8,862 research outputs found
Nonlinear Preconditioning: How to use a Nonlinear Schwarz Method to Precondition Newton's Method
For linear problems, domain decomposition methods can be used directly as
iterative solvers, but also as preconditioners for Krylov methods. In practice,
Krylov acceleration is almost always used, since the Krylov method finds a much
better residual polynomial than the stationary iteration, and thus converges
much faster. We show in this paper that also for non-linear problems, domain
decomposition methods can either be used directly as iterative solvers, or one
can use them as preconditioners for Newton's method. For the concrete case of
the parallel Schwarz method, we show that we obtain a preconditioner we call
RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) which is
similar to ASPIN (Additive Schwarz Preconditioned Inexact Newton), but with all
components directly defined by the iterative method. This has the advantage
that RASPEN already converges when used as an iterative solver, in contrast to
ASPIN, and we thus get a substantially better preconditioner for Newton's
method. The iterative construction also allows us to naturally define a coarse
correction using the multigrid full approximation scheme, which leads to a
convergent two level non-linear iterative domain decomposition method and a two
level RASPEN non-linear preconditioner. We illustrate our findings with
numerical results on the Forchheimer equation and a non-linear diffusion
problem
Realization of Artificial Ice Systems for Magnetic Vortices in a Superconducting MoGe Thin-film with Patterned Nanostructures
We report an anomalous matching effect in MoGe thin films containing pairs of
circular holes arranged in such a way that four of those pairs meet at each
vertex point of a square lattice. A remarkably pronounced fractional matching
was observed in the magnetic field dependences of both the resistance and the
critical current. At the half matching field the critical current can be even
higher than that at zero field. This has never been observed before for
vortices in superconductors with pinning arrays. Numerical simulations within
the nonlinear Ginzburg-Landau theory reveal a square vortex ice configuration
in the ground state at the half matching field and demonstrate similar
characteristic features in the field dependence of the critical current,
confirming the experimental realization of an artificial ice system for
vortices for the first time.Comment: To appear in Phys. Rev. Let
The Radon Monitoring System in Daya Bay Reactor Neutrino Experiment
We developed a highly sensitive, reliable and portable automatic system
(H) to monitor the radon concentration of the underground experimental
halls of the Daya Bay Reactor Neutrino Experiment. H is able to measure
radon concentration with a statistical error less than 10\% in a 1-hour
measurement of dehumidified air (R.H. 5\% at 25C) with radon
concentration as low as 50 Bq/m. This is achieved by using a large radon
progeny collection chamber, semiconductor -particle detector with high
energy resolution, improved electronics and software. The integrated radon
monitoring system is highly customizable to operate in different run modes at
scheduled times and can be controlled remotely to sample radon in ambient air
or in water from the water pools where the antineutrino detectors are being
housed. The radon monitoring system has been running in the three experimental
halls of the Daya Bay Reactor Neutrino Experiment since November 2013
Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach
We consider the Langevin equation with multiplicative noise term which
depends on time and space. The corresponding Fokker-Planck equation in
Stratonovich approach is investigated. Its formal solution is obtained for an
arbitrary multiplicative noise term given by , and the
behaviors of probability distributions, for some specific functions of %
, are analyzed. In particular, for , the physical
solutions for the probability distribution in the Ito, Stratonovich and
postpoint discretization approaches can be obtained and analyzed.Comment: 6 pages in LATEX cod
An increase in under hydrostatic pressure in the superconducting doped topological insulator NbBiSe
We report an unexpected positive hydrostatic pressure derivative of the
superconducting transition temperature in the doped topological insulator \NBS
via SQUID magnetometry in pressures up to 0.6 GPa. This result is contrary
to reports on the homologues \CBS and \SBS where smooth suppression of is
observed. Our results are consistent with recent Ginzburg-Landau theory
predictions of a pressure-induced enhancement of in the nematic
multicomponent state proposed to explain observations of rotational
symmetry breaking in doped BiSe superconductors.Comment: 5 pages, 5 figure
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