On the cost efficiency of mixing optimization

In this study we discuss the cost efficiency of the optimization of a new prototypical mixing flow, the Fourier sine flow, an extension of the sine flow. The Fourier sine flow stirs a mixture on a two-dimensional torus by blinking, at prescribed switching times, two orthogonal velocity fields with profiles represented by a Fourier sine series. We derive a family of mixers of increasing complexity by truncating the series to one, two, three and four modes. We consider the optimization of the velocity profiles and the optimization of the stirring protocol. We implement the former by computing, at each iteration, the amplitudes and phase shifts of the Fourier modes synthesizing the velocity profiles that minimize the mix-norm, our cost function, i.e. maximize the quality of mixing. We implement the latter by selecting, at each iteration, the best performing of the two orthogonal stirring velocity fields, i.e. the velocity field that minimizes the mix-norm. To obtain a physically meaningful optimization problem, we constrain the kinetic energy of the flow to be the same among all mixers and use the viscous dissipation as an estimate of the power input needed to operate the mixers. We characterize the performance of the mixers using three cost functions: the homogenization time, the computational cost of optimization and the total energy consumption. We test the mixers on a range of admissible power inputs using two representative switching times. We report some surprising results. Mixers equipped with the velocity profile optimization and a periodic stirring protocol cannot be optimal, i.e. their performance depends on the switching time chosen, independently of the number of Fourier modes used in the optimization. Apparently, optimal mixers can be obtained only by coupling velocity profile and stirring protocol optimizations. The computational cost of the optimization depends only on the number of Fourier modes used and grows by about an order of magnitude for each Fourier mode added to the optimization. At low power inputs, the coupled optimizations allow us to obtain an attractive reduction of the homogenization time in combination with a reduction of the total energy required to produce it. However, increasing the power input does not guarantee a reduction of the homogenization time. Counter-intuitively, there are ranges of power inputs for which both the homogenization time and the total energy increase when increasing the power input. Finally, for large enough power inputs, optimizations with two, three and four Fourier modes perform similarly, making the former optimization the most cost-efficient

Towards the design of an optimal mixer

We define as an optimal mixer a mixing device able to deliver a uniformly optimal mixing performance over a wide range of operating and initial conditions. We consider the conceptual problem of designing an optimal mixer starting from a well-known reference mixer, the sine flow. We characterize the mixing performance of the reference mixer, and show that it performs poorly and erratically over a wide range of operating conditions and is quite sensitive to the geometry of the initial concentration field. We define as a target performance the best mixing performance the reference mixer is able to achieve. In steps we modify the design of the reference mixer. First, we optimize the time sequence of the switching protocols and show that the mixing performance of the time-optimized mixer, although substantially improved with respect to the reference mixer, is still far from achieving the target performance and being insensitive to the geometry of the initial concentration field. The analysis of the performance of the time-optimized mixer brings to light the deficiency of the actuating system used, which delivers always the same amount of shear at the same locations. We modify the actuating system by allowing the stirring velocity fields to shift along their coordinate axes. A new mixer, the space-optimized mixer, is created by equipping the reference mixer with the new actuating system and optimizing the shift of the stirring velocity field at each iteration. The space-optimized mixer is able to deliver the target performance over the upper two-thirds of the operating range. In the lower one-third, the performance of the space-optimized mixer deteriorates because of the use of a periodic protocol. A optimal mixer is finally obtained using the actuating system of the space-optimized mixer and coupling the time and shift optimizations. The resulting optimal mixer is able to deliver a uniform target performance, insensitive to the geometry of the initial conditions, over the entire operating range

Electron energy spectrum and magnetic interactions in high-T(sub c) superconductors

The character of magnetic interactions in La-Sr-Cu-O and Y-Ba-Cu-O systems is of primary importance for analysis of high-T(sub c) superconductivity in these compounds. Neutron diffraction experiments showed the antiferromagnetic ground state for nonsuperconducting La2CuO4 and YBa2Cu3O6 with the strongest antiferromagnetic superexchange being in the ab plane. The nonsuperconducting '1-2-3' system has two Neel temperatures T sub N1 and T sub N2. The first one corresponds to the ordering of Cu atoms in the CuO2 planes; T sub N2 reflects the antiferromagnetic ordering of magnetic moments in CuO chains relatively to the moments in the planes T sub N1 and T sub N2 depend strongly on the oxygen content. Researchers describe magnetic interactions in high-T superconductors based on the Linear Muffin-Tin Orbitals (LMTO) band structure calculations. Exchange interaction parameters can be defined from the effective Heisenberg hamiltonian. When the magnetic moments are not too large, as copper magnetic moments in superconducting oxides, J sub ij parameters can be defined through the non-local magnetic susceptibility of spin restricted solution for the crystal. The results of nonlocal magnetic susceptibility calculations and the values of exchange interaction parameters for La CuO and YBa2Cu3O7 systems are given in tabular form. Strong anisotropy of exchange interactions in the ab plane and along the c axis in La2CuO4 is obviously seen. The value of Neel temperature found agrees well with the experimental data available. In the planes of '1-2-3' system there are quite strong antiferromagnetic Cu-O and O-O interaction which appear due to holes in oxygen subbands. These results are in line with the magnetic model of oxygen holes pairing in high-T(sub c) superconductors

Crystal chemical and quantum chemical studies of Ba(Sr)-Nb oxide compounds

The information available on the BaO(SrO)-NbO-NbO2 system with the niobium atom in the lower oxidation degree is very limited. Very few compounds have been found previously in this system. They are BaNbO3, SrxNbO3(0,7=x=1), Ba2Nb2O9, SrNb8O14; and some suggestions on the BaNb8O14 existence have been made also. At the same time Nb-based oxide compounds could be quite interesting in the search of new noncopper high T(sub c) superconductors Researchers studied Ba(Sr) NbxO2x-2 and Ba2(Sr2)-NbxO2x-1 compositions in the phase diagram of BaO(SrO)-NbO-NbO2 system. The synthesis of the materials was carried out in vacuum at the temperatures of 1000 to 1500 C. Barium carbonate and niobium pentoxide were used as initial components. X-ray analysis was carried out

Possibility to realize spin-orbit-induced correlated physics in iridium fluorides

Recent theoretical predictions of "unprecedented proximity" of the electronic ground state of iridium fluorides to the SU(2) symmetric $j_{\mathrm{eff}}=1/2$ limit, relevant for superconductivity in iridates, motivated us to investigate their crystal and electronic structure. To this aim, we performed high-resolution x-ray powder diffraction, Ir L$_3$-edge resonant inelastic x-ray scattering, and quantum chemical calculations on Rb$_2$[IrF$_6$] and other iridium fluorides. Our results are consistent with the Mott insulating scenario predicted by Birol and Haule [Phys. Rev. Lett. 114, 096403 (2015)], but we observe a sizable deviation of the $j_{\mathrm{eff}}=1/2$ state from the SU(2) symmetric limit. Interactions beyond the first coordination shell of iridium are negligible, hence the iridium fluorides do not show any magnetic ordering down to at least 20 K. A larger spin-orbit coupling in iridium fluorides compared to oxides is ascribed to a reduction of the degree of covalency, with consequences on the possibility to realize spin-orbit-induced strongly correlated physics in iridium fluorides

IAA VLBI Analysis Center Report 2012

This report presents an overview of IAA VLBI Analysis Center activities during 2012 and the plans for the coming year