11,927 research outputs found
A Study of Energy and Locality Effects using Space-filling Curves
The cost of energy is becoming an increasingly important driver for the
operating cost of HPC systems, adding yet another facet to the challenge of
producing efficient code. In this paper, we investigate the energy implications
of trading computation for locality using Hilbert and Morton space-filling
curves with dense matrix-matrix multiplication. The advantage of these curves
is that they exhibit an inherent tiling effect without requiring specific
architecture tuning. By accessing the matrices in the order determined by the
space-filling curves, we can trade computation for locality. The index
computation overhead of the Morton curve is found to be balanced against its
locality and energy efficiency, while the overhead of the Hilbert curve
outweighs its improvements on our test system.Comment: Proceedings of the 2014 IEEE International Parallel & Distributed
Processing Symposium Workshops (IPDPSW
Some open questions in TDDFT: Clues from Lattice Models and Kadanoff-Baym Dynamics
Two aspects of TDDFT, the linear response approach and the adiabatic local
density approximation, are examined from the perspective of lattice models. To
this end, we review the DFT formulations on the lattice and give a concise
presentation of the time-dependent Kadanoff-Baym equations, used to asses the
limitations of the adiabatic approximation in TDDFT. We present results for the
density response function of the 3D homogeneous Hubbard model, and point out a
drawback of the linear response scheme based on the linearized Sham-Schl\"uter
equation. We then suggest a prescription on how to amend it. Finally, we
analyze the time evolution of the density in a small cubic cluster, and compare
exact, adiabatic-TDDFT and Kadanoff-Baym-Equations densities. Our results show
that non-perturbative (in the interaction) adiabatic potentials can perform
quite well for slow perturbations but that, for faster external fields, memory
effects, as already present in simple many-body approximations, are clearly
required.Comment: 15 pages, submitted to Chemical Physic
Magnetism in the single-band Hubbard model
A self-consistent spectral density approach (SDA) is applied to the Hubbard
model to investigate the possibility of spontaneous ferro- and
antiferromagnetism. Starting point is a two-pole ansatz for the single-electron
spectral density, the free parameter of which can be interpreted as energies
and spectral weights of respective quasiparticle excitations. They are
determined by fitting exactly calculated spectral moments. The resulting
self-energy consists of a local and a non-local part. The higher correlation
functions entering the spin-dependent local part can be expressed as
functionals of the single-electron spectral density. Under certain conditions
for the decisive model parameters (Coulomb interaction U, Bloch-bandwidth W,
band occupation n, temperature T) the local part of the self-energy gives rise
to a spin-dependent band shift, thus allowing for spontaneous band magnetism.
As a function of temperature, second order phase transitions are found away
from half filling, but close to half filling the system exhibits a tendency
towards first order transitions. The non-local self-energy part is determined
by use of proper two-particle spectral densities. Its main influence concerns a
(possibly spin-dependent) narrowing of the quasiparticle bands with the
tendency to stabilize magnetic solutions. The non-local self-energy part
disappears in the limit of infinite dimensions. We present a full evaluation of
the Hubbard model in terms of quasiparticle densities of states, quasiparticle
dispersions, magnetic phase diagram, critical temperatures (Tc, Tn) as well as
spin and particle correlation functions. Special attention is focused on the
non-locality of the electronic self-energy, for which some rigorous limiting
cases are worked out.Comment: 13 pages, LaTex, 26 figures included (eps), corrected typo
Kinetic energy cascades in quasi-geostrophic convection in a spherical shell
We consider triadic nonlinear interaction in the Navier-Stokes equation for
quasi-geostrophic convection in a spherical shell. This approach helps
understanding the origin of kinetic energy transport in the system and the
particular scheme of mode interaction, as well as the locality of the energy
transfer. The peculiarity of convection in the sphere, concerned with
excitation of Rossby waves, is considered. The obtained results are compared
with our previous study in Cartesian geometry
Kinematic simulation for stably stratified and rotating turbulence
The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the rapid distortion theory (RDT) to a kinematic simulation (KS) of the Boussinesq equation with a Coriolis term.
Scalings for one- and two-particle horizontal and vertical diffusions in purely rotating turbulence are proposed for small Rossby numbers.
Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in purely rotating turbulence both in the horizontal and the vertical directions. It is observed that both rotation and stratification decrease the pair diffusivity and improve the validity of the locality-in-scale hypothesis. In the case of stratification the range of scales over which the locality-in-scale hypothesis is observed is increased.
It is found that rotation decreases the diffusion in the horizontal direction as well as, though to a much lesser extent, in the vertical direction
Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model
We study time-dependent electron transport through an Anderson model. The
electronic interactions on the impurity site are included via the self-energy
approximations at Hartree-Fock (HF), second Born (2B), GW, and T-Matrix level
as well as within a time-dependent density functional (TDDFT) scheme based on
the adiabatic Bethe-Ansatz local density approximation (ABALDA) for the
exchange correlation potential. The Anderson model is driven out of equilibrium
by applying a bias to the leads and its nonequilibrium dynamics is determined
by real-time propagation. The time-dependent currents and densities are
compared to benchmark results obtained with the time-dependent density matrix
renormalization group (tDMRG) method. Many-body perturbation theory beyond HF
gives results in close agreement with tDMRG especially within the 2B
approximation. We find that the TDDFT approach with the ABALDA approximation
produces accurate results for the densities on the impurity site but
overestimates the currents. This problem is found to have its origin in an
overestimation of the lead densities which indicates that the exchange
correlation potential must attain nonzero values in the leads.Comment: 11 pages, 9 figure
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