4,289 research outputs found
Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations
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
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
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
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
- …