44 research outputs found
Edge Channel Interference Controlled by Landau Level Filling
We study the visibility of Aharonov-Bohm interference in an electronic
Mach-Zehnder interferometer (MZI) in the integer quantum Hall regime. The
visibility is controlled by the filling factor and is observed only
between and 1.0, with an unexpected maximum near .
Three energy scales extracted from the temperature and voltage dependences of
the visibility change in a very similar way with the filling factor, indicating
that the different aspects of the interference depend sensitively on the local
structure of the compressible and incompressible strips forming the quantum
Hall edge channels.Comment: 5 pages, 5 figures, final version accepted for publication in Phys.
Rev.
Counting Statistics and Dephasing Transition in an Electronic Mach-Zehnder Interferometer
It was recently suggested that a novel type of phase transition may occur in
the visibility of electronic Mach-Zehnder Interferometers. Here, we present
experimental evidence for the existence of this transition. The transition is
induced by strongly non-Gaussian noise that originates from the strong coupling
of a quantum point contact to the interferometer. We provide a transparent
physical picture of the effect, by exploiting a close analogy to the
neutrino-oscillations of particle physics. In addition, our experiment
constitutes a probe of the singularity of the elusive full counting statistics
of a quantum point contact.Comment: 7 pages, 4 figures (+Supplement 8 pages, 9 figures
Nonlocal vortex motion in mesoscopic amorphous Nb0.7Ge0.3 structures
We study nonlocal vortex transport in mesoscopic amorphous Nb0.7Ge0.3
samples. A dc current I is passed through a wire connected via a perpendicular
channel, of a length L= 2-5 um, with a pair of voltage probes where a nonlocal
response Vnl ~ I is measured. The maximum of Rnl=Vnl/I for a given temperature
occurs at an L-independent magnetic field and is proportional to 1/L. The
results are interpreted in terms of the dissipative vortex motion along the
channel driven by a remote current, and can be understood in terms of a simple
model.Comment: 4 pages, 3 figure
Tsunami observations by coastal ocean radar
When tsunami waves propagate across the open ocean, they are steered by the Coriolis effect and refraction due to gentle gradients in the bathymetry on scales longer than the wavelength. When the wave encounters steep gradients at the edges of continental shelves and at the coast, the wave becomes nonlinear and conservation of momentum produces squirts of surface current at the head of submerged canyons and in coastal bays. High frequency (HF) coastal ocean
radar is well conditioned to observe the surface current bursts at the edge of the continental shelf and give a warning of 40 minutes to 2 hours when the shelf is 50
to 200km wide. The period of tsunami waves is invariant over changes in bathymetry and is in the range 2 to 30 minutes. Wavelengths for tsunamis (in 500 to 3000m depth) are in the range 8.5 to over 200 km, and on a shelf where the depth is about 50m (as in the Great Barrier Reef (GBR)) the wavelengths are in the range 2.5 to 30 km. In the use of HF radar technology, there is a trade-off between the precision of surface current speed measurements and time
resolution. It is shown that the phased array HF ocean surface radar being deployed in the GBR and operating in a routine way for mapping surface currents, can resolve surface current squirts from tsunamis in the wave period
range 20 to 30 minutes and in the wavelength range greater than about 6 km. An advantage in signal-to-noise ratio can be obtained from the prior knowledge of the spatial pattern of the squirts at the edge of the continental shelf, and it is estimated that, with this analysis, the time resolution of the GBR radar may be reduced to about 2.5 minutes, which corresponds to a capability to detect tsunamis at the shelf edge in the period range 5 to 30 minutes. It is estimated that the lower limit of squirt velocity detection at the shelf edge would correspond to a tsunami with water elevation of about 2.5 cm in the open ocean. This means
that the GBR HF radar is well conditioned for use as a monitor of small, as well as larger, tsunamis and has the potential to contribute to the understanding of tsunami genesis research
A rarefaction-tracking method for hyperbolic conservation laws
We present a numerical method for scalar conservation laws in one space
dimension. The solution is approximated by local similarity solutions. While
many commonly used approaches are based on shocks, the presented method uses
rarefaction and compression waves. The solution is represented by particles
that carry function values and move according to the method of characteristics.
