Instability and evolution of nonlinearly interacting water waves

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schr?dinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large-amplitude freak waves in deep water.     

Excited states and two-photon absorption of some novel thiophenyl Pt(II)-ethynyl derivatives

The photophysical characterization of two new compounds related to bis((4-(phenylethynyl)phenyl)ethynyl)bis(tributylphosphine)platinum(II), here abbreviated Pt1, is reported. For the first new compound ATP1, the inner phenyl rings (closer to the Pt atom) in Pt1 are replaced by thiophene rings bridging at the 2,5-positions. In compound ATP2, the outer phenyl groups are replaced by thiophene rings bonded at the 2-position. Specifically, we report on the fluorescence quantum yield, two-photon absorption, triplet decay times and two-photon absorption induced emission spectra of the molecules in THF solutions. The results were compared with those of Pt1 and Pt1 capped with an acetonide-protected 2,2-bis(methylol)propionic acid (bis-MPA) ester group (Pt1-G1). The photophysical properties of the organic dye 7-(diethylamino)coumarin (Coumarin 110) were determined and used as a reference material. The two-photon absorption cross section around 720-740 nm of ATP1 and ATP2 was found to be of the same order of magnitude as for Pt1-G1, i.e., between 5 and 10 GM, but slightly larger for ATP1 than for ATP2 (1 GM = 1 G?ppert-Mayer = 10(-50) (cm(4) s)/photon). The fluorescence decay time of all compounds was found to be very short (subnanosecond) with quantum yields 0.0045, 0.0007, 0.0011 and 0.0020 for ATP1, ATP2, Pt1-G1 and Pt1, respectively, measured at excitation wavelength 373 nm. Just as Pt1 and Pt1-G1, both thiophenyl derivatives showed large intersystem crossing capabilities and phosphorescence, characteristic for a triplet state that can enhance the nonlinear absorption and optical power limiting by triplet state absorption. The phosphorescence emission of the thiophenyl derivatives was red-shifted in comparison with Pt1 and Pt1-G1, and the phosphorescence decay times were on the order of 200-500 ns, as for the Pt1 compound.     

In Situ Optical Investigations of Hypervelocity Impact Induced Dynamic Fracture

One of the prominent threats in the endeavor to develop next-generation space assets is the risk of space debris impact in earth’s orbit and micrometeoroid impact damage in deep space. To date, there is no study available which concentrates on the analysis of dynamic crack growth from hypervelocity impacts on such structures, resulting in their eventual catastrophic degradation. Experiments conducted using a unique two-stage light-gas gun facility have examined the in situ dynamic fracture of brittle polymers subjected to this high-energy-density event. Optical techniques of caustics and photoelasticity, combined with high-speed photography, analyze crack growth behavior of Mylar and Homalite 100 thin plates after impact at velocities ranging from 3 to 7 km/s (7,000–15,500 mph). Results indicate that even under extreme impact conditions of out-of-plane loading, highly localized heating, and energetic impact phenomena involving plasma formation and ejecta, the dynamic fracture process occurs during a deformation regime dominated by in-plane loading.     

Focusing of Strong Shocks in an Annular Shock Tube

Focusing of strong shock waves in a gas-filled thin convergence chamber with various forms of the reflector boundary is investigated experimentally and numerically. The convergence chamber is mounted at the end of the horizontal co-axial shock tube. The construction of the convergence chamber allows the assembly of the outer chamber boundaries of various shapes. Boundaries with three different shapes have been used in the present investigation—a circle, an octagon and a smooth pentagon. The shock tube in the current study was able to produce annular shocks with the initial Mach number in the range M _s = 2.3 − 3.6. The influence of the shape of the boundary on the shape and properties of the converging and reflected shock waves in the chamber has then been investigated both experimentally and numerically. It was found that the form of the converging shock is initially governed by the shape of the reflector and the nonlinear interaction between the shape of the shock and velocity of shock propagation. Very close to the center of convergence the shock obtains a square-like form in case of a circular and octagonal reflector boundary. This is believed to stem from the instability of the converging shock front triggered by the disturbances in the flow field. The outgoing, reflected shocks were also observed to be influenced by the shape of the boundary through the flow ahead as created by the converging shocks.     

