On the stability of finitely deformed elastic membranes

Summary The stability of a uniformly inflated and extended circular thin tube of elastic material is examined. Stability criteria are obtained for fixed ends and for a tube with a fixed end and an end with a rigid closure. The criteria apply to tubes under constant internal pressure, inflated by a gas, or filled with an incompressible fluid. The stability of a spherical membrane inflated by a gas is also investigated. Numerical results are presented for an empirical strain-energy function for rubber-like materials.

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Zusammenfassung Der Teil II bringt die Untersuchung eines aufgeblasenen dünnen Schlauches mit Kreisquerschnitt aus elastischem Material, für den sich bei festen Enden und im Fall mit einem festen Ende und einem starren Verschluß Stabilitätskriterien ergeben. Diese Kriterien lassen sich auf Rohre, die mit einem Gas oder mit einer inkompressiblen Flüssigkeit gefüllt sind, anwenden. Ferner wird die Stabilität einer mit Gas aufgeblasenen sphärischen Membran betrachtet. Abschließend werden numerische Resultate für eine empirische Formänderungsfunktion für gummiähnliche Materialien angegeben.

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For Part I see Z. ang. Math. Phys.22, 1016 (1971).     

Exchange reactions of organomercury compounds

Spectroscopic studies (PMR and UV) have been carried out on mixtures of symmetrical organomercury compounds at room temperature in DMSO, pyridine, and ethanol as solvents. It has been shown that for a range of diarylmercurials, Ar₂Hg, and di-(acetaldehyde)mercury, Hg(CH₂CHO)₂, an exchange reaction occurs with the formation in solution of the unsymmetrical compound ArHgCH₂CHO. Facile exchange also occurs between pairs of diarylmercurials. A mechanism involving a four centre transition state is proposed. Simple dialkylmercurials do not undergo this exchange under mild conditions.     

Quantum coherence between two atoms beyond Q=10(15)

We place two atoms in quantum superposition states and observe coherent phase evolution for 3.4×10(15) cycles. Correlation signals from the two atoms yield information about their relative phase even after the probe radiation has decohered. This technique allowed a frequency comparison of two (27)Al(+) ions with fractional uncertainty 3.7(-0.8)(+1.0)×10(-16)/√[τ/s]. Two measures of the Q factor are reported: The Q factor derived from quantum coherence is 3.4(-1.1)(+2.4)×10(16), and the spectroscopic Q factor for a Ramsey time of 3 s is 6.7×10(15). We demonstrate a method to detect the individual quantum states of two Al(+) ions in a Mg(+)-Al(+)-Al(+) linear ion chain without spatially resolving the ions.