Singular vortices in regular flows

A review of the theory of quasigeostrophic singular vortices embedded in regular flows is presented with emphasis on recent results. The equations governing the joint evolution of singular vortices and regular flow, and the conservation laws (integrals) yielded by these equations are presented. Using these integrals, we prove the nonlinear stability of a vortex pair on the f-plane with respect to any small regular perturbation with finite energy and enstrophy. On the β-plane, a new exact steady-state solution is presented, a hybrid regular-singular modon comprised of a singular vortex and a localized regular component. The unsteady drift of an individual singular β-plane vortex confined to one layer of a two-layer fluid is considered. Analysis of the β-gyres shows that the vortex trajectory is similar to that of a barotropic monopole on the β-plane. Non-stationary behavior of a dipole interacting with a radial flow produced by a point source in a 2D fluid is examined. The dipole always survives after collision with the source and accelerates (decelerates) in a convergent (divergent) radial flow.     

Pulsed‐laser polymerization‐gel permeation chromatographic determination of the propagation‐rate coefficient for the methyl acrylate dimer: A sterically hindered monomer

The methyl acrylate dimer (MAD) is a sterically hindered macromonomer, and the propagating radical can fragment to an unsaturated end group. The propagation‐rate coefficient (k_p) for MAD was obtained by pulsed‐laser polymerization (PLP). The Mark–Houwink–Sakaruda parameters required for the analysis of the molecular weight distributions (MWDs) were obtained by multiple‐detector gel permeation chromatography (GPC) with on‐line viscometry. The small radical created by the fragmentation results in a short‐chain polymer that means the MWD may no longer be given by that expected for “ideal” PLP conditions; simulations suggest that the degree of polymerization required for “ideal” PLP conditions can be obtained from the primary point of inflection provided the GPC traces also show a clear secondary inflection point (radicals terminated by the second, rather than the first, pulse subsequent to initiation). Over the temperature range of 40–75 °C, the data can be best fitted by k_p/dm³ mol^?1 s^?1 = 10^6.1 exp(?29.5 kJ mol^?1), with a moderately large joint confidence interval for the Arrhenius parameters. The data are consistent with an increased activation energy and reduced frequency factor as compared with acrylate or methacrylate; both of these changes can be ascribed to hindrance. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3902–3915, 2001     

Inclusion complexes of α‐cyclodextrin and (AB)n block copolymers

Cyclodextrins thread onto polymer chains to form inclusion complexes, especially when the polymer is hydrophobic relative to the solvent. Selective threading might occur when the polymer architecture contains both hydrophobic and hydrophilic segments. α‐Cyclodextrin formed crystalline inclusion complexes with (AB)_n microblock copolymers, where the A block was a linear alkyl segment containing a single double bond and the B block was an exact length segment of poly(ethylene oxide). The complexes were isolated and characterized by solution and solid‐state NMR, X‐ray diffraction, differential scanning calorimetry, and thermogravimetric analysis. Each method confirmed complex formation and showed that the physical properties of the complexes were distinct from those of its individual components. The X‐ray data were consistent with known inclusion complexes having a channel or column crystal structure. The stoichiometry of the complex formation, 2.3 α‐cyclodextrin rings per polymer repeat unit, was determined by NMR analysis of the complexes and from an analysis of the inclusion complex yields. The data suggest that the inclusion complex stoichiometry is defined by the increasing insolubility of the polymer–cyclodextrin complex. Solid‐state NMR data were consistent with a preference for threading onto hydrophobic segments of the (AB)_n polymer. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2731–2739, 2001     

Variations of mixed Hodge structure, Higgs fields, and quantum cohomology

Following C. Simpson, we show that every variation of graded-polarized mixed Hodge structure defined over ℚ carries a natural Higgs bundle structure which is invariant under the ℂ^* action studied in [20]. We then specialize our construction to the context of [6], and show that the resulting Higgs field θ determines (and is determined by) the Gromov–Witten potential of the underlying family of Calabi–Yau threefolds. Received: 14 February 2000     

Biosurfactants from potato process effluents

High-solids (HS) and low-solids (LS) potato process effluents were tested as substrates for surfactin production. Tests used effluents diluted 1∶10, unamended and amended with trace minerals or corn steep liquor. Heat pretreatment was necessary for surfactin production from effluents due to indigenous bacteria, whose spores remained after autoclaving. Surfactin production from LS surpassed HS in all cases. Surfactin yields from LS were 66% lower than from a pure culture in an optimized potatostarch medium. LS could potentially be used without sterilization for surfactin production for low-value applications such as environmental remediation or oil recovery.     

