3,827 research outputs found
Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems
The purpose of this work is twofold. First, we demonstrate analytically
that the classical Newmark family as well as related integration
algorithms are variational in the sense of the Veselov formulation of
discrete mechanics. Such variational algorithms are well known to be
symplectic and momentum preserving and to often have excellent global
energy behavior. This analytical result is veried through numerical examples
and is believed to be one of the primary reasons that this class
of algorithms performs so well.
Second, we develop algorithms for mechanical systems with forcing,
and in particular, for dissipative systems. In this case, we develop integrators
that are based on a discretization of the Lagrange d'Alembert
principle as well as on a variational formulation of dissipation. It is
demonstrated that these types of structured integrators have good numerical
behavior in terms of obtaining the correct amounts by which
the energy changes over the integration run
Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics
We describe a powerful and intuitive technique for modeling light-matter
interactions in classical and quantum nanoplasmonics. Our approach uses a
quasinormal mode expansion of the Green function within a metal nanoresonator
of arbitrary shape, together with a Dyson equation, to derive an expression for
the spontaneous decay rate and far field propagator from dipole oscillators
outside resonators. For a single quasinormal mode, at field positions outside
the quasi-static coupling regime, we give a closed form solution for the
Purcell factor and generalized effective mode volume. We augment this with an
analytic expression for the divergent LDOS very near the metal surface, which
allows us to derive a simple and highly accurate expression for the electric
field outside the metal resonator at distances from a few nanometers to
infinity. This intuitive formalism provides an enormous simplification over
full numerical calculations and fixes several pending problems in quasinormal
mode theory
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