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.     

Dynamics of Abelian Higgs vortices in the near Bogomolny regime

The aim of this paper is to give an analytical discussion of the dynamics of the Abelian Higgs multi-vortices whose existence was proved by Taubes ([JT82]). For a particular value of a parameter of the theory, , called the Higgs self-coupling constant, there is no force between two vortices and there exist static configurations corresponding to vortices centred at any set of points in the plane. This is known as the Bogomolny regime. We will develop some formal asymptotic expansions to describe the dynamics of these multi-vortices for close, but not equal to, this critical value. We shall then prove the validity of these asymptotic expansions. These expansions allow us to give a finite dimensional Hamiltonian system which describes the vortex dynamics. The configuration space of this system is the moduli space—the space of solutions of the static equations modulo gauge equivalence. The kinetic energy term in the Hamiltonian is obtained from the natural metric on the moduli space given by theL ² inner product of the tangent vectors. The potential energy gives the intervortex potential which is non-zero when is not given by its critical value. Thus the reduced equations for the evolution of the vortex parameters take the form of geodesics, with force terms to express the departure from the Bogomolny regime. The geodesics are geodesics on the moduli space with respect to the metric defined by theL ² inner product of the tangent vectors, in accordance with Manton's suggestion ([Man82]). This allows an understanding of the two main phenomenological issues—first of all there is the right angle scattering phenomenon, according to which two vortices passing through one another scatter through ninety degrees. Secondly there is the conjecture from numerical calculations that vortices repel for greater than the critical value, and attract for less than this value. The results of this paper allow a rigorous understanding of the right angle scattering phenomenon ([Sam92, Hit88]) and reduce the question of attraction or repulsion in the near Bogomolny regime to an understanding of the potential energy term in the Hamiltonian ([JR79]).     

Stereochemically controlled synthesis of unsaturated acids via diphenylphosphinoyl (Ph2PO) -ketoacids

Acylation of phosphine oxide anions with derivatives of cyclic anhydrides or oxidative cleavage of cyclic allyl phosphine oxides gives Ph₂PO-ketoacids: reduction, separation of diastereoisomers, and completion of the Horner-Wittig reaction gives single isomers ($\text{E}$) or ($\text{Z}$) of unsaturated acids.     

Inelastic incoherent neutron scattering measurements of intact cells and tissues and detection of interfacial water

We have previously used inelastic incoherent neutron scattering spectroscopy to investigate the properties of aqueous suspensions of biomolecules as a function of hydration. These experiments led to the identification of signals corresponding to interfacial (hydration) water at low water content. A prediction from these studies was that in the crowded environment inside living cells, a significant proportion of the water would be interfacial, with profound implications for biological function. Here we describe the first inelastic incoherent neutron scattering spectroscopy studies of living cells and tissues. We find that the interfacial water signal is similar to that observed for water interacting with purified biomolecules and other solutes, i.e., it is strongly perturbed in the librational and translational intermolecular optical regions of the spectrum at 20-150 meV. The ratio of interfacial water compared to total water in cells (approximately 30%) is in line with previous experimental data for hydration water and calculations based on simple assumptions.     

Liquid chromatography/tandem mass spectrometry analysis of chloramphenicol in cooked crab meat

A liquid chromatography/tandem mass spectrometry (LC/MS/MS) method is described for the extraction, cleanup, determination, and confirmation of chloramphenicol (CAP) in cooked crab meat. The method involves pulverization of cooked crab meat with dry ice; extraction of the CAP into ethyl acetate (EtOAc); evaporation (by N2) of the EtOAc; addition of methanol, aqueous NaCl, and heptane; extraction of the lipids into the heptane, followed by extraction of the aqueous phase with EtOAc; evaporation (by N2) of the EtOAc; dissolution into methanol-water; filtration; and separation/detection/confirmation using LC/MS/MS. Crab meat was fortified at 0.25, 0.50, and 1.0 ng/g (ppb) chloramphenicol. Average absolute recoveries were 67, 84, and 86%, respectively, with relative standard deviation values all less than 1%. Four daughter ions (m/z 152, 176, 194, and 257) were monitored off the m/z 321 precursor ion. Determination was based on a standard curve using the peak areas of the m/z 152 daughter ion (the base peak) for standard solutions equivalent to 0.10, 0.20, 0.50, and 1.0 ppb in tissue (made with control crab extract). A set of 6 matrix controls (unfortified crab meat) was also analyzed, in which no chloramphenicol was detected. For identification purposes, the ion ratios (of each daughter ion versus the base daughter ion) of the fortified crab versus those of the chloramphenicol standards agreed within 10% (relative) at fortified chloramphenicol concentrations of 0.25-1.0 ppb.     

Modeling the gel electrophoresis of short duplex DNA by Brownian dynamics: cubic gel lattice with direct interaction

The technique of Brownian dynamics is used to model the electrophoretic mobility of spherical and rod-like particles in a three-dimensional cubic gel lattice. In addition to excluded volume interactions between the migrating particle and the gel, direct interactions are also included. The methodology is first applied to spherical particles in the absence of direct interactions and the resulting mobilities are shown to agree with independent studies. The methodology is then applied to rod-like models of short duplex DNA fragments 10-50 base pairs in length. In the absence of direct interactions between gel and DNA, calculated mobilities show a much weaker dependence on gel concentration than observed in experiments of DNA in Tris-acetate buffer and polyacrylamide gels. When an attractive interaction between gel and DNA of approximately -0.3 k(B)T per base pair at contact is included, good agreement between calculated and experimental mobilities is achieved.     

From solution-phase to solid-phase enyne metathesis: crossover in the relative performance of two commonly used ruthenium pre-catalysts

A crossover in the ability of two distinct ruthenium-based metathesis pre-catalysts to effect the synthesis of dialkenylboronic esters in solution and on the solid-phase was observed. Specifically, while the Grubbs 2nd generation pre-catalyst 3 affords a greater degree of conversion to product than the Hoveyda-Grubbs pre-catalyst 2 in a solution-phase enyne-metathesis reaction, this trend is reversed in the solid-phase variant. Systematic investigation showed this trend to be general, regardless of variations in the homoallylic alcohol and alkynylboronic ester components of the reaction, as well as in the type of solid support employed. Experiments to determine a mechanistic hypothesis for this trend highlighted the significance of the ruthenium remaining bound to the substrate after metathetic rearrangement and found the presence of phosphine ligand to be detrimental to the success of the solid-phase reaction. Therefore, these results suggest an expanded role for phosphine-free pre-catalysts, such as 2, in challenging solid-phase metathesis reactions.