40,697 research outputs found
Arc-Length Continuation and Multigrid Techniques for Nonlinear Elliptic Eigenvalue Problems
We investigate multi-grid methods for solving linear systems arising from arc-length continuation techniques applied to nonlinear elliptic eigenvalue problems. We find that the usual multi-grid methods diverge in the neighborhood of singular points of the solution branches. As a result, the continuation method is unable to continue past a limit point in the Bratu problem. This divergence is analyzed and a modified multi-grid algorithm has been devised based on this analysis. In principle, this new multi-grid algorithm converges for elliptic systems, arbitrarily close to singularity and has been used successfully in conjunction with arc-length continuation procedures on the model problem. In the worst situation, both the storage and the computational work are only about a factor of two more than the unmodified multi-grid methods
Activation barrier scaling and crossover for noise-induced switching in a micromechanical parametric oscillator
We explore fluctuation-induced switching in a parametrically-driven
micromechanical torsional oscillator. The oscillator possesses one, two or
three stable attractors depending on the modulation frequency. Noise induces
transitions between the coexisting attractors. Near the bifurcation points, the
activation barriers are found to have a power law dependence on frequency
detuning with critical exponents that are in agreement with predicted universal
scaling relationships. At large detuning, we observe a crossover to a different
power law dependence with an exponent that is device specific.Comment: 5 pages, 5 figure
In-vivo magnetic resonance imaging of hyperpolarized silicon particles
Silicon-based micro and nanoparticles have gained popularity in a wide range
of biomedical applications due to their biocompatibility and biodegradability
in-vivo, as well as a flexible surface chemistry, which allows drug loading,
functionalization and targeting. Here we report direct in-vivo imaging of
hyperpolarized 29Si nuclei in silicon microparticles by MRI. Natural physical
properties of silicon provide surface electronic states for dynamic nuclear
polarization (DNP), extremely long depolarization times, insensitivity to the
in-vivo environment or particle tumbling, and surfaces favorable for
functionalization. Potential applications to gastrointestinal, intravascular,
and tumor perfusion imaging at sub-picomolar concentrations are presented.
These results demonstrate a new background-free imaging modality applicable to
a range of inexpensive, readily available, and biocompatible Si particles.Comment: Supplemental Material include
Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator
We study noise-enhanced frequency mixing in an underdamped micromechanical
torsional oscillator. The oscillator is electrostatically driven into
bistability by a strong, periodic voltage at frequency . A second,
weak ac voltage is applied at a frequency close to . Due to
nonlinearity in the system, vibrations occur at both and
. White noise is injected into the excitation, allowing the
system to occasionally overcome the activation barrier and switch between the
two states. At the primary drive frequency where the occupations of the two
states are approximately equal, we observe noise-induced enhancement of the
oscillation amplitudes at both and the down-converted frequency
, in agreement with theoretical predictions. Such enhancement
occurs as a result of the noise-induced interstate transitions becoming
synchronous with the beating between the two driving frequencies.Comment: 4 pages 5 figure
Statistical variability in implant-free quantum-well MOSFETs with InGaAs and Ge: a comparative 3D simulation study
Introduction of high mobility channel materials including III-Vs and Ge into future CMOS generations offer the
potential for enhanced transport properties compared to Si. The Implant Free Quantum Well (IFQW) architecture
offers an attractive design to introduce these materials, providing excellent electrostatic integrity. Statistical variability introduced by the discreteness of charge and granularity of matter has become a key factor for current and future generations of MOSFETs and in this work numerical simulations are used to critically assess the statistical
variability in IFQW transistors and compare results with equivalent conventional Si ‘bulk’ MOSFETs
Supernarrow spectral peaks near a kinetic phase transition in a driven, nonlinear micromechanical oscillator
We measure the spectral densities of fluctuations of an underdamped nonlinear
micromechanical oscillator. By applying a sufficiently large periodic
excitation, two stable dynamical states are obtained within a particular range
of driving frequency. White noise is injected into the excitation, allowing the
system to overcome the activation barrier and switch between the two states.
While the oscillator predominately resides in one of the two states for most
excitation frequencies, a narrow range of frequencies exist where the
occupations of the two states are approximately equal. At these frequencies,
the oscillator undergoes a kinetic phase transition that resembles the phase
transition of thermal equilibrium systems. We observe a supernarrow peak in the
power spectral densities of fluctuations of the oscillator. This peak is
centered at the excitation frequency and arises as a result of noise-induced
transitions between the two dynamical states.Comment: 4 pages, 4 figure
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