Nearly hamiltonian systems in two degrees of freedom

Perturbed systems of differential equations are studied which are close to Hamiltonian systems of the type for which small divisor problems arise. If the non-Hamiltonian terms involve both damping and self-excitation, behavior characteristic of Hamiltonian systems can occur but is confined to small regions of space in which these opposite effects are in balance. The results provide a partial justification for truncating the Fourier series occurring in these problems. The principle method is local averaging, which is used to obtain global results by compactness arguments.     

On the Structure of Nilpotent Normal Form Modules

The set of vector fields that are in normal form with respect to a given linear part has the structure of a module and is best described by giving the Stanley decomposition of that module. An algorithm is presented that produces a Stanley decomposition for the module of equivariants of the flow of a nilpotent linear vector field, given a Stanley decomposition for the ring of invariants. This reduces the study of nilpotent normal forms to classical invariant theory plus this one additional algorithm. Both the inner product normal form (Elphick) and the sl(2) normal form (Cushman-Sanders) are covered within a single theory, and simplified (non-equivariant) versions of each normal form are presented.     

Mode-specific tunneling dynamics in the ground electronic state of tropolone

The mode specificity of proton-transfer dynamics in the ground electronic state (X (1)A(1)) of tropolone has been explored at near-rotational resolution by implementing a fully coherent variant of stimulated emission pumping within the framework of two-color resonant four-wave mixing spectroscopy. Three low-lying (E(vib) approximately 550-750 cm(-1)) vibrational features, assigned to nu(30)(a(1)), nu(32)(b(2)), and nu(31)nu(38)(a(1)), have been interrogated under ambient, bulk-gas conditions, with term energies determined for the symmetric and antisymmetric (tunneling) components of each enabling the attendant tunneling-induced bifurcations of 1.070(9), 0.61(3), and 0.07(2) cm(-1) to be extracted. The dependence of tunneling rate (or hydron migration efficiency) on vibrational motion is discussed in terms of corresponding atomic displacements and permutation-inversion symmetries for the tropolone skeleton.     

On cluster kinetics and MBE growth

Based on the model of a so-called Near Surface Transition Layer (NSTL) proposed by HERMAN and ANDERSSON we discuss the possible role of clusters during MBE growth. Moreover, intentional use of small clusters instead of single atoms as beam constituents may contribute to improvements in crystal quality even at low substrate temperature and high growth rate.     

A new transvectant algorithm for nilpotent normal forms

We offer an algorithm to determine the form of the normal form for a vector field with a nilpotent linear part, when the form of the normal form is known for each Jordan block of the linear part taken separately. The algorithm is based on the notion of transvectant, from classical invariant theory.     

A quasiclassical trajectory study of the time-delayed forward scattering in the hydrogen exchange reaction

The time-delayed forward scattering mechanism recently identified by Althorpe et al. [Nature (London) 416, 67 (2002)] for the H+D(2)(v=0,j=0)-->HD(v(')=3,j(')=0)+D reaction was analyzed by using quasiclassical trajectory (QCT) methodology. The QCT results were found to match the quantum wavepacket snapshots of Althorpe et al., albeit without the quantum scattering effects. Trajectories were analyzed on the fly to investigate the dynamics of the atoms during the reaction. The dominant reaction mechanism progresses from hard collinear impacts, leading to direct recoil, toward glancing impacts. The increased time required for forward scattered trajectories is due to the rotation of the transient HDD complex. Forward scattered trajectories display symmetric stretch vibrations of the transient HDD complex, a signature of the presence of a resonance, or a quantum bottleneck state.