Solution Regularity in Optimal Control via Subgradient Analysis of the Value Function

Lipschitz regularity for solutions to nonsmooth problems in the calculus of variations is considered, where we allow for extended-real-valued Lagrangians. Conditions for regularity are given in terms of subdifferentiability properties of the value function. In particular, it is shown that there exists a Lipschitz minimizer as long as the limiting subgradient of the value function is nonempty at the point in question. The results improve upon previous results in the literature, even in the case of finite Lagrangians.     

Investigating the molecular mechanisms of in-plane mechanochemistry on cantilever arrays

Free-standing cantilevers, which directly translate specific biochemical reactions into micromechanical motion, have recently attracted much attention as label-free biosensors and micro/nano robotic devices. To exploit this mechanochemical sensing technology, it is essential to develop a fundamental understanding of the origins of surface stress. Here we report a detailed study into the molecular basis of stress generation in aqueous environments focusing on the pH titration of model mercaptohexadecanoic acid self-assembled monolayers (SAMs), using in situ reference cantilevers coated with nonionizable hexadecanethiol SAMs. Semiautomated data analysis and a statistical model were developed to quantify cyclic deprotonation/protonation reactions on multiple arrays. In-plane force titrations were found to have the sensitivity to detect ionic hydrogen bond formation between protonated and nonprotonated carboxylic acid groups in the proximity of the surface pK1/2, which generated a mean tensile differential surface stress of +1.2 +/- 0.3 mN/m at pH 6.0, corresponding to 1 pN attractive force between two adjacent MHA molecules. Conversely, the magnitude of compressive differential surface stress was found to increase progressively with pH >/= 7.0, reaching a maximum of -14.5 +/- 0.5 mN/m at pH 9.0, attributed to enhanced electrostatic repulsion between deprotonated carboxylic acid groups. However, striking differences were observed in the micromechanical responses to different ionic strength and ion species present in the aqueous environment, highlighting the critical role of counter- and co-ions on surface stress. Our findings provide fundamental insights into the molecular mechanisms of in-plane mechanochemistry, which may be exploited for biosensing and nanoactuation applications.     

Anion selectivity in zwitterionic amide-functionalised metal salt extractants

Amide-functionalised salen ligands capable of extracting metal salts have been synthesised and characterised. Single-crystal X-ray structure determinations of complexes of NiSO4, [Ni(L)(SO4)], confirm that the ionophores are in a zwitterionic form with Ni(II) bound in the deprotonated salen moiety and the SO4(2-) ion associated with protonated pendant N'-amidopiperazine groups. Treatment of [Ni(L)(SO4)] with base removes the protons from the pendant amido-amine group resulting in loss of the SO4(2-) ion and formation of metal-only complexes of type [Ni(L-2H)], which have been characterized by single-crystal X-ray diffraction. Three of the ligands with solubilities suitable for solvent extraction studies show loading and stripping pH-profiles that are suitable for the recovery of CuSO4 or CuCl2 from industrial leach solutions. The copper-only complexes, [Cu(L-2H)], are selective for Cl- over SO4(2-) in both solvent extraction and bulk liquid membrane transport experiments and were found to bind Cl- in two steps via the formation of a 1:1:1 [Cu(L-H)Cl] assembly, followed by a 1:1:2 [Cu(L)Cl2] assembly as the pH of the aqueous phase is lowered. The anion transport selectivity was evaluated for a number of other mono-charged anions and interestingly the ligands were found to display a preference for the Br- ion. To probe the influence of the Hofmeister bias on the selectivity of anion complexation, single-phase potentiometric titration experiments were employed to investigate the binding of SO4(2-) and Cl- by one of the copper only complexes, [Cu(L-2H)] in 95 %/5 % MeOH/water. Under these conditions selectivity was reversed (SO4(2-)>Cl-) confirming that the Hofmeister bias, which reflects the relative hydration energies of the anions, dominates the selectivity of anion extraction from aqueous media into CHCl3.     

