Dynamic modeling of three-phase upflow fixed-bed reactor including pore diffusion

The dynamics of a three-phase upflow fixed-bed reactor are investigated using a non-isothermal heterogeneous model including gas–liquid and liquid–solid mass transfer and diffusion/reaction phenomena inside the catalyst. The partial differential and algebraic equations involving three integration variables (time and two space coordinates) are solved via discretization of the spatial coordinates coupled with the Gear method. For a multistep hydrogenation on a shell catalyst, the model exhibits significant effects of the external and above all internal resistance to hydrogen transfer but also non-trivial internal hydrocarbons concentration profiles. A simplified model is compared with the extended one and with experimental data in transient regime. In the investigated conditions—hydrocarbons in large excess—the diffusion of hydrocarbons appears to be actually not limiting, so that the simplest model predicts accurately the transient reactor behavior

S and D Wave Mixing in High TcT_c Superconductors

For a tight binding model with nearest neighbour attraction and a small orthorhombic distortion, we find a phase diagram for the gap at zero temperature which includes three distinct regions as a function of filling. In the first, the gap is a mixture of mainly $d$-wave with a smaller extended $s$-wave part. This is followed by a region in which there is a rapid increase in the $s$-wave part accompanied by a rapid increase in relative phase between $s$ and $d$ from 0 to $\pi$. Finally, there is a region of dominant $s$ with a mixture of $d$ and zero phase. In the mixed region with a finite phase, the $s$-wave part of the gap can show a sudden increase with decreasing temperature accompanied with a rapid increase in phase which shows many of the characteristics measured in the angular resolved photoemission experiments of Ma {\em et al.} in $\rm Bi_2Sr_2CaCu_2O_8$Comment: 12 pages, RevTeX 3.0, 3 PostScript figures uuencoded and compresse

Self-generated magnetic flux in YBa2_2Cu3_3O7−x_{7-x} grain boundaries

Grain boundaries in YBa$_2$Cu$_3$O$_{7-x}$ superconducting films are considered as Josephson junctions with a critical current density $j_c(x)$ alternating along the junction. A self-generated magnetic flux is treated both analytically and numerically for an almost periodic distribution of $j_c(x)$. We obtained a magnetic flux-pattern similar to the one which was recently observed experimentally.Comment: 7 pages, 3 figure

Phenomenological BCS theory of the high-TcT_c cuprates

A BCS model characterized by a phenomenological pair potential with on-site ($V_0$), nearest ($V_1$), and next nearest ($V_2$) neighbour coupling constants, and an empirical quasiparticle dispersion taken from angle-resolved photoemission spectra is considered. The model can consistently explain the experimental data concerning the pair state of the hole doped cuprates. Three ingredients are required to make the interpretation possible: the existence of flat bands, a very small effective on-site repulsion, and a slightly dominating effective nnn attraction $V_2$ of the order of 60-80meV with a ratio $V_2/V_1 \approx 1.5$.Comment: 13 pages, uuencoded Postscrip

Phenomenological Models for the Gap Anisotropy of Bi-2212 as Measured by ARPES

Recently, high resolution angle-resolved photoemission spectroscopy has been used to determine the detailed momentum dependence of the superconducting gap in the high temperature superconductor Bi-2212. In this paper, we first describe tight binding fits to the normal state dispersion and superlattice modulation effects. We then discuss various theoretical models in light of the gap measurements. We find that the simplest model which fits the data is the anisotropic s-wave gap $\cos(k_x)\cos(k_y)$, which within a one-band BCS frame- work suggests the importance of next near neighbor Cu-Cu interactions. Various alternative interpretations of the observed gap are also discussed, along with the implications for microscopic theories of high temperature superconductors.Comment: 14 pages, revtex, 9 uuencoded postscript figure

Relativistic calculations of the lifetimes and hyperfine structure constants in 67^{67}Zn+^{+}

This work presents accurate {\it ab initio} determination of the magnetic dipole (M1) and electric quadrupole (E2) hyperfine structure constants for the ground and a few low-lying excited states in $^{67}$Zn$^{+}$, which is one of the interesting systems in fundamental physics. The coupled-cluster (CC) theory within the relativistic framework has been used here in this calculations. Long standing demands for a relativistic and highly correlated calculations like CC can be able to resolve the disagreements among the lifetime estimations reported previously for a few low-lying states of Zn$^{+}$. The role of different electron correlation effects in the determination of these quantities are discussed and their contributions are presented.Comment: 9 pages, 1 figure. submitted to J. Phys. B Fast Trac

Superconducting gap node spectroscopy using nonlinear electrodynamics

We present a method to determine the nodal structure of the energy gap of unconventional superconductors such as high $T_c$ materials. We show how nonlinear electrodynamics phenomena in the Meissner regime, arising from the presence of lines on the Fermi surface where the superconducting energy gap is very small or zero, can be used to perform ``node spectroscopy'', that is, as a sensitive bulk probe to locate the angular position of those lines. In calculating the nonlinear supercurrent response, we include the effects of orthorhombic distortion and $a-b$ plane anisotropy. Analytic results presented demonstrate a systematic way to experimentally distinguish order parameters of different symmetries, including cases with mixed symmetry (for example, $d+s$ and $s+id$). We consider, as suggested by various experiments, order parameters with predominantly $d$-wave character, and describe how to determine the possible presence of other symmetries. The nonlinear magnetic moment displays a distinct behavior if nodes in the gap are absent but regions with small, finite, values of the energy gap exist.Comment: 18 pages, Revtex, 9 postscript figures. Submitted to Phys. Rev

Grain Boundary Induced Magneto-Far Infrared Resonances in Superconducting YBa2_2Cu3_3O7−δ_{7-\delta } Thin Films

Spectral features induced by 45$^{\circ }$ in-plane misoriented grains have been observed in the far infrared magneto-transmission of YBa$_2$Cu$_3$O$_{7-\delta }$ thin films. Two strong dispersive features are found at 80 and 160 $cm^{-1}$ and a weaker one at 116 $cm^{-1}$. The data can be well represented by Lorentzian oscillator contributions to the conductivity. Several possible interpretations are discussed. We conclude that the resonances are due to vortex core excitations.Comment: Latex file (14 pages) + 4 Postscript figures, uuencode

Twin boundaries in d-wave superconductors

Twin boundaries in orthorhombic d-wave superconductors are investigated numerically using the Bogoliubov-deGennes formalism within the context of an extended Hubbard model. The twin boundaries are represented by tetragonal regions of variable width, with a reduced chemical potential. For sufficiently large twin boundary width and change in chemical potential, an induced s-wave component may break time-reversal symmetry at a low temperature. This temperature, and the magnitude of the complex component, are found to depend strongly on electron density. The results are compared with recent tunneling measurements.Comment: ReVTeX, 4 pages, 4 postscript figure