Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems

We consider multi-objective convex optimal control problems. First we state a relationship between the (weakly or properly) efficient set of the multi-objective problem and the solution of the problem scalarized via a convex combination of objectives through a vector of parameters (or weights). Then we establish that (i) the solution of the scalarized (parametric) problem for any given parameter vector is unique and (weakly or properly) efficient and (ii) for each solution in the (weakly or properly) efficient set, there exists at least one corresponding parameter vector for the scalarized problem yielding the same solution. Therefore the set of all parametric solutions (obtained by solving the scalarized problem) is equal to the efficient set. Next we consider an additional objective over the efficient set. Based on the main result, the new objective can instead be considered over the (parametric) solution set of the scalarized problem. For the purpose of constructing numerical methods, we point to existing solution differentiability results for parametric optimal control problems. We propose numerical methods and give an example application to illustrate our approach.     

Room temperature magnetocaloric effect in Pr1.75Sr1.25Mn2O7 double-layered perovskite manganite system

Abstract

In this work, we have studied on double-layered perovskite (Ruddlesden–Popper) manganite structure in Pr_1.75Sr_1.25Mn₂O₇ synthesised by sol–gel method. The crystal structure of the double-layered perovskite is found as tetragonal from the X-ray diffraction analysis with I4/mmm space group. A high Curie temperature, T_C = 305 K is observed from the temperature dependence of magnetisation measurement. The isothermal magnetisation curves showed that magnetic phase transition is second order due to the positive slope of the Arrott plots. Maximum magnetic entropy change (ΔS_M) and adiabatic temperature change (ΔT_ad) values are calculated as 3.99 J kg^?1 K^?1 and 2.1 K under external magnetic field of 70 kOe, respectively. Since our double-layered perovskite manganite sample has desired T_C value and relatively high ΔS_M, it can be a potential candidate as a magnetocaloric material for room temperature magnetic cooling systems.     

Stabilized nodal‐based finite element methods for the magnetic induction problem

We consider the time‐dependent magnetic induction model as a step towards the resistive magnetohydrodynamics model in incompressible media. Conforming nodal‐based finite element approximations of the induction model with inf‐sup stable finite elements for the magnetic field and the magnetic pseudo‐pressure are investigated. Based on a residual‐based stabilization technique proposed by Badia and Codina, SIAM J. Numer. Anal. 50 (2012), pp. 398–417, we consider a stabilized nodal‐based finite element method for the numerical solution. Error estimates are given for the semi‐discrete model in space. Finally, we present some examples, for example, for the magnetic flux expulsion problem, Shercliff's test case and singular solutions of the Maxwell problem. Copyright © 2015 John Wiley & Sons, Ltd.     

Synthesis of oxazoline functionalized polypropene using metallocene catalysts

Using two different zirconocene/MAO catalyst systems, propene was copolymerized with the comonomers 2‐(9‐decene‐1‐yl)‐1,3‐oxazoline and 2‐(4‐(10‐undecene‐1‐oxo)phenyl)‐1,3‐oxazoline, respectively. The catalysts used were rac‐Et[Ind]₂ZrCl₂ and rac‐Me₂Si[2‐Me‐4, 5‐BenzInd]₂ZrCl₂. Up to 0.53 mol‐% oxazoline could be incorporated into polypropene. Oxazoline content, molecular weight, degree of isotacticity and melting behavior were dependent on the catalyst system, comonomer structure and comonomer concentration in the feed.     

Electrical and dielectric properties of Al/p-Si and Al/perylene/p-Si type diodes in a wide frequency range

The perylene(C20H12) layer effect on the electrical and dielectric properties of Al/p-Si(MS) and Al/perylene/p-Si(MPS) diodes have been investigated and compared in the frequency range of 0.7 kHz–2 MHz. Experimental results show that C–V characteristics give an anomalous peak for two structures at low frequencies due to interface states(Nss) and series resistance(Rs). The increases in C and G/ω at low frequencies confirm that the charges at interface can easily follow an ac signal and yield excess capacitance and conductance. The frequency-dependent dielectric constant(ε) and dielectric loss(ε) are subtracted using C and G/ω data at 1.5 V. The ε and ε values are found to be strongly dependent on frequency and voltage, and their large values at low frequencies can be attributed to the excess polarization coming from charges at traps. Plots of ln(σac)–ln(ω) for two structures have two linear regions, with slopes of 0.369 and 1.166 for MS, and of 0.077 and 1.061 for MPS, respectively. From the C 2–V characteristics, the doping acceptor atom concentration(NA) and barrier height(ΦB) for Schottky barrier diodes(SBDs) of MS and MPS types are also obtained to be 1.484 × 1015 and 1.303 × 1015cm 3, and 1.10 and 1.13 eV, respectively.     

Experimental determination of interfacial energies for Ag2Al solid solution in the CuAl2--Ag2Al system

The equilibrated grain boundary groove shapes of solid solution Ag2Al in equilibrium with an Al-Cu-Ag liquid were observed from a quenched sample with a radial heat flow apparatus.The Gibbs-Thomson coefficient,solid-liquid interfacial energy and grain boundary energy of the solid solution Ag2Al have been determined from the observed grain boundary groove shapes.The thermal conductivity of the solid phase and the thermal conductivity ratio of the liquid phase to solid phase for Ag2Al-28.3 at the %CuAl2 alloy at the melting temperature have also been measured with a radial heat flow apparatus and Bridgman type growth apparatus,separately.