A comparison of results of axial-tension,rotating-beam and pressurized-cylinder fatigue tests

In a previous paper by Davidson, Eisenstadt and Reiner, it was noted that, as the diameter ratio of an open-end, thick-walled cylinder approached unity, the stress state due to internal pressure approaches that of uniaxial tension. It was, therefore, proposed that the fatigue life of a cyclically pressurized thick-walled cylinder might be predicted from the results of axialtension fatigue tests. In this paper, the results of the thick-walled-cylinder fatigue tests, reported in Ref. 2, extrapolated to a diameter ratio of unity, are compared with the results of axial-tension fatigue tests on the same material. The effect of oil in contact with the surface of the axial fatigue specimens and that of varying the cyclic speed from 1800 cpm to 200 cpm are investigated. Rotating beam fatigue test results for the same material are also reported. The results of the axial-tension fatigue tests do not agree with the extrapolated thick-walled cylinder results in the range of fatigue lives from 10⁴ to 10⁶ cycles with the cylinder results showing the shorter lives. For less than 10⁴ cycles, the results converge. No effect of cyclic speed or of oil in contact with the surface was found. The results of the rotating-beam tests generally lie between the axial-tension and extrapolated cylinder results.     

Concerted Ring Opening and Cycloaddition of Chiral Epoxy Enolsilanes with Dienes

Silyl‐triflate‐catalyzed (4+3) cycloadditions of epoxy enolsilanes with dienes provide a mild and chemoselective synthetic route to seven‐membered carbocycles. Epoxy enolsilanes containing a terminal enolsilane and a single stereocenter undergo cycloaddition with almost complete conservation of enantiomeric purity, a finding that argues against the involvement of oxyallyl cation intermediates which have been previously proposed for these types of reactions. Reported are theoretical and experimental investigations of the cycloaddition mechanism. The major enantiomers of the cycloadducts are derived from S_N2‐like reactions of the silylated epoxide with the diene, in which stereospecific ring opening and formation of the two new C? C bonds occur in a single step. Calculations predict, and experiments confirm, that the observed small losses of enantiomeric purity are traced to a triflate‐mediated double S_N2 cycloaddition pathway.     

A spectral method for nonlinear elliptic equations

Let Ω be an open, simply connected, and bounded region in \(\mathbb {R}^{d}\), d ≥ 2, and assume its boundary ?Ω is smooth and homeomorphic to \(\mathbb {S}^{d-1}\). Consider solving an elliptic partial differential equation L u = f(?, u) over Ω with zero Dirichlet boundary value. The function f is a nonlinear function of the solution u. The problem is converted to an equivalent elliptic problem over the open unit ball \(\mathbb {B}^{d}\) in \(\mathbb {R}^{d}\), say \(\widetilde {L}\widetilde {u} =\widetilde {f}(\cdot ,\widetilde {u})\). Then a spectral Galerkin method is used to create a convergent sequence of multivariate polynomials \(\widetilde {u} _{n}\) of degree ≤ n that is convergent to \(\widetilde {u}\). The transformation from Ω to \(\mathbb {B}^{d}\) requires a special analytical calculation for its implementation. With sufficiently smooth problem parameters, the method is shown to be rapidly convergent. For \(u\in C^{\infty } \left (\overline {\Omega }\right ) \) and assuming ?Ω is a C ^∞ boundary, the convergence of \(\left \Vert \widetilde {u} -\widetilde {u}_{n}\right \Vert _{H^{1}}\) to zero is faster than any power of 1/n. The error analysis uses a reformulation of the boundary value problem as an integral equation, and then it uses tools from nonlinear integral equations to analyze the numerical method. Numerical examples illustrate experimentally an exponential rate of convergence. A generalization to ?Δu + γ u = f(u) with a zero Neumann boundary condition is also presented.     

