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$^{3}$) to monitor the radon concentration of the underground experimental halls of the Daya Bay Reactor Neutrino Experiment. H$^{3}$ 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 25$^{\circ}$C) with radon concentration as low as 50 Bq/m$^{3}$. This is achieved by using a large radon progeny collection chamber, semiconductor $\alpha$-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 $g(x,t)=D(x)T(t)$, and the behaviors of probability distributions, for some specific functions of $D(x)$% , are analyzed. In particular, for $D(x)\sim | x| ^{-\theta /2}$, 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 TcT_c under hydrostatic pressure in the superconducting doped topological insulator Nb0.25_{0.25}Bi2_2Se3_3

We report an unexpected positive hydrostatic pressure derivative of the superconducting transition temperature in the doped topological insulator \NBS via $dc$ 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 $T_c$ is observed. Our results are consistent with recent Ginzburg-Landau theory predictions of a pressure-induced enhancement of $T_c$ in the nematic multicomponent $E_u$ state proposed to explain observations of rotational symmetry breaking in doped Bi$_2$Se$_3$ superconductors.Comment: 5 pages, 5 figure