A hybrid MPI-OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence

A hybrid scheme that utilizes MPI for distributed memory parallelism and OpenMP for shared memory parallelism is presented. The work is motivated by the desire to achieve exceptionally high Reynolds numbers in pseudospectral computations of fluid turbulence on emerging petascale, high core-count, massively parallel processing systems. The hybrid implementation derives from and augments a well-tested scalable MPI-parallelized pseudospectral code. The hybrid paradigm leads to a new picture for the domain decomposition of the pseudospectral grids, which is helpful in understanding, among other things, the 3D transpose of the global data that is necessary for the parallel fast Fourier transforms that are the central component of the numerical discretizations. Details of the hybrid implementation are provided, and performance tests illustrate the utility of the method. It is shown that the hybrid scheme achieves near ideal scalability up to ~20000 compute cores with a maximum mean efficiency of 83%. Data are presented that demonstrate how to choose the optimal number of MPI processes and OpenMP threads in order to optimize code performance on two different platforms.Comment: Submitted to Parallel Computin

A minimal two-band model for the superconducting Fe-pnictides

Following the discovery of the Fe-pnictide superconductors, LDA band structure calculations showed that the dominant contributions to the spectral weight near the Fermi energy came from the Fe 3d orbitals. The Fermi surface is characterized by two hole surfaces around the $\Gamma$ point and two electron surfaces around the M point of the 2 Fe/cell Brillouin zone. Here, we describe a 2-band model that reproduces the topology of the LDA Fermi surface and exhibits both ferromagnetic and $q=(\pi,0)$ spin density wave (SDW) fluctuations. We argue that this minimal model contains the essential low energy physics of these materials.Comment: 5 figures, 5 page

Charge and spin collective modes in a quasi-1D model of Sr2RuO4

Given that Sr2RuO4 is a two-component p-wave superconductor, there exists the possibility of well defined collective modes corresponding to fluctuations of the relative phase and spin-orientation of the two components of the order parameter. We demonstrate that at temperatures much below Tc, these modes have energies small compared to the pairing gap scale if the superconductivity arises primarily from the quasi 1D (dxz and dyz) bands, while it is known that their energies become comparable to the pairing gap scale if there is a substantial involvement of the quasi 2D (dxy) band. Therefore, the orbital origin of the superconductivity can be determined by measuring the energies of these collective modes.Comment: 11 pages (6 pages for main text), 2 figure

Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution

We study the phase diagram of the Hubbard model in the limit where U, the onsite repulsive interaction, is much smaller than the bandwidth. We present an asymptotically exact expression for T$_c$, the superconducting transition temperature, in terms of the correlation functions of the non-interacting system which is valid for arbitrary densities so long as the interactions are sufficiently small. Our strategy for computing T$_c$ involves first integrating out all degrees of freedom having energy higher than an unphysical initial cutoff $\Omega_0$. Then, the renormalization group (RG) flows of the resulting effective action are computed and T$_c$ is obtained by determining the scale below which the RG flows in the Cooper channel diverge. We prove that T$_c$ is independent of $\Omega_0$. Using this method, we find a variety of unconventional superconducting ground states in two and three dimensional lattice systems and present explicit results for T$_c$ and pairing symmetries as a function of the electron concentration.Comment: 18 pages, 17 figure