Polarisation parameters in neutral pion photoproduction

The polarisation parameters Σ, P and T have been measured for the process γp→π⁰p in the photon energy range 1300–2100 MeV and c.m. angles between 30° and 110°, in an experiment with a polarised beam and polarised target. The results are compared with a recent theoretical analysis which fits data from threshold to 16 GeV. The new data are in general agreement with the analysis, but with some significant discrepancies in detail.     

Coherent dynamics of the localized vibrational modes of hydrogen in CaF2

We report the observation of giant quantum coherence effects in the localized modes of ionized hydrogen in synthetic fluorite. Infrared free induction decay experiments on the substitutional H- center show dramatic modulations at negative delay times due to interference between multiple vibrational levels. Spectrally resolving the degenerate four wave mixing signal allows unambiguous assignments of the participating vibrational states. The dependence of the signal intensity upon the delay path between the exciting free electron laser pulses can be accounted for in terms of the resonant third order polarization with a common dephasing time for the excited states.     

Line frequency expressions for triply degenerate fundamentals of spherical top molecules appropriate for large angular momentum

For states of high angular momentum we obtain expressions for the transition frequencies in the triply degenerate fundamental of a “heavy” spherical top, that are accurate to spectroscopic resolution, without tedious calculation of octahedral (or tetrahedral) vector coupling coefficients or diagonalization of matrices. Our calculations are based upon the physical assumption that as the molecule rotates with larger angular momentum it behaves like a symmetric top with the coupled pure rotational angular momentum quantized along either the four- or threefold body-fixed axes. We find that the approximate calculation which involves only 3-J symbols quite accurately reproduces the result of a complete diagonalization of the Hamiltonian, so that for all but the most accurate saturated absorption spectra theoretical analysis may be carried out without reference to the octahedral (or tetrahedral) subgroup of the rotation group.     

High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers

The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a time-averaged sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered (Re _c  = 10⁴), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motion-induced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stall-like vortices which convect downstream close to the airfoil. At the lowest value of Reynolds number (Re _c  = 10⁴), transition effects are observed to be minor and the dynamic stall vortex system remains fairly coherent. For Re _c  = 4 × 10⁴, the dynamic-stall vortex system is laminar at is inception, however shortly afterwards, it experiences an abrupt breakdown associated with the onset of spanwise instability effects. The computed phased-averaged structures for both values of Reynolds number are found to be in good agreement with the experimental data. Finally, the effect of structural compliance on the unsteady flow past a membrane airfoil is investigated. The membrane deformation results in mean camber and large fluctuations which improve aerodynamic performance. Larger values of lift and a delay in stall are achieved relative to a rigid airfoil configuration. For Re _c = 4.85 × 10⁴, it is shown that correct prediction of the transitional process is critical to capturing the proper membrane structural response.     

Zwitterionic macrocyclic metal sulfate extractants containing 3-dialkylaminomethylsalicylaldimine units

10,25-Di-tert-alkyl-14,21-dimethyl-3,6,14,21-tetraazatricyclo[21.3.1.18,12]octacosa-1(27),2,6,8,10,12(28),23,25-octaene-27,28-diol macrocycles form Ni(II) and Cu(II) complexes in which the metal cation and the sulfate anion are bound in separated sites in a zwitterionic form of the ligand. The nonyl-substituted macrocycle shows a higher affinity for SO(4)(2-) and a lower binding strength for Cu(2+) than open chain analogues, the pH-dependences for which fall in ranges which allow loading of CuSO(4) at pH approximately 4 and easy stripping to recycle the ligand. X-Ray structure determinations of the Cu(II) and Ni(II) sulfate complexes of the tert-butyl substituted ligand suggest that the de-tuning of M(2+)-binding results from a distortion from planarity of the "salen" N(2)O(2)(2-) donor set imposed by the incorporation of the hexamethylene strap in the ligand and reveal that the sulfate is bound as a hydrate in a 2:2:2:2, ligand-M(2+)-SO(4)(2-)-H(2)O, assembly.