Oscillatory wave fronts in chains of coupled nonlinear oscillators

Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress $F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate, for $F_{cd} < |F| < F_{cs}$ stable static and moving wave fronts coexist, and for $|F| > F_{cs}$ (static Peierls stress) there are only stable moving wave fronts. For piecewise linear models, extending an exact method of Atkinson and Cabrera's to chains with damped dynamics corroborates this description. For smooth nonlinearities, an approximate analytical description is found by means of the active point theory. Generically for small or zero damping, stable wave front profiles are non-monotone and become wavy (oscillatory) in one of their tails.Comment: 18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev.

Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure

Beyond Kinetic Relations

We introduce the concept of kinetic equations representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries, link the instantaneous value of the velocity of a defect with an instantaneous value of the driving force. The new approach generalizes kinetic relations by implying a relation between the velocity and the driving force which is nonlocal in time. To make this relations explicit one needs to integrate the system of kinetic equations. We illustrate the difference between kinetic relation and kinetic equations by working out in full detail a prototypical model of an overdamped defect in a one-dimensional discrete lattice. We show that the minimal nonlocal kinetic description containing now an internal time scale is furnished by a system of two ordinary differential equations coupling the spatial location of defect with another internal parameter that describes configuration of the core region.Comment: Revised version, 33 pages, 9 figure

Upper limits from five years of blazar observations with the VERITAS Cherenkov telescopes

Between the beginning of its full-scale scientific operations in 2007 and 2012, the VERITAS Cherenkov telescope array observed more than 130 blazars; of these, 26 were detected as very-high-energy (VHE; E > 100 GeV) γ-ray sources. In this work, we present the analysis results of a sample of 114 undetected objects. The observations constitute a total live-time of ~570 hr. The sample includes several unidentified Fermi-Large Area Telescope (LAT) sources (located at high Galactic latitude) as well as all the sources from the second Fermi-LAT catalog that are contained within the field of view of the VERITAS observations. We have also performed optical spectroscopy measurements in order to estimate the redshift of some of these blazars that do not have spectroscopic distance estimates. We present new optical spectra from the Kast instrument on the Shane telescope at the Lick observatory for 18 blazars included in this work, which allowed for the successful measurement or constraint on the redshift of four of them. For each of the blazars included in our sample, we provide the flux upper limit in the VERITAS energy band. We also study the properties of the significance distributions and we present the result of a stacked analysis of the data set, which shows a 4σ excess