Related papers: Next generation extended Lagrangian first principl…
We present a Total Lagrangian finite element framework for finite-deformation multibody dynamics. The framework combines a compact kinematic representation, a deformation-gradient-based formulation, an element-agnostic constitutive…
The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…
Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different…
The dynamical phase-space of axisymmetric Canham-Helfrich (CH) cells is constructed from a Hamiltonian field recapitulating membrane curvature-elasticity and systemic restrictions. Guiding principles are reparametrization to convert a…
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are build on our previously developed…
A relativistic light front formulation of nuclear dynamics is developed and applied to treating infinite nuclear matter in a method which includes the correlations of pairs of nucleons: this is light front Brueckner theory. We start with a…
A new electronic structure model is developed in which the ground state energy of a molecular system is given by a Hartree-Fock-like expression with parametrized one- and two-electron integrals over an extended (minimal + polarization) set…
A general framework for performing event-driven simulations of systems with semi-flexible or rigid bodies interacting under impulsive torques and forces is outlined. Two different approaches are presented. In the first, the dynamics and…
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex…
We use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, first-order Lagrangian functionals and their associated Euler-Lagrange PDEs, subject to contact transformations. The first chapter contains an…
We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to…
We show that following the standard mantra of quantum chemistry and diagonalizing the Born-Oppenheimer (BO) Hamiltonian $\hat H_{\rm BO}(\bm R)$ is not the optimal means to construct potential energy surfaces. A better approach is to…
We introduce a general technique to compute finite temperature electronic properties by a novel covariant formulation of the electronic partition function. By using a rigorous variational upper bound to the free energy we are led to the…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…
We present a new formalism which allows to derive the general Lagrangian dynamical equations for the motion of gravitating particles in a non--flat Friedmann universe with arbitrary density parameter $\Omega$ and no cosmological constant.…
Recently, Lobb and Nijhoff initiated the study of variational (Lagrangian) structure of discrete integrable systems from the perspective of multi-dimensional consistency. In the present work, we follow this line of research and develop a…
A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both…
The molecular Schr\"odinger equation is rewritten in terms of non-unitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear)…
Degenerate Cahn-Hilliard phase-field models provide a robust approximation of surface-diffusion-driven interface motion without explicit front tracking. In computations, however, the geometric volume enclosed by the interface -- the region…
Conventional theoretical and computational approaches to fully coupled quantum molecular dynamics, i.e. when both the electrons and nuclei are treated as quantum-mechanical particles, are impractical for all but the smallest chemical…