Rut depth, soil compaction and rolling resistance when using bogie tracks

There are few studies of rolling resistance for bogie tracks on forestry machines. The aim of this study was to compare the effects of wheels and two types of bogie tracks on rut formation, cone index, and vehicle rolling resistance on some typical forest soils in Sweden. In an experiment, two types of tracks were put on a trailer with a bogie with hydraulic extension on the pulling bar giving the trailer repeatable travelling speed. Loads of 0 and 9.9 Mg were used on the trailer. The main results of this study are: Compared to rather wide and soft tires, tracks on the bogie reduced rut depth by up to 40% and cone index in the ruts by about 10%, although the tracks increased the mass on the trailer by 10–12%. The relative rolling resistance coefficient was not higher for tracks than for wheels. Further studies should be conducted to show the effect of track tension on rolling resistance and flotation and of the effects of tracks on heavy vehicles on subsoil compaction.     

Modulational and filamentational instabilities of intense photon pulses and their dynamics in a photon gas

It is shown that an intense photon pulse interacting nonlinearly with sound waves in a photon gas is subjected to modulational and filamentational instabilities. Starting from a new set of coupled equations governing nonlinear photon-photon interactions, we derive a dispersion relation which depicts the temporal and spatial amplification rates of the modulational and filamentational instabilities. The long term behavior of the modulationally unstable waves renders collapse of a photon beam as well as the formation of cylindrically symmetric photonic solitons. The results can have relevance to the understanding of the nonlinear photonic pulse propagation in astrophysical environments as well as in forthcoming intense laser-matter interaction experiments.     

Nonlinear theory for a quantum diode in a dense Fermi magnetoplasma

We present a simple analytical nonlinear theory for quantum diodes in a dense Fermi magnetoplasma. By using the steady-state quantum hydrodynamical equations for a dense Fermi magnetoplasma, we derive coupled nonlinear Schr?dinger and Poisson equations. The latter are numerically solved to show the effects of the quantum statistical pressure, the quantum tunneling (or the quantum diffraction), and the external magnetic field strength on the potential and electron density profiles in a quantum diode at nanometer scales. It is found that the quantum statistical pressure introduces a lower bound on the steady electron flow in the quantum diode, while the quantum diffraction effect allows the electron tunneling at low flow speeds. The magnetic field acts as a barrier, and larger potentials are needed to drive currents through the quantum diode.     

Weak and strong wall boundary procedures and convergence to steady-state of the Navier–Stokes equations

We study the influence of different implementations of no-slip solid wall boundary conditions on the convergence to steady-state of the Navier–Stokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steady-state for coarse meshes. It is also demonstrated that all the stable approaches produce the same convergence rate as the mesh size goes to zero. The numerical results obtained by using a fully nonlinear finite volume solver support the theoretical findings from the linear analysis.     

UV excimer radiation from dielectric-barrier discharges

Dielectric-barrier (silent) discharges are ideally suited for efficient excitation of high-intensity UV radiation from excimers. The molecular continuum of xenon at 172 nm could be obtained with an efficiency of close to 10%. Model calculations for excimer formation and UV efficiencies in such discharges are presented. The possibility of obtaining many other wavelengths (e.g. KrF^* at 248 nm and XeCl^* at 308 nm) and the variety of conceivable geometries (plane or cylindrical) makes this new UV source an attractive choice for many photophysical and photochemical applications.     

Trapping of plasmons in ion holes

We present analytical and numerical studies of a new electron plasma wave interaction mechanism, which reveals trapping of Langmuir waves in ion holes associated with nonisothermal ion distribution functions. This Langmuir ion hole interaction is a unique kinetic phenomenon governed by two second nonlinear differential equations in which the Langmuir wave electric field and ion hole potential are coupled in a complex fashion. Numerical analyses of our nonlinearly coupled differential equations exhibit trapping of localized Langmuir wave envelops in the ion hole, which is either standing or moving with sub-or super ion thermal speed. The resulting ambipolar potential of the ion hole is essentially negative, giving rise to bipolar slow electric fields. The present investigation thus offers a new Langmuir wave contraction scenario that has not been rigorously explored in plasma physics.