2,444 research outputs found
Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods
Recent works showed that pressure-robust modifications of mixed finite
element methods for the Stokes equations outperform their standard versions in
many cases. This is achieved by divergence-free reconstruction operators and
results in pressure independent velocity error estimates which are robust with
respect to small viscosities. In this paper we develop a posteriori error
control which reflects this robustness.
The main difficulty lies in the volume contribution of the standard
residual-based approach that includes the -norm of the right-hand side.
However, the velocity is only steered by the divergence-free part of this
source term. An efficient error estimator must approximate this divergence-free
part in a proper manner, otherwise it can be dominated by the pressure error.
To overcome this difficulty a novel approach is suggested that uses arguments
from the stream function and vorticity formulation of the Navier--Stokes
equations. The novel error estimators only take the of the
right-hand side into account and so lead to provably reliable, efficient and
pressure-independent upper bounds in case of a pressure-robust method in
particular in pressure-dominant situations. This is also confirmed by some
numerical examples with the novel pressure-robust modifications of the
Taylor--Hood and mini finite element methods
Magneto-Roton Modes of the Ultra Quantum Crystal: Numerical Study
The Field Induced Spin Density Wave phases observed in quasi-one-dimensional
conductors of the Bechgaard salts family under magnetic field exhibit both Spin
Density Wave order and a Quantized Hall Effect, which may exhibit sign
reversals. The original nature of the condensed phases is evidenced by the
collective mode spectrum. Besides the Goldstone modes, a quasi periodic
structure of Magneto-Roton modes, predicted to exist for a monotonic sequence
of Hall Quantum numbers, is confirmed, and a second mode is shown to exist
within the single particle gap. We present numerical estimates of the
Magneto-Roton mode energies in a generic case of the monotonic sequence. The
mass anisotropy of the collective mode is calculated. We show how differently
the MR spectrum evolves with magnetic field at low and high fields. The
collective mode spectrum should have specific features, in the sign reversed
"Ribault Phase", as compared to modes of the majority sign phases. We
investigate numerically the collective mode in the Ribault Phase.Comment: this paper incorporates material contained in a previous cond-mat
preprint cond-mat/9709210, but cannot be described as a replaced version,
because it contains a significant amount of new material dealing with the
instability line and with the topic of Ribault Phases. It contains 13 figures
(.ps files
Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase
We study the electronic instabilities in a 2D Hubbard model where one of the
dimensions has a finite width, so that it can be considered as a large array of
coupled chains. The finite transverse size of the system gives rise to a
discrete string of Fermi points, with respective electron fields that, due to
their mutual interaction, acquire anomalous scaling dimensions depending on the
point of the string. Using bosonization methods, we show that the anomalous
scaling dimensions vanish when the number of coupled chains goes to infinity,
implying the Fermi liquid behavior of a 2D system in that limit. However, when
the Fermi level is at the Van Hove singularity arising from the saddle points
of the 2D dispersion, backscattering and Cooper-pair scattering lead to the
breakdown of the metallic behavior at low energies. These interactions are
taken into account through their renormalization group scaling, studying in
turn their influence on the nonperturbative bosonization of the model. We show
that, at a certain low-energy scale, the anomalous electron dimension diverges
at the Fermi points closer to the saddle points of the 2D dispersion. The
d-wave superconducting correlations become also large at low energies, but
their growth is cut off as the suppression of fermion excitations takes place
first, extending progressively along the Fermi points towards the diagonals of
the 2D Brillouin zone. We stress that this effect arises from the vanishing of
the charge stiffness at the Fermi points, characterizing a critical behavior
that is well captured within our nonperturbative approach.Comment: 13 pages, 7 figure
Development of a dynamic pressure calibration technique
The report deals with work continuing on the development of a method of producing sinusoidally varying pressures of at least 34 kPa zero-to-peak with amplitude variations within plus or minus 5% up to 2 kHz for the dynamic calibration of pressure transducers. Sinusoidally varying pressures of 34 kPa zero-to-peak were produced between 40 Hz and 750 Hz by vibrating a 10-cm column of a dimethyl siloxane liquid at 36gn zero-to-peak. Damping of the liquid column was accomplished by packing the fixture tube with a number of smaller diameter tubes
