Optimal topological simplification of discrete functions on surfaces

We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse theory and persistent homology. Our method completely removes homological noise with persistence less than 2{\delta}, constructively proving the tightness of a lower bound on the number of critical points given by the stability theorem of persistent homology in dimension two for any input function. We also show that an optimal solution can be computed in linear time after persistence pairs have been computed.Comment: 27 pages, 8 figure

Liquid Crystal-Solid Interface Structure at the Antiferroelectric-Ferroelectric Phase Transition

Total Internal Reflection (TIR) is used to probe the molecular organization at the surface of a tilted chiral smectic liquid crystal at temperatures in the vicinity of the bulk antiferroelectric-ferroelectric phase transition. Data are interpreted using an exact analytical solution of a real model for ferroelectric order at the surface. In the mixture T3, ferroelectric surface order is expelled with the bulk ferroelectric-antiferroelectric transition. The conditions for ferroelectric order at the surface of an antiferroelectric bulk are presented

Comparison of coherent and weakly incoherent transport models for the interlayer magnetoresistance of layered Fermi liquids

The interlayer magnetoresistance of layered metals in a tilted magnetic field is calculated for two distinct models for the interlayer transport. The first model involves coherent interlayer transport and makes use of results of semi-classical or Bloch-Boltzmann transport theory. The second model involves weakly incoherent interlayer transport where the electron is scattered many times within a layer before tunneling into the next layer. The results are relevant to the interpretation of experiments on angular-dependent magnetoresistance oscillations (AMRO) in quasi-one- and quasi-two-dimensional metals. We find that the dependence of the magnetoresistance on the direction of the magnetic field is identical for both models except when the field is almost parallel to the layers. An important implication of this result is that a three-dimensional Fermi surface is not necessary for the observation of the Yamaji and Danner oscillations seen in quasi-two- and quasi-one-dimensional metals, respectively. A universal expression is given for the dependence of the resistance at AMRO maxima and minima on the magnetic field and scattering time (and thus the temperature). We point out three distinctive features of coherent interlayer transport: (i) a beat frequency in the magnetic oscillations of quasi-two-dimensional systems, (ii) a peak in the angular-dependent magnetoresistance when the field is sufficiently large and parallel to the layers, and (iii) a crossover from a linear to a quadratic field dependence for the magnetoresistance when the field is parallel to the layers. Properties (i) and (ii) are compared with published experimental data for a range of quasi-two-dimensional organic metals and for Sr2RuO4.Comment: 21 pages, RevTeX + epsf, 4 figures. Published version. Subsection added. References update

Ultra-fast self-assembly and stabilization of reactive nanoparticles in reduced graphene oxide films.

Nanoparticles hosted in conductive matrices are ubiquitous in electrochemical energy storage, catalysis and energetic devices. However, agglomeration and surface oxidation remain as two major challenges towards their ultimate utility, especially for highly reactive materials. Here we report uniformly distributed nanoparticles with diameters around 10 nm can be self-assembled within a reduced graphene oxide matrix in 10 ms. Microsized particles in reduced graphene oxide are Joule heated to high temperature (∼1,700 K) and rapidly quenched to preserve the resultant nano-architecture. A possible formation mechanism is that microsized particles melt under high temperature, are separated by defects in reduced graphene oxide and self-assemble into nanoparticles on cooling. The ultra-fast manufacturing approach can be applied to a wide range of materials, including aluminium, silicon, tin and so on. One unique application of this technique is the stabilization of aluminium nanoparticles in reduced graphene oxide film, which we demonstrate to have excellent performance as a switchable energetic material

Possible Triplet Electron Pairing and an Anisotropic Spin Susceptibility in Organic Superconductors (TMTSF)_2 X

We argue that (TMTSF)_2 PF_6 compound under pressure is likely a triplet superconductor with a vector order parameter d(k) \equiv (d_a(k) \neq 0, d_c(k) = ?, d_{b'}(k) = 0); |d_a(k)| > |d_c(k)|. It corresponds to an anisotropic spin susceptibility at T=0: \chi_{b'} = \chi_0, \chi_a \ll \chi_0, where \chi_0 is its value in a metallic phase. [The spin quantization axis, z, is parallel to a so-called b'-axis]. We show that the suggested order parameter explains why the upper critical field along the b'-axis exceeds all paramagnetic limiting fields, including that for a nonuniform superconducting state, whereas the upper critical field along the a-axis (a \perp b') is limited by the Pauli paramagnetic effects [I. J. Lee, M. J. Naughton, G. M. Danner and P. M. Chaikin, Phys. Rev. Lett. 78, 3555 (1997)]. The triplet order parameter is in agreement with the recent Knight shift measurements by I. J. Lee et al. as well as with the early results on a destruction of superconductivity by nonmagnetic impurities and on the absence of the Hebel-Slichter peak in the NMR relaxation rate.Comment: 4 pages, 1 eps figur

Magnetic-Field Variations of the Pair-Breaking Effects of Superconductivity in (TMTSF)2ClO4

We have studied the onset temperature of the superconductivity Tc_onset of the organic superconductor (TMTSF)2ClO4, by precisely controlling the direction of the magnetic field H. We compare the results of two samples with nearly the same onset temperature but with different scattering relaxation time tau. We revealed a complicated interplay of a variety of pair-breaking effects and mechanisms that overcome these pair-breaking effects. In low fields, the linear temperature dependences of the onset curves in the H-T phase diagrams are governed by the orbital pair-breaking effect. The dips in the in-plane field-angle phi dependence of Tc_onset, which were only observed in the long-tau sample, provides definitive evidence that the field-induced dimensional crossover enhances the superconductivity if the field direction is more than about 19-degrees away from the a axis. In the high-field regime for H//a, the upturn of the onset curve for the long-tau sample indicates a new superconducting state that overcomes the Pauli pair-breaking effect but is easily suppressed by impurity scatterings. The Pauli effect is also overcome for H//b' by a realization of another state for which the maximum of Tc_onset(phi) occurs in a direction different from the crystalline axes. The effect on Tc_onset of tilting the applied field out of the conductive plane suggests that the Pauli effect plays a significant role in determining Tc_onset. The most plausible explanation of these results is that (TMTSF)2ClO4 is a singlet superconductor and exhibits Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in high fields.Comment: 12 pages, 10 figures. To be published in J. Phys. Soc. Jpn. (vol.77, 2008