static gravitational fields interacting with thermal fields. Our approach employs the usual imaginary time formalism as well as the equivalence between the static and space-time independent external…
We investigate non-degenerate Lagrangians of the form $$ \int f(u_x, u_y, u_t) dx dy dt $$ such that the corresponding Euler-Lagrange equations $ (f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})_t=0 $ are integrable by the method of hydrodynamic…
We introduce the boundary conditions corresponding to the imaginary-time (Matsubara) formalism for the finite-temperature partition function in $d+1$ dimensions as {\em constraints} in the path integral for the vacuum amplitude (the…
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles…
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…
We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…
In an effective hadronic theory constructed to describe long-range nuclear physics, the dynamics of the vacuum can be expanded in terms with zero or a finite number of derivatives acting on the fields. Thus vacuum dynamics can always be…
The Lagrange-Flux schemes are Eulerian finite volume schemes that make use of an approximate Riemann solver in Lagrangian description with particular upwind convective fluxes. They have been recently designed as variant formulations of…