Nonlinear Programming

Journal of the Operational Research Society -     

Primary and secondary nucleation of the transition between the A and B phases of superfluid 3He

We have studied nucleation in superfluid 3He across the A-B phase transition driven by a magnetic field, in a controllable environment at very low temperatures. Both B-->A and A-->B secondary nucleation appear to be governed by the survival of pockets of the new phase trapped at surfaces. We find that, at fields near B(AB), primary A-->B nucleation cannot be triggered by ionizing or neutron irradiation even at very high intensities. In our cell primary A-->B nucleation can only be triggered externally by mild mechanical shock.     

Shear flow and Kelvin-Helmholtz instability in superfluids

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.     

Selective resonant energy transfer from all trans β-carotene to dimeric chlorophyll a in vitro

From analysis of the excitation spectrum of the 625 and 688 nm fluorescence of dimeric chlorophyll a (Chl a). and the 668 nm fluorescence of the monomer in the presence or absence of all-trans β-carotene it is concluded that resonant energy transfer occurs between β-carotene and dimeric Chl a. This transfer could involve the 2¹A⁻_g electronic state of all-trans β-carotene which is resonant with the second set of pseudo-exciton states of the dimer.     

Experimental determination of cascade parameters of a hearing-aid microphone via the two-load method

Presented in this article is a computer-aided experimental method for obtaining the cascade parameters of the two-port model of a miniature hearing-aid microphone. The method is an adaptation of the "two-load" method [D.P. Egolf and R.G. Leonard, J. Acoust. Soc. Am. 62, 1013-1023 (1977)] to acoustoelectric, rather than electroacoustic, transducers. The cascade parameters of a particular microphone, determined by this method, were within 2.5 dB of the manufacturer's published open-circuit sensitivity data. In an attempt to further verify the numerical cascade-parameter data, a two-port model of the microphone was used to simulate experimental voltages developed across two different complex electrical load impedances attached to the microphone. The results showed experimental/simulation differences of no greater than 3.0 dB at any frequency. The two-port microphone model and associated cascade parameters are currently being incorporated into a computer-based plan for mathematical simulation of an entire in situ hearing aid.     

Deciphering the mechanistic dichotomy in the cyclization of 1-(2-ethynylphenyl)-3,3-dialkyltriazenes: competition between pericyclic and pseudocoarctate pathways

The mechanistic aspects of the cyclization of (2-ethynylphenyl)triazenes under both thermal and copper-mediated conditions are reported. For cyclization to an isoindazole, a carbene mechanistic pathway is proposed. The carbene intermediate can react with oxygen, dimerize to give an alkene, or be trapped either intermolecularly (using 2,3-dimethyl-2-butene to generate a cyclopropane) or intramolecularly (using a biphenyl moiety at the terminus of the acetylene to form a fluorene). Density-functional theory (DFT) calculations support a pseudocoarctate pathway for this type of cyclization. Thermal cyclization to give a cinnoline from (2-ethynylphenyl)triazenes is proposed to occur through a pericyclic pathway. DFT calculations predict a zwitterionic dehydrocinnolinium intermediate that is supported by deuterium trapping studies as well as cyclizations performed using a 2,2,6,6-tetramethylpiperidine moiety at the 3-position of the triazene.