Does the circadian variation of ß2-adrenoceptor sites on peripheral mononuclear leukocytes (MNL) reflect the circadian variation of different MNL subsets
Development of dynamic calibration methods for POGO pressure transducers
Two dynamic pressure sources are described for the calibration of pogo pressure transducers used to measure oscillatory pressures generated in the propulsion system of the space shuttle. Rotation of a mercury-filled tube in a vertical plane at frequencies below 5 Hz generates sinusoidal pressures up to 48 kPa, peak-to-peak; vibrating the same mercury-filled tube sinusoidally in the vertical plane extends the frequency response from 5 Hz to 100 Hz at pressures up to 140 kPa, peak-to-peak. The sinusoidal pressure fluctuations can be generated by both methods in the presence of high pressures (bias) up to 55 MPa. Calibration procedures are given in detail for the use of both sources. The dynamic performance of selected transducers was evaluated using these procedures; the results of these calibrations are presented. Calibrations made with the two sources near 5 Hz agree to within 3% of each other
A dynamic pressure source for the calibration of pressure transducers
A dynamic pressure source is described for producing sinusoidally varying pressures of up to 34 kPa zero to peak, over the frequency range of approximately 50 Hz to 2 kHz. The source is intended for the dynamic calibration of pressure transducers. The transducer to be calibrated is mounted near the base of the thick walled aluminum tube forming the vessel so that the pressure sensitive element is in contact with the liquid in the tube. A section of the tube is filled with small steel balls to damp the motion of the 10-St dimethyl siloxane working fluid in order to extend the useful frquency range to higher frequencies than would be provided by an undamped system. The dynamic response of six transducers provided by the sponsor was evaluated using the pressure sources; the results of these calibrations are given
Decomposing the scattered field of two-dimensional metaatoms into multipole contributions
We introduce a technique to decompose the scattered near field of
two-dimensional arbitrary metaatoms into its multipole contributions. To this
end we expand the scattered field upon plane wave illumination into cylindrical
harmonics as known from Mie theory. By relating these cylin- drical harmonics
to the field radiated by Cartesian multipoles, the contribution of the lowest
order electric and magnetic multipoles can be identified. Revealing these
multipoles is essential for the design of metamaterials because they largely
determine the character of light propagation. In par- ticular, having this
information at hand it is straightforward to distinguish between effects that
result either from the arrangement of the metaatoms or from their particular
design
On the self-similarity in quantum Hall systems
The Hall-resistance curve of a two-dimensional electron system in the
presence of a strong perpendicular magnetic field is an example of
self-similarity. It reveals plateaus at low temperatures and has a fractal
structure. We show that this fractal structure emerges naturally in the
Hamiltonian formulation of composite fermions. After a set of transformations
on the electronic model, we show that the model, which describes interacting
composite fermions in a partially filled energy level, is self-similar. This
mathematical property allows for the construction of a basis of higher
generations of composite fermions. The collective-excitation dispersion of the
recently observed 4/11 fractional-quantum-Hall state is discussed within the
present formalism.Comment: 7 pages, 4 figures; version accepted for publication in Europhys.
Lett., new version contains energy calculations for collective excitations of
the 4/11 stat
Self-energy corrections to anisotropic Fermi surfaces
The electron-electron interactions affect the low-energy excitations of an
electronic system and induce deformations of the Fermi surface. These effects
are especially important in anisotropic materials with strong correlations,
such as copper oxides superconductors or ruthenates. Here we analyze the
deformations produced by electronic correlations in the Fermi surface of
anisotropic two-dimensional systems, treating the regular and singular regions
of the Fermi surface on the same footing. Simple analytical expressions are
obtained for the corrections, based on local features of the Fermi surface. It
is shown that, even for weak local interactions, the behavior of the
self-energy is non trivial, showing a momentum dependence and a self-consistent
interplay with the Fermi surface topology. Results are compared to experimental
observations and to other theoretical results.Comment: 13 pages, 10 figure
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