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We consider the design of synthetic embedded feedback circuits that can implement desired changes in the concentration of the output of a biomolecular process (reference tracking in control terminology). Such systems require the use of a "subtractor", to generate an error signal that captures the difference between the current and desired value of the process output. Unfortunately, standard implementations of the subtraction operator using chemical reaction networks are one-sided, i.e. they cannot produce negative error signals. Previous attempts to deal with this problem by representing signals as the difference in concentrations of two different biomolecular species lead to a doubling of the number of chemical reactions required to generate the circuit, hence sharply increasing the difficulty of experimental implementations and limiting the complexity of potential designs. Here we propose an alternative approach that introduces a degradation term into the classical proportion-integral control scheme. The extra tuning flexibility of the resulting PI-Deg controller compensates for the limitations of the one-sided subtraction operator, providing robust high-performance tracking of concentration changes with a minimal number of chemical reactions.

We have measured transport properties as a function of temperature and pressure up to 30GPa in the NaxCoO2 system. For the x=0.5 sample the transition temperature at 53K increases with pressure, while paradoxically the sample passes from an insulating to a metallic ground state. A similar transition is observed in the x=0.31 sample under pressure. Compression on the x=0.75 sample transforms the sample from a metallic to an insulating state. We discuss our results in terms of interactions between band structure effects and Na+ order., 18 pages, 5 figures

The structure of Na0.5CoO2, the low-temperature insulator that separates the antiferromagnetic and normal metals in the NaxCoO2 phase diagram, is studied by high-resolution powder neutron diffraction at temperatures between 10 and 300 K. Profile analysis confirms that it has an orthorhombic symmetry structure, space group Pnmm, consisting of layers of edge-sharing CoO6 octahedra in a triangular lattice, with Na ions occupying ordered positions in the interleaving planes. The oxygen content is found to be stoichiometric within 1%, indicating that the Na concentration accurately determines the electronic doping. The Na ordering creates two distinct Co sites, in parallel chains running along one crystallographic direction. The differences in their Co-O bond distances and the derived bond valence sums, reflections of the degree of charge ordering in this phase, are very small.

Recently discovered class of cobaltate superconductors (Na0.3CoO2.nH2O) is a novel realization of interacting quantum electron systems in a triangular network with low-energy degrees of freedom. We employ angle-resolved photoemission spectroscopy to uncover the nature of microscopic electron motion in the parent superconductors for the first time. Results reveal a large hole-like Fermi surface (consistent with Luttinger theorem) generated by the crossing of super-heavy quasiparticles. The measured quasiparticle parameters collectively suggest a two orders of magnitude departure from the conventional Bardeen-Cooper-Schrieffer electron dynamics paradigm and unveils cobaltates as a rather hidden class of relatively high temperature superconductors., 5 pages, 4 figures, 1 table

The hydration phase diagram for sodium cobalt oxyhydrate, Na0.3CoO2*yH2O (y=0, 0.6, 1.3), was determined as a function of relative humidity at 298K. It is found that greater than 75% relative humidity is needed for complete hydration of anhydrous Na0.3CoO2 to the superconducting phase Na0.3CoO2*1.3H2O. Dehydration studies show that a minimum of 43% relative humidity is needed to maintain the stability of the fully hydrated superconducting phase. The intermediate hydrate, Na0.3CoO2*0.6H2O, is stable between 10% and 50% relative humidity on hydration, and 35% to 0% relative humidity on dehydration., submitted to Mat. Res. Bull., 4 pages, 4 figures

The superconducting-state heat capacity of Na$_{0.3}$CoO$_{2}$$\cdot$1.3H$_{2}$O shows unusual, marked deviations from BCS theory, at all temperatures. At low temperatures the heat capacity has the $T^2$ dependence characteristic of line nodes in the energy gap, rather than the exponential temperature dependence of a fully gapped, conventional superconductor. At temperatures of the order of one fifth of the critical temperature and above, the deviations are strikingly similar to those of MgB$_2$, which are known to be a consequence of the existence of substantially different energy gaps on different sheets of the Fermi surface. A two-gap fit to the Na$_{0.3}$CoO$_{2}$$\cdot$1.3H${_2}$O data gives gap amplitudes of 45% and 125% of the BCS value, on parts of the Fermi surface that contribute, respectively, 45% and 55% to the normal-state density of states. The temperature of the onset of the transition to the vortex state is independent of magnetic field, which shows the presence of unusually strong fluctuations., to appear in Chinese Journal of Physics

The determination by powder neutron diffraction of the ambient temperature crystal structures of compounds in the NaxCoO2 family, for 0.3 < x, 15 pages, 1 tables, 6 figures Submitted to Physical Review B

We present an angle-resolved photoemission study of Na0.7CoO2, the host cobaltate of the NaxCoO2.yH2O series. Our results show a large hexagonal-like hole-type Fermi surface, an extremely narrow strongly renormalized quasiparticle band and a small Fermi velocity. Along the Gamma to M high symmetry line, the quasiparticle band crosses the Fermi level from M toward Gamma consistent with a negative sign of effective single-particle hopping (t ): t is estimated to be about 8 meV which is on the order of exchange coupling J in this system. This suggests that t ~ J ~ 10 meV is an important energy scale in the system. Quasiparticles are well defined only in the T-linear resistivity regime. Small single particle hopping and unconventional quasiparticle dynamics may have implications for understanding the unusual behavior of this new class of compounds., Revised text, Added Figs, Submitted to PRL

Neutron scattering has been used to investigate the crystal structure and lattice dynamics of superconducting Na0.3CoO2 1.4(H/D)2O, and the parent Na0.3CoO2 material. The structure of Na0.3CoO2 consists of alternate layers of CoO2 and Na and is the same as the structure at higher Na concentrations. For the superconductor, the water forms two additional layers between the Na and CoO2, increasing the c-axis lattice parameter of the hexagonal P63/mmc space group from 11.16 A to 19.5 A. The Na ions are found to occupy a different configuration from the parent compound, while the water forms a structure that replicates the structure of ice. Both types of sites are only partially occupied. The CoO2 layer in these structures is robust, on the other hand, and we find a strong inverse correlation between the CoO2 layer thickness and the superconducting transition temperature (TC increases with decreasing thickness). The phonon density-of-states for Na0.3CoO2 exhibits distinct acoustic and optic bands, with a high-energy cutoff of ~100 meV. The lattice dynamical scattering for the superconductor is dominated by the hydrogen modes, with librational and bending modes that are quite similar to ice, supporting the structural model that the water intercalates and forms ice-like layers in the superconductor., 14 pages, 7 figures, Phys. Rev. B (in press). Minor changes + two figures removed as requested by referee