The Interaction of Shocks with Dispersive Waves II. Incompressible-Integrable Limit

This is the second in a two-part series of articles in which we analyze a system similar in structure to the well-known Zakharov equations from weak plasma turbulence theory, but with a nonlinear conservation equation allowing finite time shock formation. In this article we analyze the incompressible limit in which the shock speed is large compared to the underlying group velocity of the dispersive wave (a situation typically encountered in applications). After presenting some exact solutions of the full system, a multiscale perturbation method is used to resolve several basic wave interactions. The analysis breaks down into two categories: the nonlinear limit and the linear limit, corresponding to the form of the equations when the group velocity to shock speed ratio, denoted by ε, is zero. The former case is an integrable limit in which the model reduces to the cubic nonlinear Schrödinger equation governing the dispersive wave envelope. We focus on the interaction of a “fast” shock wave and a single hump soliton. In the latter case, the ε=0 problem reduces to the linear Schrödinger equation, and the focus is on a fast shock interacting with a dispersive wave whose amplitude is cusped and exponentially decaying. To motivate the time scales and structure of the shock-dispersive wave interactions at lowest orders, we first analyze a simpler system of ordinary differential equations structurally similar to the original system. Then we return to the fully coupled partial differential equations and develop a multiscale asymptotic method to derive the effective leading-order shock equations and the leading-order modulation equations governing the phase and amplitude of the dispersive wave envelope. The leading-order interaction equations admit a fairly complete analysis based on characteristic methods. Conditions are derived in which: (a) the shock passes through the soliton, (b) the shock is completely blocked by the soliton, or (c) the shock reverses direction. In the linear limit, a phenomenon is described in which the dispersive wave induces the formation of a second, transient shock front in the rapidly moving hyperbolic wave. In all cases, we can characterize the long-time dynamics of the shock. The influence of the shock on the dispersive wave is manifested, to leading order, in the generalized frequency of the dispersive wave: the fast-time part of the frequency is the shock wave itself. Hence, the frequency undergoes a sudden jump across the shock layer.In the last section, a sequence of numerical experiments depicting some of the interesting interactions predicted by the analysis is performed on the leading-order shock equations.     

Die Bestimmung von Methylpropan

Ohne Zusammenfassung     

Comparison between biokinetics of inhaled plutonium nitrate and gadolinium oxide in humans and animals

Due to the paucity of human data after inhalation of different chemical forms of radionuclides, the implications for human exposure are often based on animal studies. This paper describes biokinetic studies of plutonium nitrate and gadolinium oxide in human volunteers and rats. The results, together with information from other studies with radionuclides, suggests that animal studies can be used with advantage for assessing the biokinetic behavior in humans, and for providing guidance on the assessment of intake and optimal monitoring regimens.     

A simple derivation of Vonnegut's equation for the determination of interfacial tension by the spinning drop technique

A simple derivation of Vonnegut's equation for use in the determination of interfacial tension by the spinning drop technique is described. The derivation involves a cylindrical approximation and calculates the kinetic energy of rotation of the system from a consideration of its moment of inertia.     

The determination of lead and nickel by atomic-absorption spectrometry with a flameless wire loop atomizer

In an extension of studies of flameless atomizers for atomic-absorption spectrometry, an electrically heated tungsten-rhenium alloy wire loop was examined. Reduction of metallic salts to ground-state metal atoms was accomplished with the high temperature produced by the loop. Lead and nickel were investigated. Experimental parameters such as wavelength, slit width, atomization temperature and sheathing gas flow rate were optimized. Absolute detection limits of 6.6·10^?10 and 1.2·10^?10, and absolute sensitivities of 7·10^?10 and 8·10^?11 g of lead, were established for unenclosed and enclosed cells, respectively. The interferences of twenty cations and sixteen anions were studied; foreign cations generally enhanced the lead absorption by retarding its vaporization, allowing the slow detection system to respond more efficiently. Nickel was investigated as a representative less volatile metal; an absolute detection limit of 1.6·10^?9 and an absolute sensitivity of 9·10^?10 g of nickel were established.     

