We study the dynamics of generic unfoldings of saddle-node circle local diffeomorphisms from the measure theoretical point of view, obtaining statistical and stochastic stability results for deterministic and random perturbations in this kind of one-parameter families. CONTENTS

The problem of sampling low lying, first-order saddle points on a high dimensional surface is discussed and a method presented for improving the sampling efficiency. The discussion is in the context of an energy surface for a system of atoms and thermally activated transitions in solids treated within the harmonic approximation to transition state theory. Given a local minimum as an initial sta...

The quantitative analysis of molecular density matrices in terms of oriented quasi-atomic orbitals (QUAOs) is shown to yield detailed conceptual insight into the dissociation of dioxetane on the basis of ab initio wave functions. The QUAOs persist and can be followed throughout the reaction path. The kinetic bond orders and the orbital populations of the QUAOs quantitatively reveal the changes ...

In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and more general Weyl symbols that represent density matrix arbitrary mixed states. A formal solution to is given by Marinov's path integral. this paper we demonstrate integral can be regarded as natural link between several conceptual, geometric, dynamical issues in mechanics. unifying perspective...

We study the dynamics of generic unfoldings of saddle-node circle local diffeo-morphisms from the measure theoretical point of view, obtaining statistical and stochastic stability results for deterministic and random perturbations in this kind of one-parameter families.

EON is a software package that uses distributed computing, systematic coarse graining and bookkeeping of minima and first order saddle points too speed up adaptive kinetic Monte Carlo simulations. It can be used to optimize continuously differentiable functions of a large number of variables. The approach is based on finding minima of the cost function by traversing low-lying, first-order saddl...

In this paper, stability and bifurcation of piecewise affine systems is investigated. In the stability analysis, stability of the origin and existence of limit cycles are investigated by means of the radial growth rate, which describes the behavior of the radial direction of the trajectories. In the bifurcation analysis, Hopf bifurcation and saddle-node bifurcation is discussed. The radial grow...