Fluctuation Effects And Order Parameter Symmetry In The Cuprate Superconductors

Effect of phase fluctuations on superconducting states with anisotropic order parameters is studied in a BCS like lattice model of cuprate superconductors. The degradation of the mean field transition temperature due to phase fluctuations is estimated within a Kosterlitz-Thouless scenario. Values of the interaction parameters for optimal doping, corresponding to a stable superconducting state of $S_{xy}$ symmetry, which fit the nodal structure of the superconducting order parameter in the Bi2212 compound, are obtained. The angular position of the node is found to be insensitive to the dopant concentration.Comment: Latex file, 8 output pages, 5 figures (available from Authors on request), to appear in Europhysics Letter

Effective Vortex Mass from Microscopic Theory

We calculate the effective mass of a single quantized vortex in the BCS superconductor at finite temperature. Based on effective action approach, we arrive at the effective mass of a vortex as integral of the spectral function $J(\omega)$ divided by $\omega^3$ over frequency. The spectral function is given in terms of the quantum-mechanical transition elements of the gradient of the Hamiltonian between two Bogoliubov-deGennes (BdG) eigenstates. Based on self-consistent numerical diagonalization of the BdG equation we find that the effective mass per unit length of vortex at zero temperature is of order $m (k_f \xi_0)^2$ ($k_f$=Fermi momentum, $\xi_0$=coherence length), essentially equaling the electron mass displaced within the coherence length from the vortex core. Transitions between the core states are responsible for most of the mass. The mass reaches a maximum value at $T\approx 0.5 T_c$ and decreases continuously to zero at $T_c$.Comment: Supercedes prior version, cond-mat/990312

Modeling low pressure collisional plasma sheath with space-charge effect

The present work develops a computationally efficient one-dimensional subgrid embedded finite element formulation for plasma-sheath dynamics. The model incorporates space-charge effect throughout the whole plasma and the sheath region using multifluid equations. Secondary electron emission is not considered. A third-order temperature dependent polynomial is used to self-consistently calculate the rate of ionization in the plasma dynamic equations. The applications include dc and rf sheath inside a glow discharge tube where the noble gas is immobile, and a partially ionized plasma sheath inside an electric propulsion thruster channel in which the gas flows. The electron and ion number densities of the numerical solution decrease in the sheath region as expected. The ion velocity and electron temperature profiles also exhibit the expected behavior. The computed sheath potential compares well with the available experimental data. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69919/2/PHPAEN-10-6-2578-1.pd

A pulse size estimation method for reduced-order models

Model-Order Reduction (MOR) is an important technique that allows Reduced-Order Models (ROMs) of physical systems to be generated that can capture the dominant dynamics, but at lower cost than the full order system. One approach to MOR that has been successfully implemented in fluid dynamics is the Eigensystem Realization Algorithm (ERA). This method requires only minimal changes to the inputs and outputs of a CFD code so that the linear responses of the system to unit impulses on each input channel can be extracted. One of the challenges with the method is to specify the size of the input pulse. An inappropriate size may cause a failure of the code to converge due to non-physical behaviour arising during the solution process. This paper addresses this issue by using piston theory to estimate the appropriate input pulse size