Synthesis of simplified analogues of eleutherobin via a Claisen rearrangement/RCM strategy

The enantioselective synthesis of a number of simplified analogues of the cytotoxic natural product eleutherobin is reported.     

The effect of modeled drag reduction on the wall region

The low-dimensional model derived for the wall region of a turbulent boundary layer (Aubry et al., 1988) is applied to a drag-reduced flow. In agreement with some experimental results, drag reduction is modeled by thickening the wall region, which is achieved by applying stretching transformations to the original flow. By application of a Galerkin projection, a set of ordinary differential equations (ODEs) is obtained whose structure is identical to the set corresponding to the unmodified flow. The coefficients of the ODEs are modified in a nontrivial way. The bifurcation diagrams plotted for different values of the stretching parameter are different in detail but the structure is globally the same. In particular, the intermittent behavior which Aubry et al. identified with the cyclic bursting events experimentally observed is still present. The scenario by which intermittency appears through a subcritical Hopf bifurcation in which a heteroclinic cycle is created and disappears through a bifurcation to traveling waves is identical. These results hold for values of the stretching between 1 and 2.65, the value at which the top of the buffer layer reaches the centerline of the pipe. This is in agreement with experimental results for flows whose drag is reduced but which still display intermittency. The bifurcations occur in the stretched flow at increased levels of dissipation (relative to the unstretched flow), consistent with theoretical pictures of drag reduction, in which the increase of scale is due to stabilization by an increase of dissipation in the turbulent part of the flow. Moreover, this method is a systematic way to perturb the coefficients of the ODEs of Aubry et al. (1988). Under this kind of perturbation, the behavior of the solution (in the part of the bifurcation diagram physically relevant) is found to be extremely robust.     

Ambipolar hexa-peri-hexabenzocoronene-fullerene hybrid materials

A new class of self-assembling hexa-peri-hexbenzocoronene (HBC)-fullerene hybrid materials has been synthesized and characterized. Photoluminescence experiments indicate that energy transfer processes can be tuned in these donor-acceptor systems by varying the length and nature of the linker group. In preliminary device testing, ambipolar charge transport behavior is observed in organic field effect transistors, while single active component organic photovoltaic devices consisting of these materials achieved a maximum external quantum efficiency of 30%.     

Microwave bonding of poly(methylmethacrylate) microfluidic devices using a conductive polymer

Component binding within microfluidic devices is a problem that has long been seeking a solution. In this investigation, the use of microwave radiation to seal PMMA components has been investigated using polyaniline as an absorber that is capable of inducting interfacial bonding. Straight microchannels were machined into PMMA using a Datron CAT3DM6 CNC machine with widths and depths across a range of 100-1000 μm. Prototype fluidic devices were prepared with channel patterns utilizing varying feature sizes, bends and flow profiling to demonstrate the application of the technique to real microfluidic devices. Experimental data illustrated the successful bonding of channels in the range stated previously and bonding (tensile) strength was assessed via pull tests on bonded PMMA using an Engstrom Zwick 100 tensile testing system (Engstrom Ltd, US). Coherent, defect free seals were attained with breakage tests requiring an excess of 1 kN force.     

On hereditarily small sets in ZF

We show in (the usual set theory without Choice) that for any set X, the collection of sets Y such that each element of the transitive closure of is strictly smaller in size than X (the collection of sets hereditarily smaller than X) is a set. This result has been shown by Jech in the case (where the collection under consideration is the set of hereditarily countable sets).     

Substituent effects on the disproportionation—combination rate constant ratios for gas‐phase halocarbon radicals,Part 5: Reactions of CF3 + CF3CH2CHCH3 and CF3CH2CHCH3 + CF3CH2CHCH3

Rate constant ratios, k_d/k_c for the disproportionation/combination reaction have been measured as 0.07 ± 0.02 when an H is removed from the CH₂ position of the CF₃CH₂CHCH₃ radical and as 0.24 ± 0.03 when the H is removed from the CH₃ position in the reaction with the CF₃ radical. For the self‐reaction between two CF₃CH₂CHCH₃ radicals, k_d/k_c has been measured as 0.27 ± 0.03 when the H is removed from the CH₂ position and as 0.47 ± 0.04 when the H is removed from the CH₃ position. The branching fraction, corrected for the number of hydrogens at each site, is 0.70 favoring the methyl position when the acceptor radical is CF₃ and 0.54 when CF₃CH₂CHCH₃ is the acceptor radical. Branching fraction results show that the CF₃ substituent on the CF₃CH₂CHCH₃ radical hinders disproportionation when CF₃ is the acceptor radical. When the accepting radical is CF₃CH₂CHCH₃ the CF₃ substituent may slightly impede the disproportionation reaction, but the branching ratio is nearly statistical. The effect of substituents on the donor radical, CF₃CH₂CHX, will be discussed for the series X = H, CF₃, Cl, and CH₃ when the acceptor radical is CF₃. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 549–557, 2001     

Chaos in a mapping describing elastoplastic oscillations

We study the local and global dynamical behavior of a two dimensional piecewise linear map which describes the asymptotic motions of a single degree of freedom, parametrically excited, elastoplastic oscillator after it has settled down to purely elastic oscillations. We give existence and stability conditions for periodic orbits and prove that chaos, in the form of a Smale horseshoe, exists at specific, but representative, parameter values. We interpret simulations of the elastoplastic oscillator itself in the light of these results.Partially supported by NSF grant number MSS-9016626.Partially supported by AFOSR 91-0329.     

Homoclinic orbits for eventually autonomous planar flows

We prove theorems giving conditions sufficient for the existence of homoclinic orbits for two dimensional, time-dependent vector fields which are autonomous for all sufficiently large values of the independent variable. We give applications to second order equations such as those arising in waveguide studies as well as explicit examples which illustrate our assumptions.Dedicated to Klaus Kirchgässner on the occasion of his sixtieth birthdayResearch supported by the National Science Foundation under DMS 87-03656 and the U. S. Army Office through the Mathematical Sciences Institute of Cornell University, Contract DAAG-29-85C-0018.     

Efficient solution of two-stage stochastic linear programs using interior point methods

Solving deterministic equivalent formulations of two-stage stochastic linear programs using interior point methods may be computationally difficult due to the need to factorize quite dense search direction matrices (e.g., AA ^T ). Several methods for improving the algorithmic efficiency of interior point algorithms by reducing the density of these matrices have been proposed in the literature. Reformulating the program decreases the effort required to find a search direction, but at the expense of increased problem size. Using transpose product formulations (e.g., A ^T A) works well but is highly problem dependent. Schur complements may require solutions with potentially near singular matrices. Explicit factorizations of the search direction matrices eliminate these problems while only requiring the solution to several small, independent linear systems. These systems may be distributed across multiple processors. Computational experience with these methods suggests that substantial performance improvements are possible with each method and that, generally, explicit factorizations require the least computational effort.