Semi-Resonant Interactions and Frequency Dividers

A theory describing the behavior of a system as it evolves slowly through internal nonlinear resonances is presented. The energy sharing process is seen to be quite complex as it depends crucially on both nonlinear and frequency detuning effects. Two phenomena are discussed in detail although the general ideas are applicable to many situations. Firstly we examine the interaction between the quadratically coupled oscillators whose natural frequencies are in the ratio 2:1 for a limited period of time. Such a system is shown to be an extremely useful switching device. Secondly we examine the time dependent Duffing equation and find that smooth forward and reverse transitions occur without the presence of dissipation.     

Atomic and molecular ions in intense ultra-fast laser fields

The interaction of a 60 fs 790 nm laser pulse with beams of Ar⁺, C⁺, H₂ ⁺, HD⁺ and D₂ ⁺ are discussed. Intensities up to 10¹⁶ Wcm^-2 are employed. An experimental z-scanning technique is used to resolve the intensity dependent processes in the confocal volume.Received: 6 January 2003, Published online: 15 July 2003PACS: 32.80.Fb Photoionization of atoms and ions - 33.80.Rv Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states) - 42.50.Hz Strong-field excitation of optical transitions in quantum systems; multiphoton processes; dynamic Stark shift     

Probabilistic determination of two-phase flow regimes in horizontal tubes utilizing an automated image recognition technique

Probabilistic two-phase flow map data is experimentally obtained for R134a at 25.0, 35.0, and 49.7°C, R410A at 25.0°C, mass fluxes from 100 to 600 kg/m²-s, qualities from 0 to1 in 8.00, 5.43, 3.90, and 1.74 mm I.D. single, smooth, adiabatic, horizontal tubes in order to extend probabilistic two-phase flow map modeling techniques to single tubes. A new web camera based flow visualization technique utilizing an illuminated diffuse striped background was used to enhance images, detect fine films, and aid in the automated image recognition process developed in the present study. This technique has an average time fraction classification error of less than 0.01.     

Optical measurement of liquid film thickness and wave velocity in liquid film flows

Two optical techniques are described for measurement of a liquid film's surface. Both techniques make use of the total internal reflection which occurs at a liquid-vapor interface due to the refractive index difference between a liquid and a vapor. The first technique is used for film thickness determination. A video camera records the distance between a light source and the rays which are reflected back from the liquid-vapor interface. This distance can be shown to be linearly proportional to film thickness. The second technique measures surface wave velocities. Two photo sensors, spaced a fixed distance apart, are used to record the time varying intensity of light reflected from the liquid-vapor interface. The velocity is then deduced from the time lag between the two signals.The authors appreciate the support of the Air Conditioning and Refrigeration Center at the University of Illinois at Urbana-Champaign under project 45.     

Whitecapping

The work we describe addresses the process of whitecapping. We first argue that, when the winds are strong enough, the ocean surface must develop an alternative means to dissipate energy when its flux from large to small scales becomes too large. We then show that the resulting Phillips' spectrum, which holds at small or meter length scales, is dominated by sharp crested waves. We next idealize such a sea locally by a family of close to maximum amplitude Stokes waves and show, using highly accurate simulation algorithms based on a conformal map representation, that perturbed Stokes waves develop the universal feature of an overturning plunging jet. We analyze both the cases when surface tension is absent and present. In the latter case, we show the plunging jet is regularized by capillary waves that rapidly become nonlinear Crapper waves in whose trough pockets whitecaps may be spawned. We are careful not to claim this as the definitive mechanism for whitecaps because three‐dimensional effects, although qualitatively discussed, are not included in the analysis.     

Studies of structural effects on the half-wave potentials of mononuclear and dinuclear nickel(II) diphosphine/dithiolate complexes

Two series of mononuclear Ni(II) complexes of the formula (PNP)Ni(dithiolate) where PNP = R2PCH2N(CH3)CH2PR2, R = Et and Ph, have been synthesized containing dithiolate ligands that vary from five- to seven-membered chelate rings. Two series of dinuclear Ni(II) complexes of the formula {[(diphosphine)Ni]2(dithiolate)}(X)2 (X = BF4 or PF6) have been synthesized in which the chelate ring size of the dithiolate and diphosphine ligands have been systematically varied. The structures of the alkylated mononuclear complex, [(PNPEt)Ni(SC2H4SMe)]OTf, and the dinuclear complex, [(dppeNi)2(SC3H6S)](BF4)2, have been determined by X-ray diffraction studies. The complexes have been studied by cyclic voltammetry to determine how the half-wave potentials of the Ni(II/I) couples vary with chelate ring size of the ligands. For the mononuclear complexes, this potential becomes more positive as the natural bite angle of the dithiolate ligand increases. However, the potentials of the Ni(II/I) couples of the dinuclear complexes do not show a dependence on the chelate ring size of the ligands. Other aspects of the reduction chemistry of these complexes have been explored.     

Model studies of colloidal silica precipitation using biosilica extracts from<Emphasis Type="Italic"> Equisetum telmateia</Emphasis>

Structural materials containing silicon are produced in single celled organisms through to higher plants and animals. Hydrated amorphous silica is a colloidal mineral of infinite functionality that is formed into structures with microscopic and macroscopic form. Proteins and proteoglycans are suggested to play a critical role in the catalysis of silica polycondensation and in structure direction during the formation of these magnificent structures. This article extends knowledge on the effect of protein containing biosilica extracts from Equisetum telmateia on the kinetics of silica formation and structure regulation. Utilising potassium silicon catecholate as the source of soluble silicon, bioextracts obtained from plant silica by dissolution of the siliceous phase with aqueous HF following extensive acid digestion of the plant cell wall were found to modify the kinetic rate constants for the formation of small silicic acid oligomers under circumneutral pH conditions and to modify the solubility of silicic acid in solution. Addition of the bioextracts at ca. 1 wt% to the reaction medium reduced the sizes and range of sizes of the fundamental silica particles formed and led to the formation of crystalline polymorphs of silica under conditions of ca. neutral pH, room temperature and in the absence of multiply charged cations, conditions assumed to be relevant to the biological mineralization environment. The ability of biological organisms to regulate the formation of silica structures with prevention of crystallinity is discussed as are the implications of this study in terms of the generation of new materials with specific form and function for industrial application.     

Spatial soliton optical switches: a soliton-based equivalent particle approach

The spatial soliton plays a fundamental role as a robust, particle-like object which can be manipulated to switch or spatially scan collimated light channels or optical pulses which are incident at an oblique angle to an interface separating two or more selffocusing Kerr slab dielectrics. The underlying equivalent particle/multiparticle theory can also be employed to predict stability properties of nonlinear surface or guided waves, to derive an analytic expression for the nonlinear Goos-Hanchen shift at a nonlinear interface and to quantify the effect of material diffusion, linear and twophoton absorption on the switching behaviour of the light beam. Pulsed spatial switching effects are studied in order to illustrate the general predictive power of the equivalent particle theory.