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The effective Hamiltonian of strongly correlated electrons on a square lattice is replaced by a renormalised Hamiltonian and the factors that renormalize the kinetic energy of holes and the Heisenberg spin-spin coupling are calculated using a Gutzwiller approximation scheme. The accuracy of this renormalization procedure is tested numerically and found to be qualitatively excellent. Within the scheme a resonant valence bond (RVB) wavefunction is found at half-filling to be lower in energy than the antiferromagnetic state. If the wavefunction is expressed in fermion operators, local SU(2) and U(l) invariance leads to a redundancy in the representation. The introduction of holes removes these local invariances and we find that a d-wave RVB state is lowest in energy. This state has a superconducting order parameter whose amplitude is linear in the density of holes.

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Magnetization plateaus, visible as anomalies in magnetic susceptibility at low temperatures, are one of the hallmarks of frustrated magnetism. We show how an extremely robust half-magnetization plateau can arise from coupling between spin and lattice degrees of freedom in a pyrochlore antiferromagnet and develop a detailed symmetry of analysis of the simplest possible scenario for such a plateau state. The application of this theory to the spinel oxides CdCr2O4 and HgCr2O4, where a robust half-magnetization plateau has been observed, is discussed.

Microfluidic paper-based analytical devices (μPADs) have emerged as a promising diagnostic platform a decade ago. In contrast to highly active academic developments, their entry into real-life applications is still very limited. This discrepancy is attributed to the gap between research developments and their practical utility, particularly in the aspects of operational simplicity, long-term stability of devices, and associated equipment. On the basis of these backgrounds, this review attempts to: 1) identify the reasons for success of paper-based devices already in the market, 2) describe the current status and remaining issues of μPADs in terms of operational complexity, signal interpretation approaches, and storage stability, and 3) discuss the possibility of mass production based on established manufacturing technologies. Finally, the state-of-the-art in commercialisation of μPADs is discussed, and the "upgrades" required from a laboratory-based prototype to an end user device are demonstrated on a specific example.

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