Solitons in a parametrically driven damped discrete nonlinear Schr\"odinger equation

We consider a parametrically driven damped discrete nonlinear Schr\"odinger (PDDNLS) equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental discrete bright solitons. We show that there are two types of onsite discrete soliton, namely onsite type I and II. We also show that there are four types of intersite discrete soliton, called intersite type I, II, III, and IV, where the last two types are essentially the same, due to symmetry. Onsite and intersite type I solitons, which can be unstable in the case of no dissipation, are found to be stabilized by the damping, whereas the other types are always unstable. Our further analysis demonstrates that saddle-node and pitchfork (symmetry-breaking) bifurcations can occur. More interestingly, the onsite type I, intersite type I, and intersite type III-IV admit Hopf bifurcations from which emerge periodic solitons (limit cycles). The continuation of the limit cycles as well as the stability of the periodic solitons are computed through the numerical continuation software Matcont. We observe subcritical Hopf bifurcations along the existence curve of the onsite type I and intersite type III-IV. Along the existence curve of the intersite type I we observe both supercritical and subcritical Hopf bifurcations.Comment: to appear in "Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations in Nonlinear Systems", B.A. Malomed, ed. (Springer, Berlin, 2012

Differential Scattering Cross-Sections for the Different Product Vibrational States in the Ion-Molecule Reaction Ar+ + N2

The charge transfer reaction Ar+ + N2 --> Ar + N2+ has been investigated in a crossed beam experiment in combination with three-dimensional velocity map imaging. Angular differential state-to-state cross sections were determined as a function of the collision energy. We found that scattering into the first excited vibrational level dominates as expected, but only for scattering in the forward direction. Higher vibrational excitations up to v'=6 have been observed for larger scattering angles. For decreasing collision energy, scattering into higher scattering angles becomes increasingly important for all kinematically allowed quantum states. Our detailed measurements indicate that a quantitative agreement between experiment and theory for this basic ion-molecule reaction now comes within reach.Comment: accepted to Phys. Rev. Let

Voltage and current spectra for matrix power converters

Matrix power converters are used for transforming one alternating-current power supply to another, with different peak voltage and frequency. There are three input lines, with sinusoidally varying voltages which are 120◦ out of phase one from another, and the output is to be delivered as a similar three-phase supply. The matrix converter switches rapidly, to connect each output line in sequence to each of the input lines in an attempt to synthesize the prescribed output voltages. The switching is carried out at high frequency and it is of practical importance to know the frequency spectra of the output voltages and of the input and output currents. We determine in this paper these spectra using a new method, which has significant advantages over the prior default method (a multiple Fourier series technique), leading to a considerably more direct calculation. In particular, the determination of the input current spectrum is feasible here, whereas it would be a significantly more daunting procedure using the prior method instead

Calculating the inherent visual structure of a landscape (inherent viewshed) using high-throughput computing

This paper describes a method of calculating the inherent visibility at all locations in a landscape (‘total viewshed’) by making use of redundant computer cycles. This approach uses a simplified viewshed program that is suitable for use within a distributed environment, in this case managed by the Condor system. Distributing the calculation in this way reduced the calculation time of our example from an estimated 34 days to slightly over 25 hours using a cluster of 43 workstations. Finally, we discuss the example ‘total viewshed’ raster for the Avebury region, and briefly highlight some of its implications