Analysis of urinary nucleosides. I. Optimisation of high performance liquid chromatography/electrospray mass spectrometry

In order to optimise the analysis of urinary nucleosides by high performance liquid chromatography/mass spectrometry (HPLC/MS), the HPLC separation of these compounds was performed at different 'flow rates' and 0.2mL/min was found to give both a better separation and ionisation. The ionisation conditions were optimised to give the best intensity of the molecules quasi-molecular ions. The ion distribution profile and ionisation in both positive and negative mode were examined and the detection of the protonated molecule in positive mode chosen for further analysis. The limits of detection of the method developed are reported and representative LC/MS and LC/MS/MS spectra shown. Typical urinary nucleoside chromatograms are presented.     

Point-splitting regularization for gauge theories: Quantum electrodynamics

As a method of regularization, point splitting has played an essential role in the recent theoretical determination of the masses of the Higgs boson and the top quark. It is the purpose of this paper to put this pointsplitting regularization on a firm basis. The result turns out to be extremely simple: replace the usual vertex factor-ieγ ^µ in quantum electrodynamics by $$ - ie(\gamma _\mu - \frac{{\not p}}{{p \cdot \delta }}\delta _\mu ),$$ wherep is the momentum of the photon line, andδ ^µ is the distance for point splitting. No additional vertices are needed.     

An automatic controlled-potential coulometer

The design and operation of an automatic controlled-potential coulometer is described. It was primarily designed for use with mg quantities of uranium, neptunium and plutonium but can in principle be used on any element possessing more than one valency state in solution. It is capable of an accuracy and precision of ±0.25% and can analyse up to 20 samples on a set programme without operator attention.     

Determination of enzyme kinetic parameters of cyclic CMP-specific phosphodiesterase by quantitative fast atom bombardment tandem mass spectrometry

The determination of cytidine 3′,5′-cyclic monophosphate-specific phosphodiesterase activity by means of fast-atom bombardment (FAB) mass Spectrometry with mass-analysed ion kinetic energy (MIKE) spectrum scanning is described. Initial efforts to determine the activity of the enzyme by this method were unsuccessful owing to the obfuscation of sample-related peaks by peaks emanating from the incubation buffer and cation adducts; dilution of buffer and a desalting procedure overcame these difficulties. In the resulting positive-ion FAB mass spectra, characteristic peaks of the enzyme substrate and product could be readily identified and the protonated molecular ions selected for MIKE scanning. By spiking enzyme incubates with known amounts of substrate and product, and measuring peak heights in the MIKE spectra of both spiked and unspiked samples, the substrate/product ratio at the end of a series of phosphodiesterase incubations was determined. From the data obtained, the K_m and V_max of the phosphodiesterase were calculated as 6.08 mM and 11 μmol min^?1 mg^?1, respectively, showing good agreement with the analogous values of 8.06 mM and 5.8 μmol^?1 min^?1 mg^?1 obtained by radioactive assay.     

Activation entropy of electron transfer reactions

We report microscopic calculations of free energies and entropies for intramolecular electron transfer reactions. The calculation algorithm combines the atomistic geometry and charge distribution of a molecular solute obtained from quantum calculations with the microscopic polarization response of a polar solvent expressed in terms of its polarization structure factors. The procedure is tested on a donor–acceptor complex in which ruthenium donor and cobalt acceptor sites are linked by a four-proline polypeptide. The reorganization energies and reaction energy gaps are calculated as a function of temperature by using structure factors obtained from our analytical procedure and from computer simulations. Good agreement between two procedures and with direct computer simulations of the reorganization energy is achieved. The microscopic algorithm is compared to the dielectric continuum calculations. We found that the strong dependence of the reorganization energy on the solvent refractive index predicted by continuum models is not supported by the microscopic theory. Also, the reorganization and overall solvation entropies are substantially larger in the microscopic theory compared to continuum models.