Chaos in thermal pulse combustion

An experimental thermal pulse combustor and a differential equation model of this device are shown to exhibit chaotic behavior under certain conditions. Chaos arises in the model by means of a progression of period-doubling bifurcations that occur when operating parameters such as combustor wall temperature or air/fuel flow are adjusted to push the system toward flameout. Bifurcation sequences have not yet been reproduced experimentally, but similarities are demonstrated between the dynamic features of pressure fluctuations in the model and experiment. Correlation dimension, Kolmogorov entropy, and projections of reconstructed attractors using chaotic time series analysis are demonstrated to be useful in classifying dynamical behavior of the experimental combustor and for comparison of test data to the model results. Ways to improve the model are suggested. (c) 1995 American Institute of Physics.     

A Comparison of Two Variational Methods

A discussion is given of the relation between the maximum functionaltheorem and Schwinger's variational principle, and it is shownthat the bound given by Schwinger's principle is better thanor the same as that given by the maximum functional theorem.     

Optimization of a conducting cooling fin with a heat sink using optimality criterion

An optimality criterion is used to obtain a minimum volume design of a conducting fin with an arbitrarily located heat sink whose volume is a design variable. The finite element method is used for the analysis. The effect of the heat sink as an active cooling device on the optimum volume of the fin is studied     

Anomalous1H NMR spectra of 3,4-dihydroisoquinolines and related compounds

Solutions of 3,4-dihydro-6,7-methylenedioxyisoquinoline (1) and analogues2–5 and9 as well as isoquinolines7 and8 in certain samples of CDCl₃, CCl₄, DMSO-d₆ or acetone-d₆ gave rise to anomalous¹Hnmr spectra with extreme line broadening, signals due to protons at C-l and C-3 most often not being seen. The spectra of1 and3 were most striking in this respect.¹Hnmr spectra of the quaternary salt10 and the model schiff base11 were normal. Several hypotheses for the observed line broadening have been considered and rejected, a slow equilibrium1 ⇆13 being one of them. NaBH₄ reduction of1 and2 followed by mass spectrometric analysis of the crude tetrahydroisoquinolines16 and17 ruled out a slow equilibrium1 ⇆14 and2 ⇆15 as contributory cause for line broadening. The crude reduction products unexpectedly contained N-ethyl species22 and25. Their formation is rationalised     

Nucleophilic SN2 displacements on penicillin-6- and cephalosporin-7- triflates; 6β-iodopenicillanic acid,a new β-lactamase inhibitor

Triflate or nonaflate esters of alkyl 6α (or β) hydroxypenicillanates are substituted (with inversion) by the soft nucleophiles iodide, bromide, chloride, azide, arylselenoxide,¹ thiocyanate, thiols, and thiolacids; carbon nucleophiles fail. Methoxide (hard) attacks the lactam bond, opening both rings to give a known¹¹ 1,4 thiazine. Iodide substitutes 7α-trifloxycephalosporins, giving 7β-iodocephalosporins.     

Further Gurtin-type Variational Principles for Linear Initial Value Problems

Following the variational principles for linear initial valueproblems associated with the wave and heat conduction equationsdiscussed by Gurtin and Leitmann and using time convolutionsit is shown that general variational principles exist for theseproblems with sources on the boundaries and within the regionunder consideration.