HIGH-ORDER-ACCURATE DISCRETIZATION STENCIL FOR AN ELLIPTIC EQUATION

The coefficients for a nine-point high-order-accurate discretization scheme for an elliptic equation ∇²u− γ²u=r₀ (∇² is the two-dimensional Laplacian operator) are derived. Examples with Dirichlet and Neumann boundary condtions are considered. In order to demonstrate the high-order accuracy of the method, numerical results are compared with exact solutions.     

METHOD–OF–LINES SOLUTION OF TIME–DEPENDENT TWO–DIMENSIONAL NAVIER–STOKES EQUATIONS

A novel approach to the development of a code for the solution of the time-dependent two-dimensional Navier–Stokes equations is described. The code involves coupling between the method of lines (MOL) for the solution of partial differential equations and a parabolic algorithm which removes the necessity of iterative solution on pressure and solution of a Poisson-type equation for the pressure. The code is applied to a test problem involving the solution of transient laminar flow in a short pipe for an incompressible Newtonian fluid. Comparisons show that the MOL solutions are in good agreement with the previously reported values. The proposed method described in this paper demonstrates the ease with which the Navier–Stokes equations can be solved in an accurate manner using sophisticated numerical algorithms for the solution of ordinary differential equations (ODEs).     

AN UNFACTORED IMPLICIT MOVING MESH METHOD FOR THE TWO-DIMENSIONAL UNSTEADY N–S EQUATIONS

An unfactored implicit time-marching method for the solution of the unsteady two-dimensional Reynolds-averaged thin layer Navier–Stokes equations is presented. The linear system arising from each implicit step is solved by the conjugate gradient squared (CGS) method with preconditioning based on an ADI factorization. The time-marching procedure has been used with a fast transfinite interpolation method to regenerate the mesh at each time step in response to the motion of the aerofoil. The main test cases examined are from the AGARD aeroelastic configurations and involve aerofoils oscillating rigidly in pitch. These test cases have been used to investigate the effect of various parameters, such as CGS tolerance and laminar/turbulent transition location, on the accuracy and efficiency of the method. Comparisons with available experimental data have been made for these cases. In order to illustrate the application of the mesh generator and flow solver to more general flows where the aerofoil deforms, results for an NACA 0012 aerofoil with an oscillating trailing edge flap are also shown.     

Alkaline Stable Anion Exchange Membranes Based on Cross-Linked Poly(arylene ether sulfone) Bearing Dual Quaternary Piperidines for Enhanced Anion Conductivity at Low Water Uptake

Alkaline stable anion exchange membranes based on the cross-linked poly(arylene ether sulfone) grafted with dual quaternary piperidine (XPAES-DP) units were synthesized. The chemical structure of the synthesized PAES-DP was validated using ¹H-NMR and FT-IR spectroscopy. The physicochemical, thermal, and mechanical properties of XPAES-DP membranes were compared with those of two linear PAES based membranes grafted with single piperidine (PAES-P) unit and conventional trimethyl amine (PAES-TM). XPAES-DP membrane showed the ionic conductivity of 0.021 S cm⁻¹ at 40 °C which was much higher than that of PAES-P and PAES-TM because of the possession of more quaternary ammonium groups in the cross-linked structure. This cross-linked structure of the XPAES-DP membrane resulted in a higher tensile strength of 18.11 MPa than that of PAES-P, 17.09 MPa. In addition, as the XPAES-DP membrane shows consistency in the ionic conductivity even after 96 h in 3 M KOH solution with a minor change, its chemical stability was assured for the application of anion exchange membrane fuel cell. The single-cell assembled with XPAES-DP membrane displayed a power density of 109 mWcm⁻² at 80 °C under 100% relative humidity.     

Downstream evolution of junction flow three-component velocity fluctuations through the lens of the diagnostic plot

Experimental measurements of the streamwise and transverse velocity components have been acquired in three spanwise/wall-normal planes in the wakes of both a streamlined ‘wing’ and a bluff ‘wing’ junction. The ‘extended’ diagnostic plot introduced by Alfredsson et al. (2011) (see figure 3 therein) is used as a benchmark to locally evaluate the departure of turbulent wing-body junction flow wakes from ‘equilibrium’ boundary layers. Both obstacles produce a secondary flow of Prandtl’s first kind, which disrupts the equilibrium implied by the universality of the extended diagnostic plot. The plane wake of the obstacle itself (away from the junction) also disrupts this equilibrium. It is found that with downstream development the boundary layer eventually recovers to the base zero-pressure-gradient ‘equilibrium’, and that this recovery process emanates from the near-wall region. The transverse velocity components are also examined in “extended diagnostic” form, revealing that the wall-normal fluctuations recover to the zero-pressure-gradient case near the wall more rapidly than the wall-parallel components.     

