20 research outputs found
Reduced order models for control of fluids using the Eigensystem Realization Algorithm
In feedback flow control, one of the challenges is to develop mathematical
models that describe the fluid physics relevant to the task at hand, while
neglecting irrelevant details of the flow in order to remain computationally
tractable. A number of techniques are presently used to develop such
reduced-order models, such as proper orthogonal decomposition (POD), and
approximate snapshot-based balanced truncation, also known as balanced POD.
Each method has its strengths and weaknesses: for instance, POD models can
behave unpredictably and perform poorly, but they can be computed directly from
experimental data; approximate balanced truncation often produces vastly
superior models to POD, but requires data from adjoint simulations, and thus
cannot be applied to experimental data.
In this paper, we show that using the Eigensystem Realization Algorithm (ERA)
\citep{JuPa-85}, one can theoretically obtain exactly the same reduced order
models as by balanced POD. Moreover, the models can be obtained directly from
experimental data, without the use of adjoint information. The algorithm can
also substantially improve computational efficiency when forming reduced-order
models from simulation data. If adjoint information is available, then balanced
POD has some advantages over ERA: for instance, it produces modes that are
useful for multiple purposes, and the method has been generalized to unstable
systems. We also present a modified ERA procedure that produces modes without
adjoint information, but for this procedure, the resulting models are not
balanced, and do not perform as well in examples. We present a detailed
comparison of the methods, and illustrate them on an example of the flow past
an inclined flat plate at a low Reynolds number.Comment: 22 pages, 7 figure
Phase fluctuations, dissipation and superfluid stiffness in d-wave superconductors
We study the effect of dissipation on quantum phase fluctuations in d-wave
superconductors. Dissipation, arising from a nonzero low frequency optical
conductivity which has been measured in experiments below , has two
effects: (1) a reduction of zero point phase fluctuations, and (2) a reduction
of the temperature at which one crosses over to classical thermal fluctuations.
For parameter values relevant to the cuprates, we show that the crossover
temperature is still too large for classical phase fluctuations to play a
significant role at low temperature. Quasiparticles are thus crucial in
determining the linear temperature dependence of the in-plane superfluid
stiffness. Thermal phase fluctuations become important at higher temperatures
and play a role near .Comment: Presentation improved, new references added (10 latex pages, 3 eps
figures). submitted to PR
Effective Actions and Phase Fluctuations in d-wave Superconductors
We study effective actions for order parameter fluctuations at low
temperature in layered d-wave superconductors such as the cuprates. The order
parameter lives on the bonds of a square lattice and has two amplitude and two
phase modes associated with it. The low frequency spectral weights for
amplitude and relative phase fluctuations is determined and found to be
subdominant to quasiparticle contributions. The Goldstone phase mode and its
coupling to density fluctuations in charged systems is treated in a
gauge-invariant manner. The Gaussian phase action is used to study both the
-axis Josephson plasmon and the more conventional in-plane plasmon in the
cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum
XY model, which incorporates important cutoff effects overlooked in previous
studies. A variational analysis of this effective model shows that in the
cuprates, quantum effects of phase fluctuations are important in reducing the
zero temperature superfluid stiffness, but thermal effects are small for .Comment: Some numerical estimates corrected and figures changed. to appear in
PRB, Sept.1 (2000
A dual-time method for the solution of the unsteady Euler equations
SIGLEAvailable from British Library Document Supply Centre- DSC:7620.858(BU-DAE-R--496) / BLDSC - British Library Document Supply CentreGBUnited Kingdo
A dual-time method for the calculation of 2D unsteady incompressible flows on moving grids
SIGLEAvailable from British Library Document Supply Centre- DSC:7620.858(BU-DAE-R--728) / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Artificial compressibility methods for the calculation of 2D inviscid incompressible flow
SIGLEAvailable from British Library Document Supply Centre- DSC:7620.858(BU-DAE--492) / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Foeppl type solutions for infinite cylinders with rounded corner square, or triangular cross-sections
SIGLEAvailable from British Library Document Supply Centre- DSC:7620.858(BU-DAE--491) / BLDSC - British Library Document Supply CentreGBUnited Kingdo
An artificial compressibility method for the solution of the 2D incompressible Navier-Stokes equations
SIGLEAvailable from British Library Document Supply Centre- DSC:7620.858(BU-DAE-R--715) / BLDSC - British Library Document Supply CentreGBUnited Kingdo