Exact solution of a boundary value problem describing the uniform cylindrical or spherical piston motion

In this paper, we construct the exact solution for fluid motion caused by the uniform expansion of a cylindrical or spherical piston into still air. Following Lighthill [1], we introduce velocity potential into the analysis and seek a similarity form of the solution. We find both numerical and analytic solutions of the second order nonlinear differential equation, with the boundary conditions at the shock and at the piston. The results obtained from the analytic solutions justify numerical solution and the approximate solution of Lighthill [1]. We find that although the approximate solution of Lighthill [1] gives remarkably good numerical results, the analytic form of that solution is not mathematically satisfactory. We also find that in case of spherical piston motion Lighthill’s [1] solution differs significantly from that of our analytic and numerical solutions. We use Pade′ approximation to extend the radius of convergence of the series solution. We also carry out some local analysis at the boundary to obtain some singular solutions.     

Mn(III)-initiated facile oxygenation of heterocyclic 1,3-dicarbonyl compounds

The Mn(III)-initiated aerobic oxidation of heterocyclic 1,3-dicarbonyl compounds, such as 4-alkyl-1,2-diphenylpyrazolidine-3,5-diones, 1,3-dialkylpyrrolidine-2,4-diones, 3-alkyl-1,5-dimethylbarbituric acids, and 3-butyl-4-hydroxy-2-quinolinone gave excellent to good yields of the corresponding hydroperoxides, which were gradually degraded by exposure to the metal initiator after the reaction to afford the corresponding alcohols. The synthesis of 30 heterocyclic 1,3-dicarbonyl compounds, the corresponding hydroperoxides and the 10 alcohols, their characterization, and the limitations of the procedure are described. In addition, the mechanism of the hydroperoxidation and the redox decomposition of the hydroperoxides are discussed.     

A low-voltage electrokinetic nanochannel drug delivery system

Recent work has elucidated the potential of important new therapeutic paradigms, including metronomic delivery and chronotherapy, in which the precise timing and location of therapeutic administration has a significant impact on efficacy and toxicity. New drug delivery architectures are needed to not only release drug continuously at precise rates, but also synchronize their release with circadian cycles. We present an actively controlled nanofluidic membrane that exploits electrophoresis to control the magnitude, duration, and timing of drug release. The membrane, produced using high precision silicon fabrication techniques, has platinum electrodes integrated at the inlet and outlet that allow both amplification and reversal of analyte delivery with low applied voltage (at or below 2 VDC). Device operation was demonstrated with solutions of both fluorescein isothiocyanate conjugated bovine serum albumin and lysozyme using fluorescence spectroscopy, fluorescence microscopy, and a lysozyme specific bio-assay and has been characterized for long-term molecular release and release reversibility. Through a combination of theoretical and experimental analysis, the relative contributions of electrophoresis and electroosmosis have been investigated. The membrane's clinically relevant electrophoretic release rate at 2 VDC exceeds the passive release by nearly one order of magnitude, demonstrating the potential to realize the therapeutic paradigm goal.     

Exact Solutions of Compressible Flow Equations with Spherical Symmetry

In this paper, we construct spherically symmetric solutions of the equations of compressible flow, which are important in the theory of explosion waves in air, water, and other media. Following McVittie [ 1 ], we write a general solution form, in terms of velocity potential, as a product of a function of time and a function of a similarity variable. First, we find solutions to the equations of motion and continuity without reference to adiabatic or isentropic relation. These solutions are quite general and can be applied to nonadiabatic motions, such as the motions of interstellar gas clouds that lose energy by radiation. All the solutions found by McVittie [ 1 ] have linear velocity profile with respect to distance. We introduce a nonlinear form of the velocity function containing an arbitrary function of the similarity variable. Adiabatic conditions lead to a second-order ODE, which we discuss in some detail. We relate our work to the earlier investigations of Taylor [ 2 ], McVittie [ 1 ], and Keller [ 3 ].     

g-factor of the first excited 4+ states in156Gd and158Gd

Relative g-factor of the first 2⁺ and 4⁺ states have been measured with the transient field technique in¹⁵⁶Gd and¹⁵⁸Gd. The precession of gamma rays depopulating the levels under study were observed, after passing through thin polarized gadolinium. The observed values agree with the predictions of the rotational model, i.c. g(4⁺)= g(2⁺), while contrasting the hypothesis that in¹⁵⁶Gd the g-factor of the 4⁺ is reduced with respect to the 2⁺, because of rotational alignment.     

Substituent effect on ionisation potential in a series of related molecules: A theoretical study in a molecular orbital framework

The effect of replacing the hydrogen atoms in thioformaldehyde by halogen atoms (F, Cl) on the ionisation potential of the non-bonding electron is analysed by using the Hellman-Feynman theorem, regarding the nuclear charge of the substituent as a parameter in the many-electron Hamiltonian. The trends predicted by our theory nicely agree with the relevant ionisation potentials computed either by applying Koopmans’ theorem or by the ΔE _SCF method. For the carbonyls, avaible experimental data indicate the reliability of our prediction.     

An asymmetric total synthesis of vitamin d3 (cholecalciferol)

The total synthesis of cholecalciferol $\text{via}$ an intramolecular Diels-Alder approach is described.     

Effects of electric fields on thermal convection in gases

Summary Extensive measurements of the coefficient of electroconvective heat transfer have been carried out in gases: air, Ar, N₂, O₂, freon-12 and freon-22, using a single platinum wire mounted along the axis of a copper cylinder. The diameter of the cylinder was 53 mm, while that of the wire was 0.025 mm. Electroconvective heat transfer coefficients have been measured as a function of electric field, pressure, orientation and frequency of the applied electric field in the earth's gravitational field. The results reveal a complicated interaction between the electric-field gradient and thermal convection. The present work indicates that the Senftleben mechanism alone cannot account for the observed phenomena.     

Filter-paper test for microgram detection of aliphatic amines

A new simple, sensitive and selective test for the detection of microgram amounts of aliphatic amines with diphenylcarbazide-soaked Whatman No. 1 filter paper as the detection medium is described. A feature of the study is the observation that the reaction does not take place in solution in the absence of the filter paper.