The effect of reverberation on the damping of bubbles

The measurement of an acoustic emission, or scatter, from a bubble is not difficult. However, an accurate interpretation of that signal in terms of the bubble dynamics may require careful consideration. The study presented here is at first sight relatively simple: comparison of the predicted and measured quality factors of injected bubbles. While the measurement is normally done by monitoring the decay of passive emissions from a bubble, this technique becomes difficult with smaller bubbles. Therefore an active technique is introduced, which removes all the frequency-dependent effects on the measurement (such as transducer response) bar one. That, critically, is the effect of the change in the bubble resonance (frequency and damping) which results from the loading on the bubble due to the reverberant field. The vast majority of theoretical treatments of bubble acoustics assume free field conditions, yet the environmental conditions rarely if ever match these. Therefore measurements of bubble damping are compared both with the established free field theory, and with a new theory relevant to the prevailing reverberant conditions (whether caused by tank surfaces, monochromatic neighboring bubbles, or both).     

Macroscopic evidence of soliton formation in multiterawatt laser-plasma interaction

A novel physical phenomenon has been observed following the interaction of an intense (10(19) W/cm(2)) laser pulse with an underdense plasma. Long-lived, macroscopic bubblelike structures have been detected through the deflection that the associated electric charge separation causes in a proton probe beam. These structures are interpreted as the remnants of a cloud of relativistic solitons generated in the plasma by the ultraintense laser pulse. This interpretation is supported by an analytical study of the soliton cloud evolution, by particle-in-cell simulations, and by a reconstruction of the proton-beam deflection.     

Ice structuring proteins - a new name for antifreeze proteins

Antifreeze proteins (AFPs) have been reported in the academic literature for many years, and are increasingly arousing interest in the technical and popular media, particularly because of their potential applications. However, the term "antifreeze" does not always accurately describe their natural function, or their application in frozen systems, where they do not prevent freezing, but control the size, shape and aggregation of ice crystals. We survey the properties and applications of AFPs and propose a more generally applicable name based on the fact that all AFPs bind to ice and consequently influence crystal growth and interactions: "Ice Structuring Proteins".     

Large-amplitude plasma wave generation with a high-intensity short-pulse beat wave

A short-pulse laser beat wave scheme for advanced particle accelerator applications is examined. A short, intense (3-ps, >10(18)-W cm(-2)) two-frequency laser pulse is produced by use of a modified chirped-pulse amplification scheme and is shown to produce relativistic plasma waves during interactions with low-density plasmas. The generation of plasma waves was observed by measurement of forward Raman scattering. Resonance was found to occur at an electron density many times that expected, owing to ponderomotive displacement of plasma within the focal region.     

Dispersion management for solitons in a Korteweg-de Vries system

The existence of "dispersion-managed solitons," i.e., stable pulsating solitary-wave solutions to the nonlinear Schrodinger equation with periodically modulated and sign-variable dispersion is now well known in nonlinear optics. Our purpose here is to investigate whether similar structures exist for other well-known nonlinear wave models. Hence, here we consider as a basic model the variable-coefficient Korteweg-de Vries equation; this has the form of a Korteweg-de Vries equation with a periodically varying third-order dispersion coefficient, that can take both positive and negative values. More generally, this model may be extended to include fifth-order dispersion. Such models may describe, for instance, periodically modulated waveguides for long gravity-capillary waves. We develop an analytical approximation for solitary waves in the weakly nonlinear case, from which it is possible to obtain a reduction to a relatively simple integral equation, which is readily solved numerically. Then, we describe some systematic direct simulations of the full equation, which use the soliton shape produced by the integral equation as an initial condition. These simulations reveal regions of stable and unstable pulsating solitary waves in the corresponding parametric space. Finally, we consider the effects of fifth-order dispersion. (c) 2002 American Institute of Physics.     

The carbenoid approach to peptide synthesis

A different approach to the synthesis of dipeptides is described based on the formation of the NHCHR1CONH-CHR2CO bond by carbenoid N-H insertion, rather than the formation of the peptide bond itself. Thus decomposition of triethyl diazophosphonoacetate catalysed by rhodium(II) acetate in the presence of N-protected amino acid amides 8 gives the phosphonates 9. Subsequent Wadsworth-Emmons reaction of 9 with aldehydes in the presence of DBU gives dehydro dipeptides 10. The reaction has been extended to a simple two-step procedure, without the isolation of the intermediate phosphonate, for conversion of a range of amino acid amides 11 into dehydro dipeptides 12 and to an N-methylamide 11 h, and for conversion of a dipeptide to tripeptide (13-->14). Direct conversion, by using methyl diazophenylacetate, of amino acid amides to phenylglycine-containing dipeptides 19 proceeds in good chemical yield, but with poor diastereoselectivity.     

New calcium germanium nitrides: Ca2GeN2, Ca4GeN4, and Ca5Ge2N6

We report three new calcium germanium nitrides synthesized as crystals from the elements in sealed niobium tubes at 760 degrees C using liquid sodium as a growth medium. Black Ca2GeN2 is isostructural with the previously reported strontium analogue. It is tetragonal P4(2)/mbc (no. 135) with a = 11.2004(8) A, c = 5.0482(6) A, and Z = 8. It contains GeN2(4-) units which have 18 valence electrons, and consequently are bent, like the isoelectronic molecule SO2. In contrast, clear, orange Ca4GeN4 with fully oxidized germanium contains isolated GeN4(8-) tetrahedra and is monoclinic P2(1)/c (no. 14) with a = 9.2823(8) A, b = 6.0429(5) A, c = 11.1612(9) A, beta = 116.498(6) degrees, and Z = 4. Clear, colorless Ca5Ge2N6, also with fully oxidized germanium, contains infinite chains, 1 infinity[GeN2N2/2(5-)], of corner-sharing tetrahedra similar to those found in pyroxenes. However, the precise structure of this latter phase has not yet been determined because of twinning problems.     

When to rush a ‘behind’ in Australian rules football: a dynamic programming approach

In Australian rules football, points are scored when the ball passes over the goal line. Six points are awarded for a goal when the ball passes between the two centre posts, and one point for a ‘behind’, when the ball passes between a centre post and an adjacent outer post. After a behind, the defending team has a free kick from the goal line. It may be worthwhile, particularly in the closing stages of a game, for a defending team voluntarily to concede a behind, by themselves passing the ball between the two outer posts, either to avert the possibility of an imminent goal or to increase the probability of scoring a goal themselves. A dynamic programming model is used to analyse this situation.     

Periodic solutions to Hamiltonian inclusions

We prove the existence of periodic trajectories of Hamiltonian inclusions, which reduce to the usual Hamiltonian equations in the presence of smoothness. This is accomplished via a direct variational principle involving a new action integral in an extended sense.