Stress relaxation of PBI based membrane electrode assemblies

Stress relaxation in the membrane electrode assemblies (MEA) in PEM fuel cells subjected to compressive loads is analyzed. This behavior is important because nonzero contact stress is required to maintain low electric resistivity in the fuel cell stack. Experimental results are used to guide the choice of the viscoelastic properties of the constituents of the MEA, the membrane and the gas diffusion layer (GDL), needed for the model. These properties are incorporated into the model that treats the membrane as a porous-viscoelastic solid, and the gas diffusion layer as a nonlinear elastic solid. Using numerical simulations (finite element method), the stress relaxation curves for the MEA are obtained for different fluid flow boundary conditions, variations in the material properties of the membrane and the GDL. The results are compared to experimental stress relaxation curves. Most of the experimental data were obtained at a temperature of 180 °C, corresponding to operating conditions, so in the model the temperature was considered fixed and equal to this value.     

Quantification techniques of mass-separation and ion yield for the detection of radioactive isotopes

Journal of Radioanalytical and Nuclear Chemistry - This research demonstrates two methods of quantifying ion yield efficiency using an inductively coupled plasma mass spectrometer. The mass...     

Simulating the effects of underground nuclear explosions with an exploding wire

Exploding wires can deposit significant amounts of energy on nS–µS timescales into a confined space. Most exploding wire studies have been performed in air but we have started to investigate enclosing the wire element in solid matrices like concrete to mimic the effects of an underground nuclear explosion. Temperatures and pressures achieved are quite sufficient to induce structural cracking and localized flash melting. As a result exploding wires would appear to form the perfect trigger for releasing chemical species in geological media to study migration behavior. Details of the apparatus and some illustrations of its potential will be given.     

Defluoroalkylation of sp3 C−F Bonds of Industrially Relevant Hydrofluoroolefins

A simple, one-pot procedure is reported for the selective defluoroalkylation of trifluoromethyl alkene derivatives with aldehydes and ketones. The reaction sequence allows construction of a new C−C bond in a highly selective manner from a single sp³ C−F bond of a CF₃ group in the presence of sp² C−F bonds. The scope incorporates industrially relevant fluorocarbons including HFO-1234yf and HFO-1234ze. No catalyst, additives or transition metals are required, rather the methodology relies on a recently developed boron reagent. Remarkably, the boron site of this reagent plays a dual role in the reaction sequence, being nucleophilic at boron in the C−F cleavage step (S_N2’) but electrophilic at boron en route to the carbon–carbon bond-forming step (S_E2’). The duplicitous behaviour is underpinned by a hydrogen atom migration from boron to the carbon atom of a carbene ligand.     

Moderately branched ultra‐high molecular weight polyethylene by using N,N′‐nickel catalysts adorned with sterically hindered dibenzocycloheptyl groups

Five examples of unsymmetrical 1,2‐bis (arylimino) acenaphthene ( L1 – L5 ), each containing one N‐2,4‐bis (dibenzocycloheptyl)‐6‐methylphenyl group and one sterically and electronically variable N‐aryl group, have been used to prepare the N,N′‐nickel (II) halide complexes, [1‐[2,4‐{(C₁₅H₁₃}₂–6‐MeC₆H₂N]‐2‐(ArN)C₂C₁₀H₆]NiX₂ (X = Br: Ar = 2,6‐Me₂C₆H₃ Ni1 , 2,6‐Et₂C₆H₃ Ni2 , 2,6‐i‐Pr₂C₆H₃ Ni3 , 2,4,6‐Me₃C₆H₂ Ni4 , 2,6‐Et₂–4‐MeC₆H₂ Ni5 ) and (X = Cl: Ar = 2,6‐Me₂C₆H₃ Ni6 , 2,6‐Et₂C₆H₃ Ni7 , 2,6‐i‐Pr₂C₆H₃ Ni8 , 2,4,6‐Me₃C₆H₂ Ni9 , 2,6‐Et₂–4‐MeC₆H₂ Ni10 ), in high yield. The molecular structures Ni3 and Ni7 highlight the extensive steric protection imparted by the ortho‐dibenzocycloheptyl group and the distorted tetrahedral geometry conferred to the nickel center. On activation with either Et₂AlCl or MAO, Ni1 – Ni10 exhibited very high activities for ethylene polymerization with the least bulky Ni1 the most active (up to 1.06  ×  10⁷ g PE mol^?1(Ni) h^?1 with MAO). Notably, these sterically bulky catalysts have a propensity towards generating very high molecular weight polyethylene with moderate levels of branching and narrow dispersities with the most hindered Ni3 and Ni8 affording ultra‐high molecular weight material (up to 1.5  ×  10⁶ g mol^?1). Indeed, both the activity and molecular weights of the resulting polyethylene are among the highest to be reported for this class of unsymmetrical 1,2‐bis (imino)acenaphthene‐nickel catalyst.