Gas and Particle Dynamics of a Contoured Shock Tube for Pre-clinical Microparticle Drug Delivery

We investigate the gas-particle dynamics of a device designed for biological pre-clinical experiments. The device uses transonic/supersonic gas flow to accelerate microparticles such that they penetrate the outer skin layers. By using a shock tube coupled to a correctly expanded nozzle, a quasi-one-dimensional, quasi-steady flow (QSF) is produced to uniformly accelerate the microparticles. The system utilises a microparticle “cassette” (a diaphragm sealed container) that incorporates a jet mixing mechanism to stir the particles prior to diaphragm rupture. Pressure measurements reveal that a QSF exit period – suitable for uniformly accelerating microparticles – exists between 155 and 220 mus after diaphragm rupture. Immediately preceding the QSF period, a starting process secondary shock was shown to form with its (x,t) trajectory comparing well to theoretical estimates. To characterise the microparticle, flow particle image velocimetry experiments were conducted at the nozzle exit, using particle payloads with varying diameter (2.7–48 μm), density (600–16,800 kg/m³) and mass (0.25–10 mg). The resultant microparticle velocities were temporally uniform. The experiments also show that the starting process does not significantly influence the microparticle nozzle exit velocities. The velocity distribution across the nozzle exit was also uniform for the majority of microparticle types tested. For payload masses typically used in pre-clinical drug and vaccine applications (≤ 1 mg), it was demonstrated that payload scaling does not affect the microparticle exit velocities. These characteristics show that the microparticle exit conditions are well controlled and are in agreement with ideal theory. These features combined with an attention to the practical requirements of a pre-clinical system make the device suitable for investigating microparticle penetration into the skin for drug delivery.     

Splitting,merging and spanwise wavenumber selection of Dean vortex pairs

Splitting, merging and spanwise wavenumber selection are studied during the initial development of Dean vortex pairs in a channel with mild curvature, an aspect ratio of 40, and an inner to outer radius ratio of 0.979. Two types of splitting events, and four types of merging events are evident from flow visualizations at Dean numbers from 75 to 220. These events are described in detail along with observations that occurrances of these different events are tied to spatial and temporal variations of spanwise wavenumbers of vortex pair spacing. Also discussed are frequency spectra of different events, recurrent phenomena, and the part played by splitting and merging in laminar to turbulent transition in curved channels.This study was sponsored by the Propulsion Directorate, U.S. Army Aviation Research and Technology Activity-AVSCOM, NASA-Defense Purchase Request 030030-P. Professor C. S. Subramanian provided assistance in setting up the traversing system and data acquisition systems used for this study. Mr. R. E. Hughes assisted in obtaining some of the results presented.     

Mechanism and origins of regio- and enantioselectivities in RhI-catalyzed hydrogenative couplings of 1,3-diynes and activated carbonyl partners: intervention of a cumulene intermediate

The mechanism of the rhodium-catalyzed reductive coupling of 1,3-diynes and vicinal dicarbonyl compounds employing H(2) as reductant was investigated by density functional theory. Oxidative coupling through 1,4-addition of the Rh(I)-bound dicarbonyl to the conjugated diyne via a seven-membered cyclic cumulene transition state leads to exclusive formation of linear adducts. Diyne 1,4-addition is much faster than the 1,2-addition to simple alkynes. The 1,2-dicarbonyl compound is bound to rhodium in a bidentate fashion during the oxidative coupling event. The chemo-, regio-, and enantioselectivities of this reaction were investigated and are attributed to this unique 1,4-addition pathway. The close proximity of the ligand and the alkyne substituent distal to the forming C-C bond controls the regio- and enantioselectivity: coupling occurs at the sterically more demanding alkyne terminus, which minimizes nonbonded interaction with the ligand. A stereochemical model is proposed that accounts for preferential formation of the (R)-configurated coupling product when (R)-biaryl phosphine ligands are used.     

Improving Physical Properties via C?H Oxidation: Chemical and Enzymatic Approaches

Physicochemical properties constitute a key factor for the success of a drug candidate. Whereas many strategies to improve the physicochemical properties of small heterocycle‐type leads exist, complex hydrocarbon skeletons are more challenging to derivatize because of the absence of functional groups. A variety of C H oxidation methods have been explored on the betulin skeleton to improve the solubility of this very bioactive, yet poorly water‐soluble, natural product. Capitalizing on the innate reactivity of the molecule, as well as the few molecular handles present on the core, allowed oxidations at different positions across the pentacyclic structure. Enzymatic oxidations afforded several orthogonal oxidations to chemical methods. Solubility measurements showed an enhancement for many of the synthesized compounds.     

MEXIT: Maximal un-coupling times for stochastic processes

Classical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts.