4,289 research outputs found

    Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations

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    Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear dif- fusion, with typical examples like the Cahn-Hilliard equation and the thin film type equation. The up-to-date theoretical explanation of the numerical stability relies on the assumption that the deriva- tive of the nonlinear potential function satisfies a Lipschitz type condition, which in a rigorous sense, implies the boundedness of the numerical solution. In this work we remove the Lipschitz assumption on the nonlinearity and prove unconditional energy stability for the stabilized semi-implicit time-stepping methods. It is shown that the size of stabilization term depends on the initial energy and the perturba- tion parameter but is independent of the time step. The corresponding error analysis is also established under minimal nonlinearity and regularity assumptions

    An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

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    In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.Comment: This paper has been accepted for publication in SCIENCE CHINA Mathematic

    Seebeck Effect in Magnetic Tunnel Junctions

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    Creating temperature gradients in magnetic nanostructures has resulted in a new research direction, i.e., the combination of magneto- and thermoelectric effects. Here, we demonstrate the observation of one important effect of this class: the magneto-Seebeck effect. It is observed when a magnetic configuration changes the charge based Seebeck coefficient. In particular, the Seebeck coefficient changes during the transition from a parallel to an antiparallel magnetic configuration in a tunnel junction. In that respect, it is the analog to the tunneling magnetoresistance. The Seebeck coefficients in parallel and antiparallel configuration are in the order of the voltages known from the charge-Seebeck effect. The size and sign of the effect can be controlled by the composition of the electrodes' atomic layers adjacent to the barrier and the temperature. Experimentally, we realized 8.8 % magneto-Seebeck effect, which results from a voltage change of about -8.7 {\mu}V/K from the antiparallel to the parallel direction close to the predicted value of -12.1 {\mu}V/K.Comment: 16 pages, 7 figures, 2 table

    Molecular beam growth of graphene nanocrystals on dielectric substrates

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    We demonstrate the growth of graphene nanocrystals by molecular beam methods that employ a solid carbon source, and that can be used on a diverse class of large area dielectric substrates. Characterization by Raman and Near Edge X-ray Absorption Fine Structure spectroscopies reveal a sp2 hybridized hexagonal carbon lattice in the nanocrystals. Lower growth rates favor the formation of higher quality, larger size multi-layer graphene crystallites on all investigated substrates. The surface morphology is determined by the roughness of the underlying substrate and graphitic monolayer steps are observed by ambient scanning tunneling microscopy.Comment: Accepted in Carbon; Discussion section added; 20 pages, 6 figures (1 updated
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