Between two neighboring particles, an interpolation is defined by an analytical
similarity solution of the conservation law. An interaction of particles
represents a collision of characteristics. The resulting shock is resolved by
merging particles so that the total area under the function is conserved. The
method is variation diminishing, nevertheless, it has no numerical dissipation
away from shocks. Although shocks are not explicitly tracked, they can be
located accurately. We present numerical examples, and outline specific
applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding
An Unstaggered Constrained Transport Method for the 3D Ideal Magnetohydrodynamic Equations
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations
in more than one space dimension must either confront the challenge of
controlling errors in the discrete divergence of the magnetic field, or else be
faced with nonlinear numerical instabilities. One approach for controlling the
discrete divergence is through a so-called constrained transport method, which
is based on first predicting a magnetic field through a standard finite volume
solver, and then correcting this field through the appropriate use of a
magnetic vector potential. In this work we develop a constrained transport
method for the 3D ideal MHD equations that is based on a high-resolution wave
propagation scheme. Our proposed scheme is the 3D extension of the 2D scheme
developed by Rossmanith [SIAM J. Sci. Comp. 28, 1766 (2006)], and is based on
the high-resolution wave propagation method of Langseth and LeVeque [J. Comp.
Phys. 165, 126 (2000)]. In particular, in our extension we take great care to
maintain the three most important properties of the 2D scheme: (1) all
quantities, including all components of the magnetic field and magnetic
potential, are treated as cell-centered; (2) we develop a high-resolution wave
propagation scheme for evolving the magnetic potential; and (3) we develop a
wave limiting approach that is applied during the vector potential evolution,
which controls unphysical oscillations in the magnetic field. One of the key
numerical difficulties that is novel to 3D is that the transport equation that
must be solved for the magnetic vector potential is only weakly hyperbolic. In
presenting our numerical algorithm we describe how to numerically handle this
problem of weak hyperbolicity, as well as how to choose an appropriate gauge
condition. The resulting scheme is applied to several numerical test cases.Comment: 46 pages, 12 figure
A class of residual distribution schemes and their relation to relaxation systems
Residual distributions (RD) schemes are a class of of high-resolution finite
volume methods for unstructured grids. A key feature of these schemes is that
they make use of genuinely multidimensional (approximate) Riemann solvers as
opposed to the piecemeal 1D Riemann solvers usually employed by finite volume
methods. In 1D, LeVeque and Pelanti [J. Comp. Phys. 172, 572 (2001)] showed
that many of the standard approximate Riemann solver methods (e.g., the Roe
solver, HLL, Lax-Friedrichs) can be obtained from applying an exact Riemann
solver to relaxation systems of the type introduced by Jin and Xin [Comm. Pure
Appl. Math. 48, 235 (1995)]. In this work we extend LeVeque and Pelanti's
results and obtain a multidimensional relaxation system from which
multidimensional approximate Riemann solvers can be obtained. In particular, we
show that with one choice of parameters the relaxation system yields the
standard N-scheme. With another choice, the relaxation system yields a new
Riemann solver, which can be viewed as a genuinely multidimensional extension
of the local Lax-Friedrichs scheme. This new Riemann solver does not require
the use Roe-Struijs-Deconinck averages, nor does it require the inversion of an
m-by-m matrix in each computational grid cell, where is the number of
conserved variables. Once this new scheme is established, we apply it on a few
standard cases for the 2D compressible Euler equations of gas dynamics. We show
that through the use of linear-preserving limiters, the new approach produces
numerical solutions that are comparable in accuracy to the N-scheme, despite
being computationally less expensive.Comment: 46 pages, 14 figure