Optimally growing boundary layer disturbances in a convergent nozzle preceded by a circular pipe

We report the findings from a theoretical analysis of optimally growing disturbances in an initially turbulent boundary layer. The motivation behind this study originates from the desire to generate organized structures in an initially turbulent boundary layer via excitation by disturbances that are tailored to be preferentially amplified. Such optimally growing disturbances are of interest for implementation in an active flow control strategy that is investigated for effective jet noise control. Details of the optimal perturbation theory implemented in this study are discussed. The relevant stability equations are derived using both the standard decomposition and the triple decomposition. The chosen test case geometry contains a convergent nozzle, which generates a Mach 0.9 round jet, preceded by a circular pipe. Optimally growing disturbances are introduced at various stations within the circular pipe section to facilitate disturbance energy amplification upstream of the favorable pressure gradient zone within the convergent nozzle, which has a stabilizing effect on disturbance growth. Effects of temporal frequency, disturbance input and output plane locations as well as separation distance between output and input planes are investigated. The results indicate that optimally growing disturbances appear in the form of longitudinal counter-rotating vortex pairs, whose size can be on the order of several times the input plane mean boundary layer thickness. The azimuthal wavenumber, which represents the number of counter-rotating vortex pairs, is found to generally decrease with increasing separation distance. Compared to the standard decomposition, the triple decomposition analysis generally predicts relatively lower azimuthal wavenumbers and significantly reduced energy amplification ratios for the optimal disturbances.     

Newtonian Dynamics from the Principle of Maximum Caliber

The foundations of Statistical Mechanics can be recovered almost in their entirety from the principle of maximum entropy. In this work we show that its non-equilibrium generalization, the principle of maximum caliber (Jaynes, Phys Rev 106:620–630, 1957), when applied to the unknown trajectory followed by a particle, leads to Newton’s second law under two quite intuitive assumptions (both the expected square displacement in one step and the spatial probability distribution of the particle are known at all times). Our derivation explicitly highlights the role of mass as an emergent measure of the fluctuations in velocity (inertia) and the origin of potential energy as a manifestation of spatial correlations. According to our findings, the application of Newton’s equations is not limited to mechanical systems, and therefore could be used in modelling ecological, financial and biological systems, among others.     

An efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems

The design of high-Q resonators such as Xylophone Bar Resonators (XBRs) capable of being fabricated using Micro-Electro-Mechanical Systems (MEMS) processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance. This paper is concerned with vibration analysis and Q optimisation of an XBR, with the method extending directly to other planar frames and straightforwardly to more complex structures. The Rayleigh–Ritz method is discussed in some detail, first treating the discrete case, followed by developing and applying a kinematical procedure to an L-frame structure. Attention is given to geometric interpretation of the Rayleigh–Ritz procedure and to developing an intuitive understanding the method before turning to the XBR case. Having developed an approximation for system dynamics, the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the support Q factor. Natural frequencies, mode shapes, and support Q values are presented and compared to Finite Element models of the same problem, with excellent agreement observed at substantially lower computational cost. For the first time in the literature, the geometric impedance tuning principle underlying the XBR design is validated and quantified, including sensitivity to manufacturing error.     

A self consistent normalized calibration protocol for three dimensional magnetic resonance gel dosimetry

In a clinical setting, mixed and inconsistent results have been reported using Magnetic Resonance Relaxation imaging of irradiated aqueous polymeric gels as a three-dimensional dosimeter, for dose verification of conformal radiation therapy. The problems are attributed to the difficulty of identifying an accurate dose calibration protocol for each delivered gel at the radiation site in a clinical setting. While careful calibration is done at the gel manufacturing site in a controlled laboratory setting, there is no guarantee that the dose sensitivity of the gels remains invariant upon delivery, irradiation, magnetic resonance imaging and storage at the clinical site. In this study, we have compared three different dose calibration protocols on aqueous polymeric gels for a variety of irradiation scenarios done in a clinical setting. After acquiring the three-dimensional proton relaxation maps of the irradiated gels, the dose distributions were generated using the off-site manufacturer provided calibration curve (Cal-1), the on-site external tube gel calibration (Cal-2) and the new on-site internal normalized gel calibration (Cal-3) protocols. These experimental dose distributions were compared with the theoretical dose distributions generated by treatment-planning systems. We observed that the experimental dose distributions generated from the Cal-1 and Cal-2 protocols were off by 10% to 40% and up to 200% above the predicted maximum dose, respectively. On the other hand, the experimental dose distributions generated from the Cal-3 protocol matched reasonably well with the theoretical dose distributions to within 10% difference. Our result suggests that an independent on-site normalized internal calibration must be performed for each batch of gel dosimeters at the time of MR relaxation imaging in order to account for the variations in dose sensitivity caused by various uncontrollable conditions in a clinical setting such as oxygen contamination, temperature changes and shelf life of the delivered gel between manufacturing and MR acquisitions.     

A determination of antioxidant efficiencies using ESR and computational methods

Using Transition-State Theory, experimental rate constants, determined over a range of temperatures, for reactions of Vitamin E type antioxidants are analysed in terms of their enthalpies and entropies of activation. It is further shown that computational methods may be employed to calculate enthalpies and entropies, and hence Gibbs free energies, for the overall reactions. Within the linear free energy relationship (LFER) assumption, that the Gibbs free energy of activation is proportional to the overall Gibbs free energy change for the reaction, it is possible to rationalise, and even to predict, the relative contributions of enthalpy and entropy for reactions of interest, involving potential antioxidants. A method is devised, involving a competitive reaction between *CH3 radicals and both the spin-trap PBN and the antioxidant, which enables the relatively rapid determination of a relative ordering of activities for a series of potential antioxidant compounds, and also of their rate constants for scavenging *CH3 radicals (relative to the rate constant for addition of *CH3 to PBN).     

Substituent exchange reactions of trimeric and tetrameric aryloxycyclophosphazenes with sodium 2,2,2-trifluoroethoxide

Substituent exchange reactions of sodium 2,2,2-trifluoroethoxide with trimeric and tetrameric aryloxycyclophosphazenes with phenoxy, 4-formylphenoxy, 4-cyanophenoxy and 4-nitrophenoxy side groups were conducted at 66 °C in THF and monitored by (31)P NMR and mass spectrometry. These are model reactions for their counterparts with high polymeric linear organophosphazenes. The ease of displacement of OAr in cyclic trimeric and tetrameric molecules by CF(3)CH(2)O increased significantly with the presence of electron-withdrawing substituents in the polyphosphazene in the order, phenoxy ? 4-formylphenoxy < 4-cyanophenoxy ≈ 4-nitrophenoxy. Fully substituted 2,2,2-trifluoroethoxyphosphazene trimer and tetramer were formed by side group exchange, but these reactions were followed by an attack by the nucleophile on the α-carbon of the 2,2,2-trifluoroethoxy groups linked to phosphorus to give a species in which one trifluoroethoxy group had been replaced by an ONa unit, and bis(trifluoroethyl) ether was formed as a side product. On the other hand, only partly exchanged species were formed when sodium phenoxide reacted with the trifluoroethoxy phosphazene trimer and tetramer, but again a product with an ONa side group was formed eventually together with phenyltrifluoroethyl ether generated via alpha-carbon attack. The relative sensitivity of 2,2,2-trifluoroethoxy and phenoxyphosphazene cyclic trimers and tetramers to the presence of trifluoroethoxide was established.