On the inflation and deflation dynamics of liquid-filled,hyperelastic balloons

We derive a reduced-order model describing the inflation and deflation dynamics of a liquid-filled hyperelastic balloon, focusing on inviscid laminar flow and the extensional motion of the balloon. We initially study the flow and pressure fields for dictated motion of the solid, which throughout deflation are obtained by solving the potential problem. However, during inflation, flow separation creates a jet within the balloon, requiring a different approach. The analyses of both flow regimes lead to a simple piecewise model, describing the fluidic pressure during inflation and deflation, which is verified by finite element computations. We then use a variational approach to derive the equation describing the interaction between the extensional mode of the balloon and the entrapped fluid, yielding a nonlinear hybrid oscillator equation. Analytical and graphical investigations of the suggested model are presented, shedding light on its static and dynamic behaviour under different operating conditions. Our simplified model and its underlying assumptions are verified utilizing a fully coupled finite element scheme, showing excellent agreement.     

Channel-Supermodular Entropies: Order Theory and an Application to Query Anonymization

This work introduces channel-supermodular entropies, a subset of quasi-concave entropies. Channel-supermodularity is a property shared by some of the most commonly used entropies in the literature, including Arimoto–Rényi conditional entropies (which include Shannon and min-entropy as special cases), k-tries entropies, and guessing entropy. Based on channel-supermodularity, new preorders for channels that strictly include degradedness and inclusion (or Shannon ordering) are defined, and these preorders are shown to provide a sufficient condition for the more-capable and capacity ordering, not only for Shannon entropy but also regarding analogous concepts for other entropy measures. The theory developed is then applied in the context of query anonymization. We introduce a greedy algorithm based on channel-supermodularity for query anonymization and prove its optimality, in terms of information leakage, for all symmetric channel-supermodular entropies.     

A New Oxygen Containing Pyclen-Type Ligand as a Manganese(II) Binder for MRI and 52Mn PET Applications: Equilibrium,Kinetic, Relaxometric,Structural and Radiochemical Studies

A new pyclen-3,9-diacetate derivative ligand (H₂3,9-OPC2A) was synthesized possessing an etheric O-atom opposite to the pyridine ring, to improve the dissociation kinetics of its Mn(II) complex (pyclen = 3,6,9,15-tetraazabicyclo(9.3.1)pentadeca-1(15),11,13-triene). The new ligand is less basic than the N-containing analogue (H₂3,9-PC2A) due to the non-protonable O-atom. In spite of its lower basicity, the conditional stability of the [Mn(3,9-OPC2A)] (pMn = −log(Mn(II)), c_L = c_Mn(II) = 0.01 mM. pH = 7.4) remains unaffected (pMn = 8.69), compared to the [Mn(3,9-PC2A)] (pMn = 8.64). The [Mn(3,9-OPC2A)] possesses one water molecule, having a lower exchange rate with bulk solvents (k_ex²⁹⁸ = 5.3 ± 0.4 × 10⁷ s⁻¹) than [Mn(3,9-PC2A)] (k_ex²⁹⁸ = 1.26 × 10⁸ s⁻¹). These mild differences are rationalized by density-functional theory (DFT) calculations. The acid assisted dissociation of [Mn(3,9-OPC2A)] is considerably slower (k₁ = 2.81 ± 0.07 M⁻¹ s⁻¹) than that of the complexes of diacetates or bisamides of various 12-membered macrocycles and the parent H₂3,9-PC2A. The [Mn(3,9-OPC2A)] is inert in rat/human serum as confirmed by ⁵²Mn labeling (nM range), as well as by relaxometry (mM range). However, a 600-fold excess of EDTA (pH = 7.4) or a mixture of essential metal ions, propagated some transchelation/transmetalation in 7 days. The H₂3,9-OPC2A is labeled efficiently with ⁵²Mn at elevated temperatures, yet at 37 °C the parent H₂3,9-PC2A performs slightly better. Ultimately, the H₂3,9-OPC2A shows advantageous features for further ligand designs for bifunctional chelators.     

Impact of High-Pressure Homogenization on the Cell Integrity of Tetradesmus obliquus and Seed Germination

Microalgae have almost unlimited applications due to their versatility and robustness to grow in different environmental conditions, their biodiversity and variety of valuable bioactive compounds. Wastewater can be used as a low-cost and readily available medium for microalgae, while the latter removes the pollutants to produce clean water. Nevertheless, since the most valuable metabolites are mainly located inside the microalga cell, their release implies rupturing the cell wall. In this study, Tetradesmus obliquus grown in 5% piggery effluent was disrupted using high-pressure homogenization (HPH). Effects of HPH pressure (100, 300, and 600 bar) and cycles (1, 2 and 3) were tested on the membrane integrity and evaluated using flow cytometry and microscopy. In addition, wheat seed germination trials were carried out using the biomass at different conditions. Increased HPH pressure or number of cycles led to more cell disruption (75% at 600 bar and 3 cycles). However, the highest increase in wheat germination and growth (40–45%) was observed at the lowest pressure (100 bar), where only 46% of the microalga cells were permeabilised, but not disrupted. Non-treated T. obliquus cultures also revealed an enhancing effect on root and shoot length (up to 40%). The filtrate of the initial culture also promoted shoot development compared to water (21%), reinforcing the full use of all the process fractions. Thus, piggery wastewater can be used to produce microalgae biomass, and mild HPH conditions can promote cell permeabilization to release sufficient amounts of bioactive compounds with the ability to enhance plant germination and growth, converting an economic and environmental concern into environmentally sustainable applications.