Correlation of tunneling spectra in Bi(2)Sr(2)CaCu(2)O(8+delta) with the resonance spin excitation

New break-junction tunneling data are reported in Bi(2)Sr(2)CaCu(2)O(8+delta) over a wide range of hole concentration from underdoped (T(c) = 74 K) to optimal doped (T(c) = 95 K) to overdoped (T(c) = 48 K). The conductances exhibit sharp dips at a voltage, Omega/e, measured with respect to the superconducting gap. Clear trends are found such that the dip strength is maximum at optimal doping and that Omega scales as 4.9kT(c) over the entire doping range. These features link the dip to the resonance spin excitation and suggest quasiparticle interactions with this mode are important for superconductivity.     

Exponential stabilization of a class of nonlinear systems: A generalized Gronwall–Bellman lemma approach

In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall–Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show the effectiveness of the proposed method.     

Zero spontaneous curvature and its effects on lamellar phase morphology and vesicle size distributions

Equimolar mixtures of dodecyltrimethylammonium chloride (DTAC) and sodium octyl sulfonate (SOSo) show a vesicle phase at >99 wt % water and a single, fluid lamellar phase for water fractions below 80 wt %. This combination is consistent with the bilayer bending elasticity kappa approximately k(B)T and zero bilayer spontaneous curvature. Caillé line shape analysis of the small-angle X-ray scattering from the lamellar phase shows that the effective kappa depends on the lamellar d spacing consistent with a logarithmic renormalization of kappa, with kappa(o) = (0.8 +/- 0.1)k(B)T. The vesicle size distribution determined by cryogenic transmission electron microscopy is well fit by models with zero spontaneous curvature to give (kappa + (kappa/2)) = (1.7 +/- 0.1)k(B)T, resulting in kappa = (1.8 +/- 0.2)k(B)T. The positive value of kappa and the lack of spontaneous curvature act to eliminate the spherulite defects found in the lamellar gel phases found in other catanionic mixtures. Current theories of spontaneous bilayer curvature require an excess of one or more components on opposite sides of the bilayer; the absence of such an excess at equimolar surfactant ratios explains the zero spontaneous curvature.