Optimal Control of Non-stationary Differential Linear Repetitive Processes

Differential repetitive processes are a distinct class of continuous-discrete 2D linear systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is the fact that information propagation in one of the two independent directions only occurs over a finite interval. Applications areas include iterative learning control and iterative solution algorithms for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modelling of numerous industrial processes such as metal rolling, and long-wall cutting etc. The new results in is paper solve a general optimal problem in the presence of non-stationary dynamics.     

Stress in elastic plates reinforced by fibres lying in concentric circles

We Consider fibre-reinforced elastic plates with the reinforcement continuously distributed in concentric circles ; such a material is locally transversely isotropic, with the circumferential direction as the preferred direction. For an annulus bounded by concentric circles, the exact solution of the traction boundary value problem is obtained. When the extension modulus in the fibre direction is large compared to other extension and shear moduli, the material is strongly anisotropic. For this case a simpler approximate solution is obtained by treating the material as inextensible in the fibre direction. It is shown that the exact solution reduces to the inextensible solution in the appropriate limit. The inextensible theory predicts the occurrence of stress concentration layers in which the direct stress is infinite ; for materials with small but finite extensibility these layers correspond to thin regions of high stress and high stress gradient. A boundary layer theory is developed for these regions. For a typical carbon fibre-resin composite, the combined boundary layer and inextensible solutions give an excellent approximation to the exact solution. The theory is applied to the problem of an isotropic plate, under uniform stress at infinity, containing a circular hole which is strengthened by the addition of an annulus of fibre-reinforced material.     

Additive Differential Pulse Voltammetry for the Study of Slow Charge Transfer Processes at Spherical Electrodes

The application of additive differential pulse voltammetry to the study of the kinetics of a charge transfer process is studied. A simple analytical solution is presented, valid for spherical electrodes of any size and for electrode processes of any reversibility. From this solution, valuable diagnostic criteria for the elucidation of the electrochemical reversibility are established based on the variation of the ADPV signal with the duration of the potential pulses, the electrode radius and the pulse height. Working curves for the determination of the kinetic parameters are also given. The value of the ADPV technique is experimentally demonstrated by studying the kinetics of the reduction of 3‐nitrophenolate^? and europium³⁺ at mercury hemispherical microelectrodes.     

Synthesis of exo enol ether-cyclic ketal isomers of substituted furanmethanol structures related to marine furanocembranoids

Oxidations of the 2-alkenylfurans 8a and 8b, using peroxy reagents, lead to the dienedione 9 and the furan epoxide 10, respectively. Treatment of the epoxide 10 with p-TSA in MeOH produces the enol ether cyclic ketal 12, which is rapidly isomerised to the furanmethanol ether 15, isolated in 80% yield. By contrast, when the propanol-substituted furan epoxide 23 was kept in CDCl₃ containing traces of HCl for 2 h, a 3:2 mixture of Z- and E-isomers of the enol ether spiro ketals 25a and 25b was produced in >92% yield; after 24 h this mixture of isomers underwent dehydration leading to the corresponding enol ether triene 26 (70%). When a solution of the dienedione 9 in H₂O-THF containing p-TSA was stirred at 25 °C for 20 h, the tertiary alcohol 27 was produced which, after a further 20 h was converted into the furan vicinal diol 29. Likewise, when the ‘cembranoid’ dienedione 31 was treated with p-TSA-H₂O, the hydroxymethyl-substituted furanobutenolide 33 was produced in 40% yield. It is probable that the enol ether cyclic hemiketals 28 and 32/34, which are related to 12 and 25, and also to the naturally occurring cembranoids 1 and 2 found in corals, are transient intermediates in the conversions leading to 29 and 33 from 9 and 31, respectively.     

Catalytic ignition of ionic liquids for propellant applications

In this proof of concept study, the ionic liquids, 2-hydroxyethylhydrazinium nitrate and 2-hydroxyethylhydrazinium dinitrate, ignited on contact with preheated Shell 405 (iridium supported on alumina) catalyst and energetically decomposed with no additional ignition source, suggesting a possible route to hydrazine replacements.     

Breaking away: violation of distortion emission phase-frequency invariance at low frequencies

The phase versus frequency function of the distortion product otoacoustic emission (DPOAE) at 2f(1) - f(2) is approximately invariant at frequencies above 1.5 kHz in human subjects when recorded with a constant f(2)/f(1). However, a secular break from this invariance has been observed at lower frequencies where the phase-gradient becomes markedly steeper. Apical DPOAEs, such as 2f(1)?- f(2), are known to contain contributions from multiple sources. This experiment asked whether the phase behavior of the ear canal DPOAE at low frequencies is driven by the phase of the component from the distortion product (DP) region at 2f(1)?- f(2), which exhibits rapid phase accumulation. Placing a suppressor tone close in the frequency to 2f(1)?- f(2) reduced the contribution of this component to the ear canal DPOAE in normal-hearing adult human ears. When the contribution of this component was reduced, the phase behavior of the ear canal DPOAE was not altered, suggesting that the breaking from DPOAE phase invariance at low frequencies is an outcome of apical-basal differences in cochlear mechanics. The deviation from DPOAE phase invariance appears to be a manifestation of the breaking from approximate scaling symmetry in the human cochlear apex.     

Fusion reactions with the one-neutron halo nucleus (15)C

The structure of (15)C, with an s(1/2) neutron weakly bound to a closed-neutron shell nucleus (14)C, makes it a prime candidate for a one-neutron halo nucleus. We have for the first time studied the cross section for the fusion-fission reaction (15)C+(232)Th at energies in the vicinity of the Coulomb barrier and compared it to the yield of the neighboring (14)C+(232)Th system measured in the same experiment. At sub-barrier energies, an enhancement of the fusion yield by factors of 2-5 was observed for (15)C, while the cross sections for (14)C match the trends measured for (12,13)C.     

Numerical simulation of partially coherent broadband optical imaging using the finite-difference time-domain method

Rigorous numerical modeling of optical systems has attracted interest in diverse research areas ranging from biophotonics to photolithography. We report the full-vector electromagnetic numerical simulation of a broadband optical imaging system with partially coherent and unpolarized illumination. The scattering of light from the sample is calculated using the finite-difference time-domain (FDTD) numerical method. Geometrical optics principles are applied to the scattered light to obtain the intensity distribution at the image plane. Multilayered object spaces are also supported by our algorithm. For the first time, numerical FDTD calculations are directly compared to and shown to agree well with broadband experimental microscopy results.     

Measurement of the spatial backscattering impulse-response at short length scales with polarized enhanced backscattering

In this Letter, we describe an easy to implement technique to measure the spatial backscattering impulse-response at length scales shorter than a transport mean free path with resolution of better than 10 μm using the enhanced backscattering phenomenon. This technique enables spectroscopic measurements throughout the visible range and sensitivity to all polarization channels. Through a combination of Monte Carlo simulations and experimental measurements of latex microspheres, we explore the various sensitivities of our technique to both intrinsic sample properties and extrinsic instrumental properties. We conclude by demonstrating the extraordinary sensitivity of our technique to the shape of the scattering phase function, including higher order shape parameters than the anisotropy factor (or first moment).