104 research outputs found
An optimally efficient technique for the solution of systems of nonlinear parabolic partial differential equations
This paper describes a new software tool that has been developed for the efficient solution of systems of linear and nonlinear partial differential equations (PDEs) of parabolic type. Specifically, the software is designed to provide optimal computational performance for multiscale problems, which require highly stable, implicit, time-stepping schemes combined with a parallel implementation of adaptivity in both space and time. By combining these implicit, adaptive discretizations with an optimally efficient nonlinear multigrid solver it is possible to obtain computational solutions to a very high resolution with relatively modest computational resources. The first half of the paper describes the numerical methods that lie behind the software, along with details of their implementation, whilst the second half of the paper illustrates the flexibility and robustness of the tool by applying it to two very different example problems. These represent models of a thin film flow of a spreading viscous droplet and a multi-phase-field model of tumour growth. We conclude with a discussion of the challenges of obtaining highly scalable parallel performance for a software tool that combines both local mesh adaptivity, requiring efficient dynamic load-balancing, and a multigrid solver, requiring careful implementation of coarse grid operations and inter-grid transfer operations in parallel
Modeling the actinides with disordered local moments
A first-principles disordered local moment (DLM) picture within the
local-spin-density and coherent potential approximations (LSDA+CPA) of the
actinides is presented. The parameter free theory gives an accurate description
of bond lengths and bulk modulus. The case of -Pu is studied in
particular and the calculated density of states is compared to data from
photo-electron spectroscopy. The relation between the DLM description, the
dynamical mean field approach and spin-polarized magnetically ordered modeling
is discussed.Comment: 6 pages, 4 figure
Superconductivity in the two dimensional Hubbard Model.
Quasiparticle bands of the two-dimensional Hubbard model are calculated using
the Roth two-pole approximation to the one particle Green's function. Excellent
agreement is obtained with recent Monte Carlo calculations, including an
anomalous volume of the Fermi surface near half-filling, which can possibly be
explained in terms of a breakdown of Fermi liquid theory. The calculated bands
are very flat around the (pi,0) points of the Brillouin zone in agreement with
photoemission measurements of cuprate superconductors. With doping there is a
shift in spectral weight from the upper band to the lower band. The Roth method
is extended to deal with superconductivity within a four-pole approximation
allowing electron-hole mixing. It is shown that triplet p-wave pairing never
occurs. Singlet d_{x^2-y^2}-wave pairing is strongly favoured and optimal
doping occurs when the van Hove singularity, corresponding to the flat band
part, lies at the Fermi level. Nearest neighbour antiferromagnetic correlations
play an important role in flattening the bands near the Fermi level and in
favouring superconductivity. However the mechanism for superconductivity is a
local one, in contrast to spin fluctuation exchange models. For reasonable
values of the hopping parameter the transition temperature T_c is in the range
10-100K. The optimum doping delta_c lies between 0.14 and 0.25, depending on
the ratio U/t. The gap equation has a BCS-like form and (2*Delta_{max})/(kT_c)
~ 4.Comment: REVTeX, 35 pages, including 19 PostScript figures numbered 1a to 11.
Uses epsf.sty (included). Everything in uuencoded gz-compressed .tar file,
(self-unpacking, see header). Submitted to Phys. Rev. B (24-2-95
Physics basis and simulation of burning plasma physics for the fusion ignition research experiment (FIRE)
The FIRE [Fusion Ignition Research Experiment] design for a burning plasma experiment is described in terms of its physics basis and engineering features. Systems analysis indicates that the device has a wide operating space to accomplish its mission, both for the ELMing H-mode reference and the high bootstrap current/high beta advanced tokamak regimes. Simulations with 1.5D transport codes reported here both confirm and constrain the systems projections. Experimental and theoretical results are used to establish the basis for successful burning plasma experiments in FIRE
Stretch and inflammation-induced Pre-B cell colony-enhancing factor (PBEF/Visfatin) and Interleukin-8 in amniotic epithelial cellsâ
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